One-body dissipation in a linear response approach

Koonin, S. E.; Hatch, Robert L.; Randrup, J.

doi:10.1016/0375-9474(77)90701-1

Cited by 86 publications

(81 citation statements)

References 3 publications

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“…1 represent the result of using the following expression, derived in Ref. 4, which corrects the wall formula for the wave-mechanical suppression of the dissipation:…”

Section: The Computer Simulationsmentioning

confidence: 99%

The excitation of an independent-particle gas—classical or quantal—by a time-dependent potential well

1995

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“…1 represent the result of using the following expression, derived in Ref. 4, which corrects the wall formula for the wave-mechanical suppression of the dissipation:…”

Section: The Computer Simulationsmentioning

confidence: 99%

The excitation of an independent-particle gas—classical or quantal—by a time-dependent potential well

1995

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“…The interest in such systems has emerged long time ago in studies of nuclear friction (one-body dissipation) [18,19]. A renewed interest is anticipated in mesoscopic physics where the shape of a quantum dots can be controlled by gate voltages.…”

Section: Model Systemsmentioning

confidence: 99%

“…For example: in Sec. 19 we are going to show that different results are obtained for the dephasing time, depending whether the process is perturbative or non-perturbative. We can express the condition for being in the nonperturbative regime as [12] …”

Section: Non-perturbative Responsementioning

confidence: 99%

“…The interest in friction calculation has started in studies of "one body dissipation" in nuclear physics [18,19]. The "wall formula" assumes that the collisions are totally uncorrelated.…”

Section: Beyond Kinetic Theorymentioning

confidence: 99%

“…The standard "thermal" fluctuation-dissipation relation µ(0) =C(0)/(2k B T ) is obtained from Eq. (19) in case of canonical ρ(E). Standard textbook formulations [44] takes linear response theory together with thermal statistical assumptions as a package deal.…”

Section: Diffusion In Energy Space and Dissipationmentioning

confidence: 99%

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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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Chaos and Energy Spreading for Time-Dependent Hamiltonians, and the Various Regimes in the Theory of Quantum Dissipation

Cohen

2000

Annals of Physics

134

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We make the first steps toward a generic theory for energy spreading and quantum dissipation. The Wall formula for the calculation of friction in nuclear physics and the Drude formula for the calculation of conductivity in mesoscopic physics can be regarded as two special results of the general formulation. We assume a time-dependent Hamiltonian H(Q, P; x(t)) with x(t)=Vt, where V is slow in a classical sense. The rate-of-change V is not necessarily slow in the quantum-mechanical sense. The dynamical variables (Q, P) may represent some``bath'' which is being parametrically driven by x. This bath may consist of just a few degrees of freedom, but it is assumed to be classically chaotic. In the case of either the Wall or Drude formula, the dynamical variables (Q, P) may represent a single particle. In any case, dissipation means an irreversible systematic growth of the (average) energy. It is associated with the stochastic spreading of energy across levels. The latter can be characterized by a transition probability kernel P t (n | m), where n and m are level indices. This kernel is the main object of the present study. In the classical limit, due to the (assumed) chaotic nature of the dynamics, the second moment of P t (n | m) exhibits a crossover from ballistic to diffusive behavior. In order to capture this crossover within quantum mechanics, a proper theory for the quantal P t (n | m) should be constructed. We define the V regimes where either perturbation theory or semiclassical considerations are applicable in order to establish this crossover. In the limit Ä 0 perturbation theory does not apply but semiclassical considerations can be used in order to argue that there is detailed correspondence, during the crossover time, between the quantal and the classical P t (n | m). In the perturbative regime there is a lack of such correspondence. Namely, P t (n | m) is characterized by a perturbative core-tail structure that persists during the crossover time. In spite of this lack of (detailed) correspondence there may be still a restricted correspondence as far as the second moment is concerned. Such restricted correspondence is essential in order to establish the universal fluctuation-dissipation relation.

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One-body dissipation in a linear response approach

Cited by 86 publications

References 3 publications

The excitation of an independent-particle gas—classical or quantal—by a time-dependent potential well

The excitation of an independent-particle gas—classical or quantal—by a time-dependent potential well

Driven Chaotic Mesoscopic Systems, Dissipation and Decoherence

Chaos and Energy Spreading for Time-Dependent Hamiltonians, and the Various Regimes in the Theory of Quantum Dissipation

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