Entropy and Temperature in finite isolated quantum systems
arXiv:2210.02380 · doi:10.1103/PhysRevE.107.034125
Abstract
We investigate how the temperature calculated from the microcanonical entropy compares with the canonical temperature for finite isolated quantum systems. We concentrate on systems with sizes that make them accessible to numerical exact diagonalization. We thus characterize the deviations from ensemble equivalence at finite sizes. We describe multiple ways to compute the microcanonical entropy and present numerical results for the entropy and temperature computed in these various ways. We show that using an energy window whose width has a particular energy dependence results in a temperature with minimal deviations from the canonical temperature.
arXiv commentv2: Updated with changes made for publication in Phys. Rev. E. 10 pages, 7 figures. v1: 9 Pages, 6 Figures
References in corpus (98)
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Many body localization and thermalization in quantum statistical mechanics
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Random Matrix Theories in Quantum Physics: Common Concepts
- Quantum thermalization through entanglement in an isolated many-body system
- The Kernel Polynomial Method
- Quench dynamics and relaxation in isolated integrable quantum spin chains
- Quantum mechanical evolution towards thermal equilibrium
- Eigenstate Thermalization Hypothesis
- The approach to thermal equilibrium in quantized chaotic systems
- Breakdown of thermalization in finite one-dimensional systems
- Thermalization and prethermalization in isolated quantum systems: a theoretical overview
- Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
- Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization
- Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems
- Alternatives to Eigenstate Thermalization
- Finite-size scaling of eigenstate thermalization
- Does a single eigenstate encode the full Hamiltonian?
- Quantum quenches and thermalization in one-dimensional fermionic systems
- Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems
- Thermal Fluctuations in Quantized Chaotic Systems
- Anomalous thermalization in ergodic systems
- Off-diagonal matrix elements of local operators in many-body quantum systems
- Microscopic diagonal entropy and its connection to basic thermodynamic relations
- Eigenstate thermalization within isolated spin-chain systems
- Inconsistent thermostatistics and negative absolute temperatures
- Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems
- Subsystem ETH
- Canonical Typicality of Energy Eigenstates of an Isolated Quantum System
- Entropy of isolated quantum systems after a quench
- Quantum chaos and thermalization in gapped systems
- Eigenstate thermalization in the two-dimensional transverse field Ising model
- The microscopic origin of thermodynamic entropy in isolated systems
- Misleading signatures of quantum chaos
- Fluctuation-Dissipation Theorem in an Isolated System of Quantum Dipolar Bosons after a Quench
- Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit
- Eigenstate thermalization in the two-dimensional transverse field Ising model: II. Off-diagonal matrix elements of observables
- Eigenstate Thermalization in a Locally Perturbed Integrable System
- Eigenstate thermalization and quantum chaos in the Holstein polaron model
- Thermalization and canonical typicality in translation-invariant quantum lattice systems
- Finite size effects in global quantum quenches: examples from free bosons in an harmonic trap and the one-dimensional Bose-Hubbard model
- Renyi Entropy of Chaotic Eigenstates
- Weak and strong typicality in quantum systems
- Thermodynamic entropy of a many body energy eigenstate
- Thermalization of Interacting Fermions and Delocalization in Fock space
- Eigenstate Thermalization, Random Matrix Theory and Behemoths
- Microcanonical quantum fluctuation theorems
- Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
- Eigenstate thermalization hypothesis and integrals of motion
- Construction of microcanonical entropy on thermodynamic pillars
- Numerical Large Deviation Analysis of Eigenstate Thermalization Hypothesis
- Speck of Chaos
- Spectral fluctuations and 1/f noise in the order-chaos transition regime
- Eigenstate thermalization hypothesis through the lens of autocorrelation functions
- Multipartite entanglement structure in the Eigenstate Thermalization Hypothesis
- Single particle excitations in disordered Weyl fluids
- Thermalisation of Local Observables in Small Hubbard Lattices
- Meaning of temperature in different thermostatistical ensembles
- Eigenstate Thermalization in Systems with Spontaneously Broken Symmetry
- Nodal portraits of quantum billiards: Domains, lines, and statistics
- The eigenstate thermalization hypothesis in constrained Hilbert spaces: a case study in non-Abelian anyon chains
- Energy level statistics of the two-dimensional Hubbard model at low filling
- Eigenstate thermalization for observables that break Hamiltonian symmetries and its counterpart in interacting integrable systems
- Test of Eigenstate Thermalization Hypothesis Based on Local Random Matrix Theory
- Eigenstate Thermalization in Long-Range Interacting Systems
- Quantum chaos and ensemble inequivalence of quantum long-range Ising chains
- Probing thermalization through spectral analysis with matrix product operators
- Unfolding of the Spectrum for Chaotic and Mixed Systems
- Continuum Goldstone spectrum of two-color QCD at finite density with staggered quarks
- Quantum quenches and work distributions in ultra-low-density systems
- Taking the temperature of a pure quantum state
- The approach to chaos in ultracold atomic and molecular physics: statistics of near-threshold bound states for Li+CaH and Li+CaF
- Understanding the three-dimensional quantum Hall effect in generic multi-Weyl semimetals
- Stringent Numerical Test of the Poisson Distribution for Finite Quantum Integrable Hamiltonians
- Spectral statistics of random geometric graphs
- Thouless Energy Challenges Thermalization on the Ergodic Side of the Many-Body Localization Transition
- On the level density of spin chains of Haldane--Shastry type
- Localization threshold of Instantaneous Normal Modes from level-spacing statistics
- Abelian Tensor Models on the Lattice
- Microscopic calculations of nuclear level densities with the Lanczos method
- Eigenstate thermalization hypothesis and eigenstate-to-eigenstate fluctuations
- Long-range level correlations in quantum systems with finite Hilbert space dimension
- Quantum chaos in nanoelectromechanical systems
- Non-invasive control of excitons in two-dimensional materials
- Signatures of quantum chaos in low-energy mixtures of few fermions
- Analytic solution to pseudo-Landau levels in strongly bent graphene nanoribbons
- Using the statistic to test for missed levels in mixed sequence neutron resonance data
- On the spectral unfolding of chaotic and mixed systems
- Eigenstate thermalization scaling in approaching the classical limit
- Generating a Fractal Butterfly Floquet Spectrum in a Class of Driven SU(2) Systems
- Assigning Temperatures to Eigenstates
- An investigation of equilibration in small quantum systems: the example of a particle in a 1D random potential
- Semiclassical shell-structure micro-macroscopic approach for the level density
- Emergence of a thermal equilibrium in a subsystem of a pure ground state by quantum entanglement
- Quantum vortex dynamics in two-dimensional neutral superfluids
- Canonical density matrices from eigenstates of mixed systems
- Thermodynamic laws in isolated systems
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- Many Body Density of States of a system of non interacting spinless fermions
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- Direct temperature readout in nonequilibrium quantum thermometry