Quantum models of relaxation

Brailovskii, A.B.; Вакс, В. Л.; Mityugov, V. V.

doi:10.3367/ufnr.0166.199607f.0795

Cited by 8 publications

(11 citation statements)

References 2 publications

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“…Though some aspects of the following discussion are rather general, it will be useful to have in mind a concrete relaxation scenario. Consider the collisional relaxation scenario, where the target system interacts with independent bath particles via successive collisions; see [35,36] and Appendix A. For our purpose the target system is H or C that interact with, respectively, the hot and cold bath.…”

Section: A Powermentioning

confidence: 99%

“…Each collision lasts a time τ col , which is much smaller than the characteristic time τ btw between two collisions. The interaction Hamiltonian between the target system and a bath particle is conserved, so that no work is done in switching the system-bath interaction on and off; see [35,36] and Appendix A 1.…”

Section: A Powermentioning

confidence: 99%

“…Note from (36,38) that the dominant factor in the efficiency ζ is the Carnot value θ 1−θ , while the subleading term is naturally negative; see (41). Likewise, the dominant factor in Qc Tc is p ≡ ln[n − 1], while the subleading term is O(1).…”

Section: The Many-level Regime: Reaching the Carnot Limit At A Fimentioning

confidence: 99%

“…The purpose of this discussion is to outline the general structure of a collisional relaxation process. Our presentation follows to [35,36].…”

Section: General Considerationmentioning

confidence: 99%

“…Convergence of the efficiency ζ (normal line) to the Carnot value ηC = 1/9 (dashed line) as a function of ln p p , where p = ln[n − 1]; see(36)(37)(38)(39).…”

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confidence: 99%

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Optimal refrigerator

2010

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We study a refrigerator model which consists of two n -level systems interacting via a pulsed external field. Each system couples to its own thermal bath at temperatures T h and T c, respectively (θ ≡ T c/T h < 1). The refrigerator functions in two steps: thermally isolated interaction between the systems driven by the external field and isothermal relaxation back to equilibrium. There is a complementarity between the power of heat transfer from the cold bath and the efficiency: the latter nullifies when the former is maximized and vice versa. A reasonable compromise is achieved by optimizing the product of the heat-power and efficiency over the Hamiltonian of the two systems. The efficiency is then found to be bounded from below by [formula: see text] (an analog of the Curzon-Ahlborn efficiency), besides being bound from above by the Carnot efficiency [formula: see text]. The lower bound is reached in the equilibrium limit θ → 1. The Carnot bound is reached (for a finite power and a finite amount of heat transferred per cycle) for ln n >> 1. If the above maximization is constrained by assuming homogeneous energy spectra for both systems, the efficiency is bounded from above by ζ CA and converges to it for n >> 1.

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Section: A Powermentioning

confidence: 99%

Section: A Powermentioning

confidence: 99%

Section: The Many-level Regime: Reaching the Carnot Limit At A Fimentioning

confidence: 99%

“…The purpose of this discussion is to outline the general structure of a collisional relaxation process. Our presentation follows to [35,36].…”

Section: General Considerationmentioning

confidence: 99%

“…Convergence of the efficiency ζ (normal line) to the Carnot value ηC = 1/9 (dashed line) as a function of ln p p , where p = ln[n − 1]; see(36)(37)(38)(39).…”

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confidence: 99%

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Optimal refrigerator

2010

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Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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The quantum measurement problem, to wit, understanding why a unique outcome is obtained in each individual experiment, is currently tackled by solving models. After an introduction we review the many dynamical models proposed over the years for elucidating quantum measurements. The approaches range from standard quantum theory, relying for instance on quantum statistical mechanics or on decoherence, to quantum-classical methods, to consistent histories and to modifications of the theory. Next, a flexible and rather realistic quantum model is introduced, describing the measurement of the z-component of a spin through interaction with a magnetic memory simulated by a Curie-Weiss magnet, including N 1 spins weakly coupled to a phonon bath. Initially prepared in a metastable paramagnetic state, it may transit to its up or down ferromagnetic state, triggered by its coupling with the tested spin, so that its magnetization acts as a pointer. A detailed solution of the dynamical equations is worked out, exhibiting several time scales. Conditions on the parameters of the model are found, which ensure that the process satisfies all the features of ideal measurements. Various imperfections of the measurement are discussed, as well as attempts of incompatible measurements. The first steps consist in the solution of the Hamiltonian dynamics for the spin-apparatus density matrixD(t). Its off-diagonal blocks in a basis selected by the spin-pointer coupling, rapidly decay owing to the many degrees of freedom of the pointer. Recurrences are ruled out either by some randomness of that coupling, or by the interaction with the bath. On a longer time scale, the trend towards equilibrium of the magnet produces a final stateD(t f ) that involves correlations between the system and the indications of the pointer, thus ensuring registration. AlthoughD(t f ) has the form expected for ideal measurements, it only describes a large set of runs. Individual runs are approached by analyzing the final states associated with all possible subensembles of runs, within a specified version of the statistical interpretation. There the difficulty lies in a quantum ambiguity: There exist many incompatible decompositions of the density matrixD(t f ) into a sum of sub-matrices, so that one cannot infer from its sole determination the states that would describe small subsets of runs. This difficulty is overcome by dynamics due to suitable interactions within the apparatus, which produce a special combination of relaxation and decoherence associated with the broken invariance of the pointer. Any subset of runs thus reaches over a brief delay a stable state which satisfies the same hierarchic property as in classical probability theory; the reduction of the state for each individual run follows. Standard quantum statistical mechanics alone appears sufficient to explain the occurrence of a unique answer in each run and the emergence of classicality in a measurement process. Finally, pedagogical exercises are proposed and lessons for future works on m...

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The thermodynamics of enhanced heat transfer: a model study

Hovhannisyan¹,

Allahverdyan²

2010

J. Stat. Mech.

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Situations where a spontaneous process of energy or matter transfer is enhanced by an external device are widespread in nature (human sweating system, enzyme catalysis, facilitated diffusion across bio-membranes, industrial heat exchangers). The thermodynamics of such processes remains however open. Here we study enhanced heat transfer by a model junction immersed between two thermal baths at different temperatures T h and Tc (T h > Tc). The transferred heat power is enhanced via controlling the junction by means of external time-dependent fields. Provided that the spontaneous heat flow process is optimized over the junction Hamiltonian, any enhancement of this spontaneous process does demand consumption and subsequent dissipation of work. The efficiency of enhancement is defined via the increment in the heat power divided over the amount of consumed work. We show that this efficiency is bounded from above by Tc/(T h − Tc). Formally this is identical to the Carnot bound for the efficiency of ordinary refrigerators which transfer heat from cold to hot. It also shares some (but not all) physical features of the Carnot bound.

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Quantum models of relaxation

Cited by 8 publications

References 2 publications

Optimal refrigerator

Optimal refrigerator

Understanding quantum measurement from the solution of dynamical models

The thermodynamics of enhanced heat transfer: a model study

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