Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
read the original abstract
We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.
This paper has not been read by Pith yet.
Forward citations
Cited by 10 Pith papers
-
Hilbert Space Fragmentation from Generalized Symmetries
Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
-
Nature abhors a vacuum: A simple rigorous example of thermalization in an isolated macroscopic quantum system
Rigorous proof that random half-chain initial states in a low-density free-fermion model thermalize, with local particle counts matching equilibrium at long times with high probability.
-
Hilbert Space Fragmentation and Gauge Symmetry
An emergent gauge symmetry valid only in a subset of sectors of the fragmented S=1 dipole-conserving spin chain enables exact quantum simulation of gauge theories using a non-gauge-invariant Hamiltonian.
-
Entanglement inequalities, black holes and the architecture of typical states
Typical states in large-N holographic CFTs exhibit UV and IR length scales set by energy and charges, producing factorization that isolates black holes via a corona of saturated entanglement wedges and extends ETH to ...
-
Topological Control of Quantum Chaos Diagnostics: OTOCs, Spectral Statistics, and Information Scrambling in Ising Model
The study demonstrates that long-range couplings and heterogeneous degree distributions in Ising spin networks on path, Erdős–Rényi, and Watts–Strogatz topologies accelerate quantum information scrambling and chaos, d...
-
Thermalization with Gaussian Quantum Cellular Automata
Provides two sets of conditions on GQCAs guaranteeing thermalization to infinite temperature via a quantum many-body generalization of the Riemann-Lebesgue lemma for states with bounded density.
-
Grand-Canonical Typicality
The paper establishes that typical states in a grand-canonical micro-canonical Hilbert subspace produce the grand-canonical density matrix and a GAP/Scrooge wave-function distribution for the subsystem.
-
Generic ETH: Eigenstate Thermalization beyond the Microcanonical
Numerical study of a qutrit lattice with conserved charge shows thermalization signatures in states outside microcanonical windows of energy and charge, supporting a generalized form of ETH called generic ETH.
-
Coherent and dissipative dynamics at quantum phase transitions
A review of equilibrium and dynamic scaling laws at quantum phase transitions, including quenches and dissipative effects treated as perturbations to critical regimes.
-
Entanglement Certification $-$ From Theory to Experiment
Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.