Equilibration of quantum hard rods in one dimension

Abstract

We study the out-of-equilibrium evolution of a strongly interacting quantum spin chain which is mapped on a system of hard rods that are coherently deposited on and removed from a lattice. We show that this closed quantum system approaches an equilibrium steady state which strongly resembles a microcanonical ensemble of classical hard rods. Starting from the fully coherent evolution equation we derive a Master equation for the evolution of the number of hard rods on the lattice. This equation does not only capture properties of the equilibrium state but also describes the dynamical non-equilibrium evolution into it for the majority of initial conditions. We analyze this in detail for hard rods of varying size.

19 pages, 8 figures

References in corpus (21)

• Thermalization and its mechanism for generic isolated quantum systems
• Relaxation and Pre-thermalization in an Isolated Quantum System
• Light-cone-like spreading of correlations in a quantum many-body system
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Quantum Quench in the Transverse Field Ising Chain
• Observation of mesoscopic crystalline structures in a two-dimensional Rydberg gas
• The Luttinger model following a sudden interaction switch-on
• Dephasing and the steady state in quantum many-particle systems
• Strong and weak thermalization of infinite non-integrable quantum systems
• Absence of Thermalization in Nonintegrable Systems
• Effective thermal dynamics following a quantum quench in a spin chain
• Nonthermal steady states after an interaction quench in the Falicov-Kimball model
• Dynamics in the Ising field theory after a quantum quench
• Quantum quenches from integrability: the fermionic pairing model
• Exact time evolution of space- and time-dependent correlation functions after an interaction quench in the 1D Bose gas
• Thermal equilibration between two quantum systems
• Thermalization of a strongly interacting closed spin system: From coherent many-body dynamics to a Fokker-Planck equation
• Thermalisation of Local Observables in Small Hubbard Lattices
• Entropic enhancement of spatial correlations in a laser-driven Rydberg gas
• Thermalization in a coherently driven ensemble of two-level systems
• Universal time-evolution of a Rydberg lattice gas with perfect blockade

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