Decoherence, tunneling, and noise-induced activation in a double-potential well at high and zero temperature

Antunes, Nuno D.; Lombardo, Fernando C.; Monteoliva, Diana; Villar, Paula I.

doi:10.1103/physreve.73.066105

Cited by 20 publications

(24 citation statements)

References 43 publications

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“…Interesting results have recently led to a better understanding of anomalous diffusion for the free QBM model, i.e., in absence of a trapping potential [30]. The dynamics of an initial Gaussian state in an anharmonic potential have also been studied [31].…”

Section: Introductionmentioning

confidence: 99%

Environment-dependent dissipation in quantum Brownian motion

et al. 2009

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The dissipative dynamics of a quantum Brownian particle is studied for different types of environment. We derive analytic results for the time evolution of the mean energy of the system for Ohmic, sub-Ohmic and super-Ohmic environments, without performing the Markovian approximation. Our results allow to establish a direct link between the form of the environmental spectrum and the thermalization dynamics. This in turn leads to a natural explanation of the microscopic physical processes ruling the system time evolution both in the short-time non-Markovian region and in the long-time Markovian one. Our comparative study of thermalization for different environments sheds light on the physical contexts in which non-Markovian dissipation effects are dominant.

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Section: Introductionmentioning

confidence: 99%

Environment-dependent dissipation in quantum Brownian motion

et al. 2009

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“…We clearly observe tunneling of the particle, resulting from a beat phenomenon between ψ(x, t) and φ 2 (x, t) [41], as the height of the barrier decreases. Such a beat phenomenon is weakened when the barrier is off the origin, because a single eigenstate is enough to localize a particle [ Fig.…”

Section: Discussion and Summarymentioning

confidence: 96%

Particle in a box with a time-dependentδ-functionpotential

Baek

Kim

2016

Phys. Rev. A

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In quantum information processing, one often considers inserting a barrier into a box containing a particle to generate one bit of Shannon entropy. We formulate this problem as a one-dimensional Schrödinger equation with a time-dependent δ-function potential. It is a natural generalization of the particle in a box, a canonical example of quantum mechanics, and we present analytic and numerical investigations on this problem. After deriving an exact Volterra-type integral equation, composed of an infinite sum of modes, we show that approximate formulas with the lowestfrequency modes correctly capture the qualitative behavior of the wave function. If we take into account hundreds of modes, our numerical calculation shows that the quantum adiabatic theorem actually gives a very good approximation even if the barrier height diverges within finite time, as long as it is sufficiently longer than the characteristic time scale of the particle. In particular, if the barrier is slowly inserted at an asymmetric position, the particle is localized by the insertion itself, in accordance with a prediction of the adiabatic theorem. On the other hand, when the barrier is inserted quickly, the wave function becomes rugged after the insertion because of the energy transfer to the particle. Regardless of the position of the barrier, the fast insertion leaves the particle unlocalized so that we can obtain meaningful information by a which-side measurement. Our numerical procedure provides a precise way to calculate the wave function throughout the process, from which one can estimate the amount of this information for an arbitrary insertion protocol.

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“…Typically the dissipation coefficient γ(t) starts with a zero value and after a short transient time, after which the system and the environment become correlated, it reaches a constant value; the normal diffusion coefficient σ 2 (t) starts also with a zero value it reaches a maximum and after the short transient time it undergoes a mild oscillatory behavior until at time scales t ≫ Ω −1 reaches a constant positive asymptotic value; the anomalous diffusion coefficient has a similar qualitative behavior but its asymptotic large time value is negative and depends on the cut off frequency. To be specific [35,36,37,45], at large time scales the normal diffusion coefficient becomes σ 2 ∼ 1 2 Ω 0 , and the anomalous diffusion becomes ∆ ∼ −2γ ln(Ω cut /Ω 0 ), where Ω cut is a suitable cut off frequency for the Ohmic environment. Thus, the vacuum fluctuations of the environment is felt primarily through the anomalous diffusion coefficient that can have a large magnitude.…”

Section: The Open Quantum Systemmentioning

confidence: 99%

“…[42] for a review. Of particular relevance to our problem is the study of decoherence in quenched phase transitions [61], and the effect of decoherence in quantum tunneling in quantum chaotic systems [43,44], or in a double-well potential [45].…”

Section: The Open Quantum Systemmentioning

confidence: 99%

“…Using large scale numerical simulations the effect of the interaction with the environment on coherent tunneling has been analyzed in the framework of an open quantum system that is classically chaotic: a harmonically driven quartic double well [43,44]. More recently [45] tunneling in a simple double well potential has been numerically simulated using the master equation at high temperature as well as at zero temperature. It is found that at zero temperature tunneling is inhibited by the environment that produces decoherence nevertheless at large time scales tunneling is still possible by an activation-like process due to the zero point fluctuations of the quantum environment.…”

Section: Introductionmentioning

confidence: 99%

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Real-time approach to tunnelling in open quantum systems: decoherence and anomalous diffusion

Calzetta¹,

Verdaguer²

2006

J. Phys. A: Math. Gen.

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Macroscopic quantum tunneling is described using the master equation for the reduced Wigner function of an open quantum system at zero temperature. Our model consists of a particle trapped in a cubic potential interacting with an environment characterized by dissipative and normal and anomalous diffusion coefficients. A representation based on the energy eigenfunctions of the isolated system, i. e. the system uncoupled to the environment, is used to write the reduced Wigner function, and the master equation becomes simpler in that representation. The energy eigenfunctions computed in a WKB approximation incorporate the tunneling effect of the isolated system and the effect of the environment is described by an equation that it is in many ways similar to a FokkerPlanck equation. Decoherence is easily identified from the master equation and we find that when the decoherence time is much shorter than the tunneling time the master equation can be approximated by a Kramers like equation describing thermal activation due to the zero point fluctuations of the quantum environment. The effect of anomalous diffusion can be dealt with perturbatively and its overall effect is to inhibit tunneling.

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Decoherence, tunneling, and noise-induced activation in a double-potential well at high and zero temperature

Cited by 20 publications

References 43 publications

Environment-dependent dissipation in quantum Brownian motion

Environment-dependent dissipation in quantum Brownian motion

Particle in a box with a time-dependentδ-functionpotential

Real-time approach to tunnelling in open quantum systems: decoherence and anomalous diffusion

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