Maß genommen!

Reimann, Alexander; Kreibe, Florian

doi:10.1007/978-3-531-18774-7_5

Cited by 3 publications

(5 citation statements)

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“…To verify that Eqs. (7,10) are satisfied quantitatively, we also show the matrix elements | E 1000 |A|E n | with a fixed value of m = 1000 for N = 11. The statistical mean value of the off-diagonal elements agrees with the theoretical estimation A √ d…”

Section: Relaxation Of the Expectation Valuesmentioning

confidence: 89%

“…The inequality (7) derives from Eqs. (10,11). For comparison, the matrix elements | E 1000 |A|E n | at N = 11 for the integrable case γ = 0 are shown in Fig.3.…”

Section: ∼ =mentioning

confidence: 99%

“…In thermodynamics, this statement is regarded as requirements for the relevant choice of the model and its macroscopic descriptions. Recently, it is shown that equilibrium states are very popular in the extremely large Hilbert space of state vectors for macroscopic quantum systems [3][4][5][6][7][8][9][10][11][12]. The expectation values with respect to a randomly sampled pure state are typically well described by equilibrium ensembles [3,9,12].…”

Section: Introductionmentioning

confidence: 99%

“…For classical systems, there exist integrable systems which do not reach an equilibrium state even after a long waiting time due to the conserved quantities. For isolated quantum systems, there are always conservative quantities such as projection operators on a specific energy eigenstates [8,10,12,17]. And it has been investigated which conservative quantities would affect the thermalization property [16].…”

Section: Introductionmentioning

confidence: 99%

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Relaxation to equilibrium of the expectation values in macroscopic quantum systems

Monnai

2011

Phys. Rev. E

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A quantum mechanical explanation of the relaxation to equilibrium is shown for macroscopic systems for nonintegrable cases and numerically verified. The macroscopic system is initially in an equilibrium state, subsequently externally perturbed during a finite time, and then isolated for a sufficiently long time. We show a quantitative explanation that the initial microcanonical state typically reaches a state whose expectation values are well approximated by the average over another microcanonical ensemble.

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Section: Relaxation Of the Expectation Valuesmentioning

confidence: 89%

“…The inequality (7) derives from Eqs. (10,11). For comparison, the matrix elements | E 1000 |A|E n | at N = 11 for the integrable case γ = 0 are shown in Fig.3.…”

Section: ∼ =mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Relaxation to equilibrium of the expectation values in macroscopic quantum systems

Monnai

2011

Phys. Rev. E

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“…These may be related to fluctuation theorems [27][28][29][30][31], which will be discussed somewhere else. In particular, the present Zubarev-type formulation of nonlinear relaxation will be useful to discuss the relaxation of quantum systems to equilibrium [32][33][34][35][36].…”

Section: Summary and Discussionmentioning

confidence: 99%

Irreversibility and entropy production in transport phenomena, II: Statistical–mechanical theory on steady states including thermal disturbance and energy supply

Suzuki

2012

Physica A: Statistical Mechanics and its Applications

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Some general aspects of nonlinear transport phenomena are discussed on the basis of two kinds of formulations obtained by extending Kubo's perturbational scheme of the density matrix and Zubarev's non-equilibrium statistical operator formulation. Both formulations are extended up to infinite order of an external force in compact forms and their relationship is clarified through a direct transformation. In order to make it possible to apply these formulations straight-forwardly to thermal disturbance, a mechanical formulation of it is given (in a more convenient form than Luttinger's formulation) by introducing the concept of a thermal field E T which corresponds to the temperature gradient and by defining its conjugate heat operator A H = j h j r j for a local internal energy h j of the thermal particle j. This yields a transparent derivation of the thermal conductivity κ of the Kubo form and the entropy production (dS/dt) irr = κE 2 T /T . Mathematical aspects on the nonequilibrium density-matrix will also be discussed. In Paper I (Physica A 390(2011)1904), the symmetry-separated von Neumann equation with relaxation terms extracting generated heat outside the system was introduced to describe the steady state of the system. In this formulation of the steady state, the internal energy H 0 t is time-independent but the field energy H 1 t (= − A t ·F ) decreases as time t increases. To overcome this problem, such a statistical mechanical formulation is proposed here as includes energy supply to the system from outside by extending the symmetry-separated von Neumann equation given in Paper I. This yields a general theory based on the density-matrix formulation on a steady state with energy supply inside and heat extraction outside and consequently with both H 0 t and H 1 t constant. Furthermore, this steady state gives a positive entropy production. The present general formulation of the current yields a compact expression of the time derivative of entropy production, which yields the plausible justification of the principle of minimum entropy production in the steady state even for nonlinear responses.

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