Cátedra Bogdan Mielnik

Bose-Einstein condensates:

Numerical techniques and applications to analog gravity

Dr. Anna Berti

Pitaevskii Center for Bose-Einstein condensation

INO-CNR and Dipartimento di Fisica, University of Trento, Italy


Abstract

When a dilute and non-interacting gas of bosons is cooled down to temperatures close to the absolute zero, a phase transition takes place, with the ordered phase being characterized by a macroscopic occupation of the lowest- energy single-particle state. This fascinating state of matter takes the name of Bose-Einstein condensate (BEC). The relatively simple theoretical description of these systems, together with the remarkable level of control in experiments, make BECs a powerful platform in the study or simulation of a wide variety of physical phenomena.

This course focuses on the theoretical and numerical description of Bose- Einstein condensates, providing a basic overview of Gross-Pitaevskii and Bogoliubov theories, as well as practical sessions devoted to the simplest computational techniques employed in numerical simulations. Particular attention will be given to the application of these concepts in the context of analog gravity, a research field which uses quantum fluids (including BECs) to investigate physical phenomena of astrophysical or cosmological interest.


Plan of the course

Lecture 1. Brief overview on Bose-Einstein condensates: Gross-Pitaevskii and Bogoliubov theory; introduction to analog gravity.

Lecture 2. Numerical techniques to determine the ground state: imaginary-time evolution vs. conjugate gradient methods.

Lecture 3. Numerical techniques for real-time evolution (split-step) and to determine spectral properties (Bogoliubov diagonalization); brief mention to protocols that allow to take into account quantum or thermal fluctuations (truncated-Wigner, stochastic GPE, among others).

Lecture 4. Practical session.

Lecture 5. Practical session.

Prerequisites

Familiarity with quantum mechanical concepts (second quantization), as well as basic knowledge of a programming language, will be assumed (I will provide pieces of code mostly written using C). No prior knowledge of general relativity or cosmology is necessary.

Información del curso

Las Cátedras Bogdan Mielnik se impartirán en inglés como parte del entrenamiento para nuestro estudiantes, aunque es posible hacer preguntas en español.

El curso tendrá lugar entre el viernes 20 y el viernes 26 de septiembre de 2024 de 15 a 17h en la Sala B del Departamento de Física del Cinvestav Zacatenco. También será posible asistir en formato virtual en la plataforma Zoom, las sesiones no serán grabadas.

Calendario:

Inscripción

Para acceder al curso y al Cinvestav, les pedimos que llenen el formulario que está al final de esta página o en esta liga. La inscripción no tiene costo. La fecha límite de inscripción es el lunes 16 de septiembre.

Constancias

Se enviará una constancia de participación a quienes asistan los cinco días del curso y así lo hayan solicitado en el formulario de inscripción. 

Dudas

Cualquier duda o comentario pueden escribir a david.bermudez@cinvestav.mx.

Formulario:

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