(Non equilibrium) Thermodynamics of Integrable models: The Generalized Gibbs Ensemble description of the classical Neumann Model

We study the motion of a classical particle subject to anisotropic harmonic forces and constrained to move on the S<sub>N-1</sub> sphere. In the integrable-systems literature this problem is known as the Neumann model. We choose the spring constants in a way that makes the connection wit...

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Detalles Bibliográficos
Autores principales:	Barbier, Damien, Cugliandolo, Leticia F., Lozano, Gustavo S., Nessi, Emilio Nicolás
Formato:	Articulo Preprint
Lenguaje:	Inglés
Publicado:	2020
Materias:	Ciencias Exactas Física Physics particles anisotropic harmonic forces Neumann model Generalized Gibbs Ensemble
Acceso en línea:	http://sedici.unlp.edu.ar/handle/10915/125577
Aporte de:	SEDICI (UNLP) de Universidad Nacional de La Plata

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institution	Universidad Nacional de La Plata
institution_str	I-19
repository_str	R-120
collection	SEDICI (UNLP)
language	Inglés
topic	Ciencias Exactas Física Physics particles anisotropic harmonic forces Neumann model Generalized Gibbs Ensemble
spellingShingle	Ciencias Exactas Física Physics particles anisotropic harmonic forces Neumann model Generalized Gibbs Ensemble Barbier, Damien Cugliandolo, Leticia F. Lozano, Gustavo S. Nessi, Emilio Nicolás (Non equilibrium) Thermodynamics of Integrable models: The Generalized Gibbs Ensemble description of the classical Neumann Model
topic_facet	Ciencias Exactas Física Physics particles anisotropic harmonic forces Neumann model Generalized Gibbs Ensemble
description	We study the motion of a classical particle subject to anisotropic harmonic forces and constrained to move on the S<sub>N-1</sub> sphere. In the integrable-systems literature this problem is known as the Neumann model. We choose the spring constants in a way that makes the connection with the so-called p = 2 spherical disordered system transparent. We tackle the problem in the N → ∞ limit by introducing a soft version in which the spherical constraint is imposed only on average over initial conditions. We show that the Generalized Gibbs Ensemble, constructed with N conserved charges in involution, captures the long-time averages of all relevant observables of the soft model after sudden changes in the parameters (quenches). We reveal the full dynamic phase diagram with four different phases in which the particles' position and momentum are both extended, only the position quasi-condenses or condenses, and both condense. The scaling properties of the fluctuations allow us to establish in which of these cases the strict and soft spherical constraints are equivalent. We thus confirm the validity of the GGE hypothesis for the Neumann model on a large portion of the dynamic phase diagram.
format	Articulo Preprint
author	Barbier, Damien Cugliandolo, Leticia F. Lozano, Gustavo S. Nessi, Emilio Nicolás
author_facet	Barbier, Damien Cugliandolo, Leticia F. Lozano, Gustavo S. Nessi, Emilio Nicolás
author_sort	Barbier, Damien
title	(Non equilibrium) Thermodynamics of Integrable models: The Generalized Gibbs Ensemble description of the classical Neumann Model
title_short	(Non equilibrium) Thermodynamics of Integrable models: The Generalized Gibbs Ensemble description of the classical Neumann Model
title_full	(Non equilibrium) Thermodynamics of Integrable models: The Generalized Gibbs Ensemble description of the classical Neumann Model
title_fullStr	(Non equilibrium) Thermodynamics of Integrable models: The Generalized Gibbs Ensemble description of the classical Neumann Model
title_full_unstemmed	(Non equilibrium) Thermodynamics of Integrable models: The Generalized Gibbs Ensemble description of the classical Neumann Model
title_sort	(non equilibrium) thermodynamics of integrable models: the generalized gibbs ensemble description of the classical neumann model
publishDate	2020
url	http://sedici.unlp.edu.ar/handle/10915/125577
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(Non equilibrium) Thermodynamics of Integrable models: The Generalized Gibbs Ensemble description of the classical Neumann Model

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