Stability of Quantum Statistical Ensembles with Respect to Local Measurements

Abstract

We introduce a stability criterion for quantum statistical ensembles describing macroscopic systems. An ensemble is called "stable" when a small number of local measurements cannot significantly modify the probability distribution of the total energy of the system. We apply this criterion to lattices of spins-1/2, thereby showing that the canonical ensemble is nearly stable, whereas statistical ensembles with much broader energy distributions are not stable. In the context of the foundations of quantum statistical physics, this result justifies the use of statistical ensembles with narrow energy distributions such as canonical or microcanonical ensembles.

14 pages, 5 figures

References in corpus (14)

• Thermalization and its mechanism for generic isolated quantum systems
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Progressive field-state collapse and quantum non-demolition photon counting
• Strong and weak thermalization of infinite non-integrable quantum systems
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Decoherence of matter waves by thermal emission of radiation
• Optically Levitating Dielectrics in the Quantum Regime: Theory and Protocols
• Thermal equilibration between two quantum systems
• Concentration of measure for quantum states with a fixed expectation value
• Decoherence by a spin thermal bath: Role of the spin-spin interactions and initial state of the bath
• Dynamics of thermalisation in small Hubbard-model systems
• Decoherence wave in magnetic systems and creation of Néel antiferromagnetic state by measurement
• Indirect retrieval of information and the emergence of facts in quantum mechanics

Cited by in corpus (5)

• Thermalization and Return to Equilibrium on Finite Quantum Lattice Systems
• Classical periodic trajectories and quantum scars in many-spin systems
• Quantum quenches with random matrix Hamiltonians and disordered potentials
• Attraction Induced by Mutual Quantum Measurements of Velocity
• Quantifying Stability of Quantum Statistical Ensembles