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

Abstract

We study a classical integrable (Neumann) model describing the motion of a particle on the sphere, subject to harmonic forces. We tackle the problem in the infinite dimensional 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 captures the long-time averages of the soft model. We reveal the full dynamic phase diagram with extended, quasi-condensed, coordinate-, and coordinate and momentum-condensed phases. The scaling properties of the fluctuations allow us to establish in which cases the strict and soft spherical constraints are equivalent, confirming the validity of the GGE hypothesis for the Neumann model on a large portion of the dynamic phase diagram.

arXiv comment5 pages, 3 figures

References in corpus (19)

• Thermalization and its mechanism for generic isolated quantum systems
• Nonequilibrium dynamics of closed interacting quantum systems
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Statistical mechanics and dynamics of solvable models with long-range interactions
• Nonequilibrium dynamical mean-field theory and its applications
• Remarks on the notion of quantum integrability
• "Light-cone" dynamics after quantum quenches in spin chains
• Universal Prethermal Dynamics of Bose Gases Quenched to Unitarity
• Quantum quench in interacting field theory: a self-consistent approximation
• Real-time and real-space spin- and energy dynamics in one-dimensional spin-1/2 systems induced by local quantum quenches at finite temperatures
• Generalised hydrodynamics of the classical Toda system
• Separation of variables for the classical and quantum Neumann model
• Quantum integrability in systems with finite number of levels
• Dynamical critical scaling and effective thermalization in quantum quenches: the role of the initial state
• The grand canonical catastrophe as an instance of condensation of fluctuations
• Generalized microcanonical and Gibbs ensembles in classical and quantum integrable dynamics
• Condensation vs Ordering: From the Spherical Models to BEC in the Canonical and Grand Canonical Ensemble
• Quenched dynamics of classical isolated systems: the spherical spin model with two-body random interactions or the Neumann integrable model
• Non-linear susceptibilities of spherical models

Cited by in corpus (7)

• Statistical mechanics of an integrable system
• Burgers turbulence in the Fermi-Pasta-Ulam-Tsingou chain
• Introduction to the dynamics of disordered systems: equilibrium and gradient descent
• Thermalization without chaos in harmonic systems
• Finite size effects and loss of self-averageness in the relaxational dynamics of the spherical Sherrington-Kirkpatrick model
• Entanglement gap, corners, and symmetry breaking
• Generalised Gibbs Ensemble for spherically constrained harmonic models