Universal locality of quantum thermal susceptibility
arXiv:1611.05738 · doi:10.1103/PhysRevA.95.052115
Abstract
The ultimate precision of any measurement of the temperature of a quantum system is the inverse of the local quantum thermal susceptibility [De Pasquale et al., Nature Communications 7, 12782 (2016)] of the subsystem with whom the thermometer interacts. If this subsystem can be described with the canonical ensemble, such quantity reduces to the variance of the local Hamiltonian, that is proportional to the heat capacity of the subsystem. However, the canonical ensemble might not apply in the presence of interactions between the subsystem and the rest of the system. In this work we address this problem in the framework of locally interacting quantum systems. We prove that the local quantum thermal susceptibility of any subsystem is close to the variance of its local Hamiltonian, provided the volume to surface ratio of the subsystem is much larger than the correlation length. This result greatly simplifies the determination of the ultimate precision of any local estimate of the temperature, and rigorously determines the regime where interactions can affect this precision.
References in corpus (38)
- Many-Body Physics with Ultracold Gases
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Nonequilibrium dynamics of closed interacting quantum systems
- Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
- Quantum many-body systems out of equilibrium
- Time-dependence of correlation functions following a quantum quench
- One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
- Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications
- The foundations of statistical mechanics from entanglement: Individual states vs. averages
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Canonical Typicality
- Quantum mechanical evolution towards thermal equilibrium
- Time evolution of local observables after quenching to an integrable model
- Many-body localization in periodically driven systems
- Breakdown of thermalization in finite one-dimensional systems
- Foundation of Statistical Mechanics under experimentally realistic conditions
- The Luttinger model following a sudden interaction switch-on
- Exact relaxation in a class of non-equilibrium quantum lattice systems
- How small can thermal machines be? The smallest possible refrigerator
- From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
- Generalized Thermalization in an Integrable Lattice System
- Alternatives to Eigenstate Thermalization
- Quantum criticality as a resource for quantum estimation
- Absence of Thermalization in Nonintegrable Systems
- Typicality for Generalized Microcanonical Ensembles
- Thermalization in Nature and on a Quantum Computer
- Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems
- Locality of temperature
- Local quantum thermal susceptibility
- Canonical thermalization
- Thermalization and canonical typicality in translation-invariant quantum lattice systems
- Precision Measurements of Temperature and Chemical Potential of Quantum Gases
- Thermodynamic length for far from equilibrium quantum systems
- Necessity of Eigenstate Thermalization
- Emergence of canonical ensembles from pure quantum states
- Dynamics of thermalization and decoherence of a nanoscale system
- Foundations of statistical mechanics from symmetries of entanglement
Cited by in corpus (22)
- Quantum thermal machines and batteries
- Thermometry in the quantum regime: Recent theoretical progress
- Precision thermometry and the quantum speed limit
- Probing the temperature of cold many-body quantum systems
- Fundamental limits on low-temperature quantum thermometry with finite resolution
- Bridging thermodynamics and metrology in non-equilibrium Quantum Thermometry
- Optimal Quantum Thermometry with Coarse-grained Measurements
- Tight bound on finite-resolution quantum thermometry at low temperatures
- Local Temperatures Out of Equilibrium
- Non-Markovian quantum thermometry
- Geometrical bounds on irreversibility in open quantum systems
- Spectral signatures of non-thermal baths in quantum thermalization
- Quantum Thermometry
- Quantifying precision loss in local quantum thermometry via diagonal discord
- Quantum thermometry in a squeezed thermal bath
- Energy measurements remain thermometrically optimal beyond weak coupling
- Structure of the Hamiltonian of mean force
- Thermometry with a Dissipative Heavy Impurity
- Properties of thermal quantum states: locality of temperature, decay of correlations, and more
- Optimal limits of continuously monitored thermometers and their Hamiltonian structure
- Optimal temperature estimation in polariton Bose-Einstein Condensate
- Temperature as perturbation in quantum mechanics