Quantum models of relaxation

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

doi:10.1070/pu1996v039n07abeh000159

Cited by 7 publications

(6 citation statements)

References 3 publications

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“…One can show that the optimal unitary amounts to a permutation of the eigenvalues (F12) (this fact can be shown similarly to the derivation presented in (9)(10)(11)(12) of the main text). Now we note that the trace over tr B amounts to summing up elements in each section.…”

Section: Minimization Of the Relaxation Timementioning

confidence: 76%

“…The relaxation progresses autonomously -no energy flow in or out happens (otherwise one would need a third system to accept/give energy and a control to switch on and off the interactions, while the relaxation is supposed to be a probably prearranged but a spontaneous process). To that end, the interaction between E and B, H EB , must satisfy [9] [H EB , H E ⊗ 1 B + 1 E ⊗ H B ] = 0.…”

Section: Appendix G: Entanglement Generation During Relaxationmentioning

confidence: 99%

“…But it is currently an open question whether the maximal efficiency is attained under realistic conditions (see e.g. [9] versus [7]), and how to characterize the very realism of those conditions. Even more generally: what is the origin of the power-efficiency dilemma?…”

mentioning

confidence: 99%

“…However, in these scenarios the system-bath interaction Hamiltonian (that governs the relaxation) is special: it depends on the engine Hamiltonian (9,14).…”

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confidence: 99%

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Carnot Cycle at Finite Power: Attainability of Maximal Efficiency

et al. 2013

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We want to understand whether and to which extent the maximal (Carnot) efficiency for heat engines can be reached at a finite power. To this end we generalize the Carnot cycle so that it is not restricted to slow processes. We show that for realistic (i.e. not purposefully-designed) enginebath interactions, the work-optimal engine performing the generalized cycle close to the maximal efficiency has a long cycle time and hence vanishing power. This aspect is shown to relate to the theory of computational complexity. A physical manifestation of the same effect is the Levinthal's paradox in the protein folding problem. The resolution of this paradox for realistic proteins allows to construct engines that can extract at a finite power 40 % of the maximally possible work reaching 90 % of the maximal efficiency. For purposefully designed engine-bath interactions, the Carnot efficiency is achievable at a large power. Reciprocating heat engines extract work operating cyclically between two thermal baths at temperatures T 1 and T 2 (T 1 > T 2 ) [1]. They have two basic characteristics: (i) efficiency, η = W/Q 1 , is the work W extracted per cycle divided by the heat input Q 1 from the hightemperature bath. (ii) Power W/τ , where τ is the cycle duration. Both these quantities have to be large for a good engine: if η is small, lot of energy is wasted; if the power is small, no sizable work is delivered over a reasonable time [1].The second law establishes the Carnot efficiency η C = 1 − T2 T1 as an upper bound for η [1]. The Carnot cycle reaches the bounding value η C in the (useless) limit, where the power goes to zero [1]. Conversely, realistic engines are not efficient, since they have to be powerful, e.g. the efficiency of Diesel engines amounts to 35-40 % of the maximal value. This power-efficiency dilemma motivated a search for the efficiency that would generally characterize the maximal power regime. One candidate for this is the Curzon-Ahlborn efficiency η CA = 1 − T 2 /T 1 [2], which is however crucially tied to the linear regime T 1 ≈ T 2 [3,4]. Beyond this regime η CA is a lower bound of η for a class of model engines [5]. Several recent models for the efficiency at the maximal power overcome η CA with η * = ηC 2−ηC [6]. As argued in [5,7,8], the maximal power regime allows for the Carnot efficiency, at least for certain models. But it is currently an open question whether the maximal efficiency is attained under realistic conditions (see e.g.[9] versus [7]), and how to characterize the very realism of those conditions. Even more generally: what is the origin of the power-efficiency dilemma? We answer these questions by analyzing a generalized Carnot cycle, which in contrast to the original Carnot cycle is not restricted to slow processes. We now summarize our answers.(1) When the N -particle engine operates at the maximal work extracted per cycle, its efficiency reaches the Carnot bound η C for N 1, while the cycle time isgiven by the relaxation time of the engine. The maximal work and the Carnot efficiency are...

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Section: Minimization Of the Relaxation Timementioning

confidence: 76%

Section: Appendix G: Entanglement Generation During Relaxationmentioning

confidence: 99%

mentioning

confidence: 99%

“…However, in these scenarios the system-bath interaction Hamiltonian (that governs the relaxation) is special: it depends on the engine Hamiltonian (9,14).…”

mentioning

confidence: 99%

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Carnot Cycle at Finite Power: Attainability of Maximal Efficiency

et al. 2013

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“…It is possible to extend the main ideas of the linearized Boltzmann equation (independent collisions with a system in equilibrium) to the quantum domain [375,376,377]. We shall first describe this scenario in general terms and then apply it to the specific situation described in § 11.2.5.…”

Section: I1 General Discussionmentioning

confidence: 99%

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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Dissipative electron transfer dynamics in mixed valence dimers: Microscopic approach to the solid state problem

Palii

Bosch

Clemente‐Juan

et al. 2013

The Journal of Chemical Physics

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We propose a microscopic analytical approach to the description of the low-temperature dissipative intracluster electron transfer dynamics in centrosymmetric one-electron mixed-valence (MV) dimers. The dissipative system (bath) is supposed to consist of the acoustic phonons of the crystal surrounding that are coupled to the delocalized electron(s) of a MV dimer. Although the concept of the bath is the spin-boson model is more generic, the present consideration is relevant, for example, to a MV bi-center impurity in an ionic crystal. The model allows us to develop an approximate microscopic approach within which the relaxation processes are explicitly taken into account without additional assumption regarding spectral function of the bath. It is assumed that initially the extra electron is localized on a certain center and then the time-dependent localization probability (averaged value of the electron dipole moment) is evaluated with the emphasis on the damping of the amplitude of the Rabi oscillations. The approach assumes the following conditions: (i) the vibrational spectrum of the crystal does not show the presence of local modes; (ii) the itinerant electron is weakly coupled to the long-waves acoustic phonons which is peculiar to fully delocalized Robin and Day class III MV systems; (iii) the Debye energy ℏωD exceeds the electronic resonance energy gap 2β (β is the electron transfer parameter). We have demonstrated that the dissipation in this case is super-ohmic with the low-frequency spectral function J(ω) ∝ ω(5). The time dependences of the localization probabilities show nearly picosecond damped oscillations. The longitudinal relaxation time T1 has been shown to be two times shorter than the decoherence time T2 thus giving the upper bound for T2, T2 ≤ 2T1.

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Quantum models of relaxation

Cited by 7 publications

References 3 publications

Carnot Cycle at Finite Power: Attainability of Maximal Efficiency

Carnot Cycle at Finite Power: Attainability of Maximal Efficiency

Understanding quantum measurement from the solution of dynamical models

Dissipative electron transfer dynamics in mixed valence dimers: Microscopic approach to the solid state problem

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