Analytical investigation of revival phenomena in the finite square-well potential

Aronstein, David L.; Stroud, C. R.

doi:10.1103/physreva.62.022102

Cited by 29 publications

(29 citation statements)

References 21 publications

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“…However, the nonequidistant nature of the involved energy spectra causes peculiar quantum effects, broadening of the initially well localized wave packets, revivals and partial revivals [1,2,3,4,5,6]. Partial revivals are in close connection with the formation of Schrödinger-cat states, which, in this context, are coherent superpositions of two spatially separated, well localized wave packets [7].…”

Section: Introductionmentioning

confidence: 99%

“…The correspondence between classical and quantum dynamics of anharmonic systems has gained significant attention in the past few years [1,2,3,4]. A short laser pulse impinging on an atom or a molecule excites a superposition of several stationary states, and the resulting wave packet follows the orbit of the corresponding classical particle in the initial stage of the time evolution.…”

Section: Introductionmentioning

confidence: 99%

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Decoherence of wave packets in an anharmonic oscillator

et al. 2003

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The time evolution of anharmonic molecular wave packets is investigated under the influence of the environment consisting of harmonic oscillators. These oscillators represent photon or phonon modes and assumed to be in thermal equilibrium. Our model explicitly incorporates the fact that in the case of a nonequidistant spectrum the rates of the environment induced transitions are different for each transition. The nonunitary time evolution is visualized by the aid of the Wigner function related to the vibrational state of the molecule. The time scale of decoherence is much shorter than that of dissipation, and gives rise to states which are mixtures of localized states along the phase space orbit of the corresponding classical particle. This behavior is to a large extent independent of the coupling strength, the temperature of the environment and also of the initial state.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Decoherence of wave packets in an anharmonic oscillator

et al. 2003

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“…Here P [ψ] is an operator acting on an arbitrary vector χ as P [ψ]χ = (ψ, χ)ψ (P [ψ] = |ψ ψ| in the Dirac notations; it is a projector whenever ψ is a unit vector); (·, ·) is a scalar product (with linearity in the second argument). Equality (8) is understood in the weak sense: for all ψ, χ ∈ L 2 (R d ) we have…”

Section: Coherent Statesmentioning

confidence: 99%

Semiclassical evolution of quantum wave packets on the torus beyond the Ehrenfest time in terms of Husimi distributions

Трушечкин

2017

Journal of Mathematical Physics

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The semiclassical long-time limit of free evolution of quantum wave packets on the torus is under consideration. Despite of simplicity of this system, there are still open questions concerning the detailed description of the evolution on time scales beyond the Ehrenfest time. One of the approaches is based on the limiting Wigner or Husimi distributions of time-evolved wave packets as the Planck constant tends to zero and time tends to infinity. We derive explicit expressions for semiclassical measures corresponding to all time scales and the corresponding stages of evolution: classical-like motion, spreading of the wave packet, and its revivals. Also we discuss limitations of the approach based on semiclassical measures and suggest its generalization.

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“…The analysis of the quantum revival reveals two types of systems. First, systems of excited localized wave packets in which the recovering of the complete wave-function destroyed by the decay processes has been studied in the context of two-level quantum systems [5][6][7], quantum wells [8][9][10][11][12] and Bose-Einstein condensates [13,14]. The second type discusses systems with discrete energy eigenvalues in which, due to the quantum recurrence theorem, the system return arbitrarily close to the initial state [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Quantum revivals and magnetization tunneling in effective spin systems

et al. 2016

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Quantum mechanical objects or nano-objects have been proposed as bits for information storage. While time-averaged properties of magnetic, quantum-mechanical particles have been extensively studied experimentally and theoretically, experimental investigations of the real time evolution of magnetization in the quantum regime were not possible until recent developments in pump-probe techniques. Here we investigate the quantum dynamics of effective spin systems by means of analytical and numerical treatments. Particular attention is paid to the quantum revival time and its relation to the magnetization tunneling. The quantum revival time has been initially defined as the recurrence time of a total wave-function. Here we show that the quantum revivals of wave-functions and expectation values in spin systems may be quite different which gives rise to a more sophisticated definition of the quantum revival within the realm of experimental research. Particularly, the revival times for integer spins coincide which is not the case for half-integer spins. Furthermore, the quantum revival is found to be shortest for integer ratios between the on-site anisotropy and an external magnetic field paving the way to novel methods of anisotropy measurements. We show that the quantum tunneling of magnetization at avoided level crossing is coherent to the quantum revival time of expectation values, leading to a connection between these two fundamental properties of quantum mechanical spins.

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Analytical investigation of revival phenomena in the finite square-well potential

Cited by 29 publications

References 21 publications

Decoherence of wave packets in an anharmonic oscillator

Decoherence of wave packets in an anharmonic oscillator

Semiclassical evolution of quantum wave packets on the torus beyond the Ehrenfest time in terms of Husimi distributions

Quantum revivals and magnetization tunneling in effective spin systems

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