Related papers: Thermalization in Krylov Basis
The eigenstate thermalization hypothesis for translation invariant quantum spin systems has been proved recently by using random matrices. In this paper, we study the subsystem version of eigenstate thermalization hypothesis for translation…
Based on the view that thermal equilibrium should be characterized through macroscopic observations, we develop a general theory about typicality of thermal equilibrium and the approach to thermal equilibrium in macroscopic quantum systems.…
We consider the question of thermalization for isolated quantum systems after a sudden parameter change, a so-called quantum quench. In part icular we investigate the pre-requisites for thermalization focusing on the statistical properties…
We study trace estimators for equilibrium thermodynamic observables that rely on the idea of typicality and derivatives thereof such as the finite-temperature Lanczos method (FTLM). As numerical examples quantum spin systems are studied.…
Krylov complexity has been proposed as a diagnostic of chaos in non-integrable lattice and quantum mechanical systems, and if the system is chaotic, Krylov complexity grows exponentially with time. However, when Krylov complexity is applied…
The emergence of statistical mechanics from quantum dynamics is a central problem in quantum many-body physics. Deriving observables aligned with the prediction of the canonical ensemble for a quantum system relies on the presence of a bath…
We study Krylov complexity in various models of quantum field theory: free massive bosons and fermions on flat space and on spheres, holographic models, and lattice models with the UV-cutoff. In certain cases we find asymptotic behavior of…
We use trapped atomic ions forming a hybrid Coulomb crystal, and exploit its phonons to study an isolated quantum system composed of a single spin coupled to an engineered bosonic environment. We increase the complexity of the system by…
We consider the common spin-1/2 XX-model in one dimension with open boundary conditions and a large but finite number of spins. The system is in thermal equilibrium at times t<0, and is subject to a weak local perturbation (quantum quench)…
We provide a pedagogical introduction to eigenstate thermalization. This phenomenon, which occurs in generic quantum systems, allows one to understand why thermalization takes place in isolated systems under unitary dynamics. We motivate…
We study thermalisation and spectral properties of extended systems connected, through their boundaries, to a thermalising Markovian bath. Specifically, we consider periodically driven systems modelled by brickwork quantum circuits where a…
Quantum thermalization describes how closed quantum systems can effectively reach thermal equilibrium, resolving the apparent incongruity between the reversibility of Schr\"odinger's equation and the second law of thermodynamics. Despite…
Recently, a novel measure for the complexity of operator growth is proposed based on Lanczos algorithm and Krylov recursion method. We study this Krylov complexity in quantum mechanical systems derived from some well-known local toric…
We explore the implications of the averaged null energy condition for thermal states of relativistic quantum field theories. A key property of such thermal states is the thermalization length. This lengthscale generalizes the notion of a…
We discuss the thermalization process in the kinetic approximation in the presence of non--zero initial anomalous quantum expectation values on top of an initial non--planckian (non--thermal) level population. Namely we derive a system of…
Thermalization is a ubiquitous process of statistical physics, in which details of few-body observables are washed out in favor of a featureless steady state. Even in isolated quantum many-body systems, limited to reversible dynamics,…
We consider the set of all initial states within a microcanonical energy shell of an isolated many-body quantum system, which exhibit the same, arbitrary but fixed non-equilibrium expectation value for some given observable $A$. On…
Eigenstate thermalization refers to the property that an energy eigenstate of a many-body system is indistinguishable from a thermal equilibrium ensemble at the same energy as far as expectation values of local observables are concerned. In…
Using the ergodicity principle for the expectation values of several types of observables, we investigate the thermalization process in isolated fermionic systems. These are described by the two-body random ensemble, which is a paradigmatic…
We discuss thermalization in a multimode quantum cavity under unitary evolution. According to general principles, an isolated system with quadratic couplings does not exhibit thermalization. However, we find that three-wave perturbation,…