Equilibration plays a fundamental role in our understanding of statistical mechanics and the long-time dynamics of many-body systems. In quantum systems, the route to equilibration is intimately related to level repulsion and quantum signatures of chaos that are encoded in their unitary evolution. Chaotic quantum systems exhibit level statistics characteristic of ensembles of random matrices. In this work, we demonstrate that single-particle chaos leads to equilibration of many noninteracting photons. We show that the underlying mechanisms for equilibration are operator spreading and quantum interference. More specifically, we demonstrate that the unitary dynamics of a general Floquet system implemented using single-mode phase shifters and multiport beamsplitters leads to equilibration of photons. We propose a realistic photonic implementation of the multiparticle kicked rotor, which is a Floquet system that we use as a concrete example of our general approach.Equilibration plays a fundamental role in our understanding of statistical mechanics and the long-time dynamics of many-body systems. In quantum systems, the route to equilibration is intimately related to level repulsion and quantum signatures of chaos that are encoded in their unitary evolution. Chaotic quantum systems exhibit level statistics characteristic of ensembles of random matrices. In this work, we demonstrate that single-particle chaos leads to equilibration of many noninteracting photons. We show that the underlying mechanisms for equilibration are operator spreading and quantum interference. More specifically, we demonstrate that the unitary dynamics of a general Floquet system implemented using single-mode phase shifters and multiport beamsplitters leads to equilibration of photons. We propose a realistic photonic implementation of the multiparticle kicked rotor, which is a Floquet system that we use as a concrete example of our general approach.

arXiv:2307.13200Physical review. B./Physical review. BSep 5, 20250 citations

Complexity of energy eigenstates as a mechanism for equilibration

Lluís Masanes, Augusto J. Roncaglia, Antonio Acín

Understanding the mechanisms responsible for the equilibration of isolated quantum many-body systems is a long-standing open problem. In this work we obtain a statistical relationship between the equilibration properties of Hamiltonians and the complexity of their eigenvectors, provided that a conjecture about the incompressibility of quantum circuits holds. We quantify the complexity by the size of the smallest quantum circuit mapping the local basis onto the energy eigenbasis. Specifically, we consider the set of all Hamiltonians having complexity $C$ , and show that almost all such Hamiltonians equilibrate if $C$ is superquadratic in the system size, which includes the fully random Hamiltonian case in the limit $C\ensuremath{\rightarrow}\ensuremath{\infty}$, and do not equilibrate if $C$ is sublinear. We also provide a simple formula for the equilibration time scale in terms of the Fourier transform of the level density. Our results are statistical and, therefore, do not apply to specific Hamiltonians. Yet they establish a fundamental link between equilibration and complexity theory.Understanding the mechanisms responsible for the equilibration of isolated quantum many-body systems is a long-standing open problem. In this work we obtain a statistical relationship between the equilibration properties of Hamiltonians and the complexity of their eigenvectors, provided that a conjecture about the incompressibility of quantum circuits holds. We quantify the complexity by the size of the smallest quantum circuit mapping the local basis onto the energy eigenbasis. Specifically, we consider the set of all Hamiltonians having complexity $C$, and show that almost all such Hamiltonians equilibrate if $C$ is superquadratic in the system size, which includes the fully random Hamiltonian case in the limit $C\ensuremath{\rightarrow}\ensuremath{\infty}$, and do not equilibrate if $C$ is sublinear. We also provide a simple formula for the equilibration time scale in terms of the Fourier transform of the level density. Our results are statistical and, therefore, do not apply to specific Hamiltonians. Yet they establish a fundamental link between equilibration and complexity theory.

arXiv:1108.0374Physical Review EMar 18, 201372 citations

Equilibration of quasi-isolated quantum systems

Vyacheslav I. Yukalov

arXiv:1202.3292Physics Letters ANov 19, 201122 citations

Equilibration and thermalization in quantum systems

Christian Gogolin

This thesis fathoms out the capabilities of the theory of quantum mechanics to explain thermodynamic behavior. It covers in particular equilibration and thermalization in closed quantum systems, typicality, time scales for equilibration, quantum integrability and its connection to thermalization, decoherence, and a maximum entropy principle. Together, the presented results form the body of the theory of pure state quantum statistical mechanics. With almost 300 references, ranging from the groundbreaking works of the early 20th century to the most recent discoveries (up to 2013), this work arguably constitutes the most comprehensive review of the literature on equilibration and thermalization in closed quantum systems. All results are presented in a unified notation and many are slightly strengthened or generalized.This thesis fathoms out the capabilities of the theory of quantum mechanics to explain thermodynamic behavior. It covers in particular equilibration and thermalization in closed quantum systems, typicality, time scales for equilibration, quantum integrability and its connection to thermalization, decoherence, and a maximum entropy principle. Together, the presented results form the body of the theory of pure state quantum statistical mechanics. With almost 300 references, ranging from the groundbreaking works of the early 20th century to the most recent discoveries (up to 2013), this work arguably constitutes the most comprehensive review of the literature on equilibration and thermalization in closed quantum systems. All results are presented in a unified notation and many are slightly strengthened or generalized.

Jan 1, 20148 citations

Approach to Equilibrium in Quantum Mechanics

Gérard G. Emch, Chuang Liu

Springer eBooksJan 1, 20021 citation

C

, and show that almost all such Hamiltonians equilibrate if

C

is superquadratic in the system size, which includes the fully random Hamiltonian case in the limit $C\ensuremath{\rightarrow}\ensuremath{\infty}$, and do not equilibrate if

C

is sublinear. We also provide a simple formula for the equilibration time scale in terms of the Fourier transform of the level density. Our results are statistical and, therefore, do not apply to specific Hamiltonians. Yet they establish a fundamental link between equilibration and complexity theory.