<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /></head><body style='font-size: 8pt; font-family: Georgia,Palatino,serif'>
<p><br /></p>
<div>
<div class="pre" style="margin: 0; padding: 0; font-family: monospace">********************************************<br /> Secretaría Departamental de Física<br /> <a href="mailto:secre2@fisica.unlp.edu.ar">secre2@fisica.unlp.edu.ar</a><br /> Cecilia Cafiero / Alejandro Chiquino<br /> Facultad de Ciencias Exactas<br /> Universidad Nacional de La Plata<br /> ********************************************</div>
</div>
<p><br /></p>
<p>-------- Mensaje original --------</p>
<table border="0" cellspacing="0" cellpadding="0">
<tbody>
<tr>
<th align="right" valign="baseline" nowrap="nowrap">Asunto:</th>
<td>Curso de Postgrado</td>
</tr>
<tr>
<th align="right" valign="baseline" nowrap="nowrap">Fecha:</th>
<td>2024-02-01 19:03</td>
</tr>
<tr>
<th align="right" valign="baseline" nowrap="nowrap">Remitente:</th>
<td>Marta Reboiro <reboiro@fisica.unlp.edu.ar></td>
</tr>
<tr>
<th align="right" valign="baseline" nowrap="nowrap">Destinatario:</th>
<td>Secretaria de Física <secre2@fisica.unlp.edu.ar></td>
</tr>
</tbody>
</table>
<p><br /></p>
<!-- html ignored --><!-- head ignored --><!-- meta ignored -->
<div dir="ltr">
<div style="color: #202124; font-family: 'Google Sans',Roboto,RobotoDraft,Helvetica,Arial,sans-serif; font-size: medium; min-height: 100%;">
<div class="gmail-nH" style="width: 1868px;">
<div class="gmail-nH">
<div class="gmail-nH gmail-aqk gmail-aql gmail-bkL" style="display: flex; background-color: transparent;">
<div class="gmail-nH gmail-bkK" style="overflow: hidden;">
<div class="gmail-nH" style="border-radius: 16px; margin-bottom: 16px; overflow-y: hidden;">
<div class="gmail-nH gmail-ar4 gmail-z">
<div class="gmail-aeI">
<div class="gmail-AO">
<div id="gmail-:3" class="gmail-Tm gmail-aeJ" style="background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-origin: initial; background-clip: initial; overflow-y: scroll; padding-right: 0px; height: 804px;">
<div id="gmail-:1" class="gmail-aeF" style="padding: 0px; vertical-align: bottom; min-height: 614px;">
<div class="gmail-nH">
<div class="gmail-nH">
<div class="gmail-nH gmail-g">
<div class="gmail-nH gmail-a98 gmail-iY" style="background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-origin: initial; background-clip: initial; min-height: 64ex; min-width: 502px; margin: 0px; padding-right: 16px;">
<div class="gmail-nH">
<div class="gmail-aHU gmail-hx" style="background-color: transparent; color: #222222; min-width: 502px; padding: 0px;">
<div>
<div class="gmail-h7 gmail-ie" style="padding-bottom: 0px; max-width: 100000px; clear: both; outline: none;">
<div class="gmail-Bk" style="margin-bottom: 0px; border-width: 0px; border-radius: 0px; float: left; width: 1495.98px; border-color: #efefef initial initial initial; border-style: solid initial initial initial;">
<div class="gmail-G3 gmail-G2" style="border-top: none; padding-top: 0px; background-color: transparent; border-right: 0px; border-bottom: 0px rgba(100,121,143,0.12); border-left: 0px; border-radius: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px;">
<div>
<div id="gmail-:1xu">
<div class="gmail-adn gmail-ads" style="border-left: none; padding: 0px; display: flex;">
<div class="gmail-gs" style="margin: 0px; min-width: 0px; padding: 0px 0px 20px; width: initial;">
<div class="gmail-">
<div id="gmail-:z4" class="gmail-ii gmail-gt" style="direction: ltr; margin: 8px 0px 0px; padding: 0px; font-size: 0.875rem; overflow-x: hidden;">
<div id="gmail-:1ws" class="gmail-a3s gmail-aiL" style="direction: initial; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-feature-settings: normal; font-stretch: normal; font-size: small; line-height: 1.5; font-family: Arial,Helvetica,sans-serif; overflow: auto hidden;">
<div dir="ltr">
<div style="font-family: 'times new roman','new york',times,serif; font-size: 16px;">
<div>Para difundir.</div>
<div>Muchas gracias,</div>
<div>M. Reboiro</div>
<div>------------------------------------------------------</div>
</div>
<div style="font-family: 'times new roman','new york',times,serif; font-size: 16px;">Durante el primer cuatrimestre de 2024 se dictará en la UNLP el curso de postgrado "<span style="font-size: 12pt; background-color: transparent;">Dinámica no-hermítica: Fundamentos y Aplicaciones.</span>", de duración cuatrimestral (16 semanas) .</div>
<div style="font-family: 'times new roman','new york',times,serif; font-size: 16px;"> </div>
<div style="font-family: 'times new roman','new york',times,serif; font-size: 16px;">Se trata de un curso no arancelado, que sólo requerirá oportunamente la inscripción de los interesados en la Secretaría de Postgrado de la Facultad de Ciencias Exactas a fin de su reconocimiento. </div>
<div style="font-family: 'times new roman','new york',times,serif; font-size: 16px;"> </div>
<div style="font-family: 'times new roman','new york',times,serif; font-size: 16px;">A continuación la información relevante: </div>
<div style="font-family: 'times new roman','new york',times,serif; font-size: 16px;"> </div>
<div style="font-family: 'times new roman','new york',times,serif; font-size: 16px;">______________________</div>
<div style="font-family: 'times new roman','new york',times,serif; font-size: 16px;">
<p style="line-height: 16px; margin-bottom: 0in; background: transparent;"><span style="font-size: 12pt;"><strong>Curso de Postgrado:</strong> Dinámica no-hermítica: Fundamentos y Aplicaciones.</span></p>
<p style="line-height: 16px; margin-bottom: 0in; background: transparent;"><span style="background-color: transparent; font-size: 12pt; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;">Primer Semestre a</span></span></span><span style="background-color: transparent; font-size: 12pt; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;">ño 2024, 16 semanas de duración, inicio </span></span></span><span style="background-color: transparent; font-size: 12pt; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;">en marzo 2024, </span></span></span><span style="background-color: transparent; font-size: 12pt; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;">horarios a convenir.</span></span></span></p>
<p style="line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="font-size: 12pt;"><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;">Carga horaria</span></span></span><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;">: </span></span></span><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;">6 horas por semana (teoría y práctica), </span></span></span><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;">4 creditos.</span></span></span></span></p>
<p style="line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="font-size: 12pt;"><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;">Modalidad: </span></span></span><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;">presencial (de haber interesados presencial y virtual)</span></span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">Interesados: ponerse en contacto por e-mail con</span></span></span></p>
<p style="line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">Marta Reboiro (</span></span></span></span><span style="color: #000080;"><u><a style="color: #000080;" href="mailto:reboiro@fisica.unlp.edu.ar"><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #1155cc;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">reboiro@fisica.unlp.edu.ar</span></span></span></span></a></u></span><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">) o</span></span></span></span></p>
<p style="line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">Romina Ramírez (</span></span></span></span><a style="color: #000080;" href="mailto:romina@mate.unlp.edu.ar"><span style="font-size: 12pt;">romina@mate.unlp.edu.ar</span></a><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">).</span></span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"> </p>
<p style="line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;"><strong>Objetivos</strong></span></span></span></span><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">: </span></span></span></span><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">El objetivo del presente curso es estudiar las propiedades relevantes de sistemas </span></span></span></span><span style="font-size: 12pt; background-color: transparent;">físicos descriptos</span></p>
<p style="line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="font-size: 12pt; background-color: transparent;"> a través de una dinámica no-hermítica, tanto desde el punto</span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">de vista de la física que describen como de la matemática necesaria para ello.</span></span></span><span style="font-size: 12pt; background-color: transparent;">Asimismo, se presentará el </span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="font-size: 12pt; background-color: transparent;">estado del desarrollo actual, incluyendo los principales resultados teóricos y experimentales.</span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"> </p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;"><strong>Contenidos:</strong></span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="font-size: 12pt; background-color: transparent;">1. Fundamentos de Matemática de la </span>diámica<span style="font-size: 12pt; background-color: transparent;"> no-</span>hermítica<span style="font-size: 12pt; background-color: transparent;">.</span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">1.1 Descomposición Espectral.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">1.2 Diagonalización de Hamiltonianos no-hermíticos.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">1.3 Pseudo-hermiticidad y Quasi-hermiticidad.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">1.4 Métrica y Espacios de Krein.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">1.5 Puntos Excepcionales.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">1.5.1 Definición y propiedades básicas.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">1.5.2 Aplicaciones Físicas. Transiciones de Fase Dinámicas.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">1.6 Sistemas de dimensión infinita.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"> </p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">2. Física clásica no-hermítica.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">2.1 Física fotónica</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">2.1.1 Propagación de ondas ópticas.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">2.1.2 Dispersión de luz en un medio complejo.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">2.2 Mecánica</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">2.3 Circuitos Eléctricos.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">2.4 Sistemas optomecánicos y optomagnéticos.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">2.5 Hidrodinámica</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">2.5.1 Acustica no-hermitica en fluidos.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">2.5.2 Polarones y plasmones.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"> </p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">3. Física cuántica no-hermítica.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">3.1 Formalismo de Proyección de Feshbach</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">3.1.1 Operadores no-hermíticos</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">3.1.2 Aplicaciones físicas.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">3.2 Enfoque a través de la óptica cuántica.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">3.2.1. Medidas inderectas y trayectorias cuánticas.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">3.2.2. Rol de la dinámica condicional.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">3.3 Física de Muchos cuerpos.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">3.3.1. Comportamiento crítico.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">3.3.2. Sistemas Físicos.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">3.3.3. Más allá de los regímenes Markovianos.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">3.4 Análisis no-hermítico de sistemas hermíticos.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"> </p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"> </p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">4. Topología de Bandas en física no-hermítica.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">4.1. Repaso de topología de bandas en sistemas hermíticos.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">4.1.1. Definición de bandas y de topología.</span></span></span></p>
<p style="line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="font-size: 12pt;"><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;">4.1.2. Sistemas protot</span></span></span><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;">í</span></span></span><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;">picos.</span></span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">4.2. Sistemas con diferencias de energía entre niveles (gap) complejo.</span></span></span></p>
<p style="line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="font-size: 12pt;"><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;">4.3. Ejemplos e invariante topo</span></span></span><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;">l</span></span></span><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;">ógicos.</span></span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">4.4. Clasificación topológica.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"> </p>
<p style="line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="font-size: 12pt;"><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;">5. Introducción al problema de la Termodin</span></span></span><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;">á</span></span></span><span style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal;"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;">mica cuántica de sistemas pseudo-hermíticos.</span></span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">5.1 Propiedades de la Función de Partición de sistema pseudo-hermíticos.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">5.2 Aplicación a sistemas abiertos.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"> </p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">6. Perspectiva.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"> </p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;"><strong>Bibliografía.</strong></span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"> </p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">1. Making sense of non-Hermitian Hamiltonians, Rep. Prog. Phys. 70(2007) 947. Bender, C. M.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">2. PT-symmetry in quantum and classical physics., World Scientific Publishing Europe Ltd, (2019). Bender, C. M.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">3. Non-selfadjoint operators in quantum physics: Mathematical aspects,ISBN: 978-1-118-85528-7 Ed. Wiley, (2015). Editors: F. Bagarello, J. P.Gazeau,F. Szafraniec, M. Znojil.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">4. Pseudo-Hermitian Hamiltonians in Quantum Physics in 2014, Interna-</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">tional Journal of Theoretical Physics 54 (2015) 3867. Znojil, M.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">5. Non-Hermitian physics. Advances in Physics 69, (2020)249. Ashida, Y.,</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">Gong, Z., Ueda, M.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">6. Non-hermitian quantum thermodynamics, Scientific Report 1 (2016)23408.Gardas B., Deffner S., Saxena A.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">7. Pseudo-Hermitian quantum mechanics with unbounded metric operators, Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences 371 (2013) 20120050. Mostafazadeh, A.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">8. Exceptional points of non-Hermitian operators, Journal of Physics A: Mathematical and General 37 (2004) 2455. Heiss, W. D.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">9. Squeezed states from a quantum deformed oscillator Hamiltonian, Physics Letters A 380 (2016) 1117. Ramirez, R and Reboiro, M.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">10. Optimal Spin Squeezed Steady State induced by the dynamics of non-</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">hermitian hamiltonians, Physica Scripta 94 (2019)85220. Ramirez, R and</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">Reboiro, M.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">11. Dynamics of finite dimensional non-hermitian systems with indefinite metric, Journal of Mathematical Physics 60(2019)012106. Ramirez, R. and</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">Reboiro, M.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">12. Exceptional Points from the Hamiltonian of a hybrid physical system:</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">Squeezing and anti-Squeezing,Diego Tielas, The European Physical Jour-</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">nal D 74,(2020) 193. Ramírez, R., Reboiro, M. and Tielas, D.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">13. Swanson Hamiltonian: non-PT-symmetry phase, J. Phys. A: Math. Theor. 55 (2021), 015303. Fernández, V., Ramírez R. and Reboiro M.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">14. Swanson Hamiltonian revisted through the Complex Scaling Method,Acta Polytechnica (Tomo Especial de la Conferencia AAMP XVIII) 62(2022)157.Fernández, V., Ramíırez R. and Reboiro M.</span></span></span></p>
<p style="font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; line-height: 16px; margin-bottom: 0in; background: transparent;" align="left"><span style="color: #222222;"><span style="font-family: 'times new roman', 'new york', times, serif;"><span style="font-size: 12pt;">15. Quantum Work from a Pseudo-hermitian Hamiltonian, Quantum Reports 4(2022)589. Reboiro, M. and Tielas, D.</span></span></span></p>
</div>
</div>
<div class="gmail-yj6qo"> </div>
<div class="gmail-adL"> </div>
</div>
</div>
<div class="gmail-hi" style="padding: 0px; width: auto; background: #f2f2f2; margin: 0px; border-bottom-left-radius: 1px; border-bottom-right-radius: 1px;"> </div>
</div>
</div>
<div class="gmail-ajx" style="clear: both;"> </div>
</div>
<div class="gmail-gA gmail-gt gmail-acV" style="font-size: 0.875rem; padding: 0px; width: auto; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-top: none; margin: 0px; background: transparent;">
<div class="gmail-gB gmail-xu" style="border-top: 0px; padding: 0px;">
<div class="gmail-ip gmail-iq" style="clear: both; margin: 0px; padding: 16px 0px; border-top: none;">
<div id="gmail-:z6">
<table class="gmail-cf gmail-wS" style="border-collapse: collapse;">
<tbody>
<tr>
<td class="gmail-amq" style="padding: 0px 16px; vertical-align: top; width: 44px;"><img id="gmail-:mb_16" class="gmail-ajn gmail-bofPge" style="width: 40px; height: 40px; display: block; border-radius: 50%;" src="https://lh3.googleusercontent.com/a/ACg8ocL6sdMnGCPUNMHAvztY_wuI8t5WIG6QZ5fdvbnjrfuI=s40-p-mo" alt="" name=":mb" /></td>
<td class="gmail-amr" style="padding: 0px; width: 1423.98px;">
<div class="gmail-nr gmail-wR" style="box-sizing: border-box; border-radius: 1px; padding: 0px; border: none; margin: 0px;">
<div class="gmail-amn" style="color: inherit; height: auto; padding: 0px; display: flex; line-height: 20px;"><span id="gmail-:1mm" class="gmail-ams gmail-bkH" style="border: 1px solid #747775; display: inline-flex; font-size: 0.875rem; background: none; border-radius: 18px; box-sizing: border-box; color: #444746; height: 36px; outline: none; padding: 0px 16px 0px 12px; min-width: 104px; margin-right: 8px;">Responder</span><span id="gmail-:1mo" class="gmail-ams gmail-bkG" style="border: 1px solid #747775; display: inline-flex; font-size: 0.875rem; background: none; border-radius: 18px; box-sizing: border-box; color: #444746; height: 36px; outline: none; padding: 0px 16px 0px 12px; min-width: 104px; margin-right: 8px;">Reenviar</span></div>
</div>
</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div> </div>
</div>
</div>
<div class="gmail-nH"> </div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="gmail-nH"> </div>
</div>
</div>
</div>
</div>
<div class="gmail-vY gmail-nq" style="width: 1868px; height: 932px; color: #202124; font-family: 'Google Sans',Roboto,RobotoDraft,Helvetica,Arial,sans-serif; font-size: medium;"> </div>
<div style="color: #202124; font-family: 'Google Sans',Roboto,RobotoDraft,Helvetica,Arial,sans-serif; font-size: medium;"> </div>
<div class="gmail-dw gmail-np" style="width: 1868px; height: 932px; overflow: hidden; color: #202124; font-family: 'Google Sans',Roboto,RobotoDraft,Helvetica,Arial,sans-serif; font-size: medium;"> </div>
<div class="gmail-ZXZutc" style="color: #202124; font-family: 'Google Sans',Roboto,RobotoDraft,Helvetica,Arial,sans-serif; font-size: medium;"> </div>
<div class="gmail-T-ays gmail-T-ays-avH" style="border-radius: 0px; background: transparent; border-width: 10px 0px; border-style: solid; border-color: transparent; color: #ffffff; font-size: 0.75rem; opacity: 0; padding: 0px; word-break: break-word; font-family: 'Google Sans',Roboto,RobotoDraft,Helvetica,Arial,sans-serif; line-height: 16px;"> </div>
</div>
</body></html>