Infinite Square-Well Potential with a Moving Wall

Doescher, S. W.; Rice, Melvin H.

doi:10.1119/1.1975291

Cited by 143 publications

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“…In this paper we use exact solutions of the time-dependent Schrödinger equation [18] to investigate the validity of Eq. 1 for an expanding quantum piston.…”

mentioning

confidence: 99%

Validity of nonequilibrium work relations for the rapidly expanding quantum piston

Quan

Jarzynski

2012

Phys. Rev. E

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Recent work by Teifel and Mahler [Eur. Phys. J. B 75, 275 (2010)] raises legitimate concerns regarding the validity of quantum nonequilibrium work relations in processes involving moving hard walls. We study this issue in the context of the rapidly expanding one-dimensional quantum piston. Utilizing exact solutions of the time-dependent Schrödinger equation, we find that the evolution of the wave function can be decomposed into static and dynamic components, which have simple semiclassical interpretations in terms of particle-piston collisions. We show that nonequilibrium work relations remains valid at any finite piston speed, provided both components are included, and we study explicitly the work distribution for this model system. In the past two decades, much attention has been devoted to theoretical predictions and experimental investigations regarding the fluctuations of small systems away from thermal equilibrium. These predictions include the nonequilbrium work relation [1,2] and the corresponding fluctuation theorem derived by Crooks [3][4][5] ρ F (+W ) ρ R (−W ) = e β(W −∆F ) ,arXiv:1112.5798v1 [cond-mat.stat-mech]

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“…In this paper we use exact solutions of the time-dependent Schrödinger equation [18] to investigate the validity of Eq. 1 for an expanding quantum piston.…”

mentioning

confidence: 99%

Validity of nonequilibrium work relations for the rapidly expanding quantum piston

Quan

Jarzynski

2012

Phys. Rev. E

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“…There is an ongoing interest [15,16] in the problem of 1D box with moving wall (also known as the infinite well problem with moving wall). If the wall is moving with constant velocity, then it is possible to transform the Schrodinger equation into a time-independent equation, and to look for the stationary states.…”

Section: Driving By Moving Wallsmentioning

confidence: 99%

Driven Chaotic Mesoscopic Systems, Dissipation and Decoherence

Cohen

2002

Dynamics of Dissipation

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Driven quantum systems, described by Hamiltonian H(Q, P, x(t)) where x(t) is a time dependent parameter, are of interest in mesoscopic physics (quantum dots), as well as in nuclear, atomic and molecular physics. Such systems tend to absorb energy. This irreversible effect is known as dissipation. More generally, x may be a dynamical variable, where the total Hamiltonian is H0(x, p) + H(Q, P ; x). In such case the interaction of (x, p) with the environmental degrees of freedom (Q, P ) leads to dephasing as well as to dissipation. It should be emphasized that even few (Q, P ) degrees of freedom can serve as a miniature heat bath, provided they have chaotic dynamics. We shall introduce a general framework for the analysis of dissipation and dephasing, and we shall clarify the tight connection to recent studies of quantum irreversibility (also referred to as "Loschmidt echo" or as the "fidelity" of quantum computation). Specific model systems that will be presented are: particle in a box driven by moving a wall, and particle in a box/ring driven by electro-motive-force. These two examples are related to studies of nuclear friction and mesoscopic conductance. Specific issues to be discussed are the limitations of kinetic theory, the capabilities of linear response theory, and the manifestation of non-perturbative quantum-mechanical effects. In particular we shall explain that random matrix theory and the semiclassical theory lead to different non-perturbative limits.

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“…In this situation we are able to completely solve the dynamics of the system by generalizing the results in Ref [4].…”

Section: B the Case Of A Uniformly Moving Domainmentioning

confidence: 99%

“…Over the years, several works appeared studying the problem of particles confined in a box with moving walls [4][5][6][7][8], sometimes focusing on boundaries having specific shapes [9][10][11]. The study of this kind of problems is relevant to several conceptual aspects of quantum mechanics, from the analysis of the semiclassical limit of a quantum (chaotic) system [12][13][14][15] to the incoming of geometric phases [16], and it is connected with the derivation of analytical solutions of the dynamics of systems governed by such mathematically complicated potentials as delta functions [17].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a particle confined in a two-dimensional dilating and deforming domain

Anzà¹,

Martino²,

Messina³

2015

Phys. Scr.

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Some recent results concerning a particle confined in a one-dimensional box with moving walls are briefly reviewed. By exploiting the same techniques used for the 1D problem, we investigate the behavior of a quantum particle confined in a two-dimensional box (a 2D billiard) whose walls are moving, by recasting the relevant mathematical problem with moving boundaries in the form of a problem with fixed boundaries and time-dependent Hamiltonian. Changes of the shape of the box are shown to be important, as it clearly emerges from the comparison between the "pantographic" case (same shape of the box through all the process) and the case with deformation.

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Infinite Square-Well Potential with a Moving Wall

Cited by 143 publications

References 0 publications

Validity of nonequilibrium work relations for the rapidly expanding quantum piston

Validity of nonequilibrium work relations for the rapidly expanding quantum piston

Driven Chaotic Mesoscopic Systems, Dissipation and Decoherence

Dynamics of a particle confined in a two-dimensional dilating and deforming domain

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