Energy Conservation, Counting Statistics, and Return to Equilibrium

Jakšić, Vojkan; Panangaden, Jane; Panati, Annalisa; Pillet, Claude-Alain

doi:10.1007/s11005-015-0769-7

Cited by 4 publications

(4 citation statements)

References 26 publications

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“…Return to equilibrium was also shown for finite quantum systems coupled to infinite reservoirs after a coupling has been turned on [18,19], and a rough argument for stability of thermal states was given recently in terms of energy probability distributions in [20]. Here, we prove that a system in a thermal state, after being locally disturbed, re-equilibrates to a thermal state provided correlations decay sufficiently quickly.…”

Section: Introductionsupporting

confidence: 57%

Thermalization and Return to Equilibrium on Finite Quantum Lattice Systems

2017

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Thermal states are the bedrock of statistical physics. Nevertheless, when and how they actually arise in closed quantum systems is not fully understood. We consider this question for systems with local Hamiltonians on finite quantum lattices. In a first step, we show that states with exponentially decaying correlations equilibrate after a quantum quench. Then, we show that the equilibrium state is locally equivalent to a thermal state, provided that the free energy of the equilibrium state is sufficiently small and the thermal state has exponentially decaying correlations. As an application, we look at a related important question: When are thermal states stable against noise? In other words, if we locally disturb a closed quantum system in a thermal state, will it return to thermal equilibrium? We rigorously show that this occurs when the correlations in the thermal state are exponentially decaying. All our results come with finite-size bounds, which are crucial for the growing field of quantum thermodynamics and other physical applications. DOI: 10.1103/PhysRevLett.118.140601 To understand the strengths and limitations of statistical physics, it makes sense to derive it from physical principles, without ad hoc assumptions. Along these lines, over the past twenty years, ideas from quantum information have given new insights into the foundations of statistical physics [1][2][3]. In particular, some progress was made towards understanding how and when thermalization occurs [4][5][6]. A large class of states of systems with weak intensive interactions (e.g., one dimensional systems) were shown to thermalize [5]. In [6], thermalization was also proved for a large class of states, in the thermodynamic limit. (We will compare the results of [6] to our results in detail below.) More recently, the equivalence of the microcanonical and canonical ensemble (i.e., thermal state) was proved for finite quantum lattice systems, when correlations in the thermal state decay sufficiently quickly [7] (see, also, [6,8]).Here, we prove thermalization results for closed quantum systems in two parts. First, we build upon previous equilibration results (e.g., Refs. [9,10]). A requirement for equilibration is that the effective dimension, defined below, is large. While there are physical arguments for this in some cases [11] (and it is true for most states drawn from the Haar measure on large subspaces [10]), there are no techniques for deciding whether a given initial state will equilibrate under a given Hamiltonian. Here, we prove that a large effective dimension is guaranteed for local Hamiltonian systems if the correlations in the initial state decay sufficiently quickly and the energy variance is sufficiently large. The latter is known for thermal states with intensive specific heat capacity and may, for large classes of states, be computed straightforwardly. The second part of thermalization is to show that the equilibrium state is locally indistinguishable from a thermal state. We prove that this occurs if the correlations in...

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Section: Introductionsupporting

confidence: 57%

Thermalization and Return to Equilibrium on Finite Quantum Lattice Systems

2017

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“…As conveyed e.g. in [JOPP11], [JPPP15] and [BJP + 15], mild assumptions ensure that the corresponding sequence of probability measures converges weakly to the measure P t of Definition 3.1 on the limiting infinitely extended system. In Appendix B, we provide proofs of this weak convergence for the models studied in Section 4.…”

Section: Setupmentioning

confidence: 99%

“…Note that, while important for the control of the tails at finite λ, the UV regularisation assumptions become irrelevant in the limit t → ∞ and then λ → 0, if one assumes return to equilibrium. Indeed, adapting [JPPP15], it can be shown that in this limit P t converges weakly to a Dirac measure in 0.…”

Section: Introductionmentioning

confidence: 96%

Control of Fluctuations and Heavy Tails for Heat Variation in the Two-Time Measurement Framework

Benoist

Panati

Raquépas

2018

Ann. Henri Poincaré

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We study heat fluctuations in the two-time measurement framework. For bounded perturbations, we give sufficient ultraviolet regularity conditions on the perturbation for the moments of the heat variation to be uniformly bounded in time, and for the Fourier transform of the heat variation distribution to be analytic and uniformly bounded in time in a complex neighborhood of 0.On a set of canonical examples, with bounded and unbounded perturbations, we show that our ultraviolet conditions are essentially necessary. If the form factor of the perturbation does not meet our assumptions, the heat variation distribution exhibits heavy tails. The tails can be as heavy as preventing the existence of a fourth moment of the heat variation.

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“…In the case where A and B are thermal reservoirs, the FCS of the total energy current was previously studied theoretically in [21]. The works [22,23] concern the FCS of energy transfer in the thermalization process of a finite level quantum system in contact with a thermal bath, a problem which is radically different from the one considered here. We also emphasize that here we are only interested in the FCS of the total energy, and not in the FCS of the individual energy variations ∆E A/B .…”

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confidence: 99%

Full statistics of energy conservation in two-time measurement protocols

et al. 2015

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The first law of thermodynamics states that the average total energy current between different reservoirs vanishes at large times. In this paper we examine this fact at the level of the full statistics of two-time measurement protocols, also known as the Full Counting Statistics. Under very general conditions, we establish a tight form of the first law asserting that the fluctuations of the total energy current computed from the energy variation distribution are exponentially suppressed in the large time limit. We illustrate this general result using two examples: the Anderson impurity model and a two-dimensional spin lattice model.

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Energy Conservation, Counting Statistics, and Return to Equilibrium

Cited by 4 publications

References 26 publications

Thermalization and Return to Equilibrium on Finite Quantum Lattice Systems

Thermalization and Return to Equilibrium on Finite Quantum Lattice Systems

Control of Fluctuations and Heavy Tails for Heat Variation in the Two-Time Measurement Framework

Full statistics of energy conservation in two-time measurement protocols

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