The effect of dissipation on quantum transmission resonance

Konno, Kohkichi; Nishida, Munehiro; Tanda, Satoshi; Hatakenaka, Noriyuki

doi:10.1016/j.physleta.2007.04.055

Cited by 4 publications

(6 citation statements)

References 24 publications

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“…Thus, the probability for finding the particles in the given space interval [−1, 1] for a given time is suppressed by dissipation resulting into the reduction of the dwell time. By using a different method, such a behavior has already been reported in [32] where the mean transversal time through a rectangular barrier reduces with dissipation. When stochastic fluctuations are taken into account, the width of the probability distribution will have an additional contribution, Eq.…”

Section: Resultsmentioning

confidence: 73%

“…Dissipative tunnelling through a parabolic repeller has been studied via quantum Langevin equation [30], realized by resistively shunted Josephson junctions, and using the Caldirola-Kanai [31] and Kostin [10] approaches. On the other hand, very recently, investigation of dissipative tunnelling times through different approaches have attracted many researchers [32][33][34][35][36]. Transmission probabilities through tunnelling and above barrier as well as dwell times are then calculated at different bath temperatures.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic Bohmian mechanics within the Schrödinger-Langevin framework: A trajectory analysis of wave-packet dynamics in a fluctuative-dissipative medium

Mousavi

Miret‐Artés

2019

Eur. Phys. J. Plus

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A Bohmian analysis of the so-called Schrödinger-Langevin or Kostin nonlinear differential equation is provided to study how thermal fluctuations of the environment affects the dynamics of the wave packet from a quantum hydrodynamical point of view. In this way, after obtaining the Schrödinger-Langevin-Bohm equation from the Kostin equation its application to simple but physically insightful systems such as the Brownian-Bohmian motion, motion in a gravity field and transmission through a parabolic repeller is studied. If a time-dependent Gaussian ansatz for the probability density is assumed, the effect of thermal fluctuations together with thermal wave packets leads to Bohmian stochastic trajectories. From this trajectory based analysis, quantum and classical diffusion coefficients for free particles, thermal arrival times for a linear potential and transmission probabilities and characteristic times such as arrival and dwell times for a parabolic repeller are then presented and discussed. I. INTRODUCTIONIt seems that the first attempt for generalizing Chandrasekhar's phenomenological theory [1] of Brownian motion to the quantum realm was made by introducing a stochastic term in the Caldirola-Kanai framework [2]. It was shown that for the Boltzmann statistics, quantum stochastic dynamics lead to a diffusion constant which is the same as that obtained from the classical Brownian motion. The effect of noise on the Brownian motion of a quantum oscillator via the corresponding Caldirola-Kanai equation with a noise term was also studied [3].On the other hand, Kostin [4,5] derived heuristically the so-called non-linear Schrödinger-Langevin equation (SL) from the quantum Langevin equation through Heisenberg position and momentum operators. This equation fulfills the unitarity condition, satisfies the uncertainty relation but violates the superposition principle due to its non-linear nature [6]. Recently, a different generalized Schrödinger equation has been proposed to describe dissipation in quantum systems [7] where the Kostin equation without the random potential is a special case of this generalized equation. Thanks to its straightforward formulation and its numerical simplicity, the Kostin equation "can be considered as a solid candidate for effective description of open quantum systems hardly accessible to quantum master equations" [8]. Although this equation has been widely used in the literature to study pure dissipative effects [8][9][10][11], only a few works are found where the presence of a stochastic or random force is introduced [8]. A generalized Schrödinger-Langevin equation has been proposed in the literature for nonlinear interaction providing a state-dependent dissipation process exhibiting multiplicative noise [12]. Afterwards, this equation has been extended to a non-Markovian problem [13].Bohmian mechanics [14][15][16] as an alternative interpretation of quantum mechanics has the advantage to give a clear picture of quantum phenomena in terms of trajectories in configuration space. This theory has ...

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Section: Resultsmentioning

confidence: 73%

Section: Introductionmentioning

confidence: 99%

Stochastic Bohmian mechanics within the Schrödinger-Langevin framework: A trajectory analysis of wave-packet dynamics in a fluctuative-dissipative medium

Mousavi

Miret‐Artés

2019

Eur. Phys. J. Plus

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“…Using a somewhat similar approach for dissipation with the latter given by a frictional force as in [11], in the present work we shall show that the counter-intuitive result found in [20] can indeed be explained.…”

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confidence: 56%

“…In [18], studying the dissipative tunneling through an inverted harmonic oscillator in context with ion transport at nanoscale, the authors showed that the phase time delay can be estimated directly in terms of a frictional coefficient. The average dwell time, τ D , through a rectangular potential barrier using a path decomposition technique was investigated in [20] leading to the counter-intuitive result that τ D in the presence of dissipation becomes smaller than that in a non-dissipative case. The traversal time behaviour for a rectangular barrier with energy losses included was described in [21] within a semiclassical approach with dissipation included in the form of a frictional force.…”

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confidence: 99%

Time in dissipative tunneling: Subtleties and applications

2017

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Characteristic features of tunneling times for dissipative tunneling of a particle through a rectangular barrier are studied within a semiclassical model involving dissipation in the form of a velocity dependent frictional force. The average dwell time and traversal time with dissipation are found to be less than those without dissipation. This counter-intuitive behaviour is reversed if one evaluates the physically relevant transmission dwell time. Apart from these observations, we find that the percentage of energy lost by the tunneling particle is higher for smaller energies. The above observations are tested and confirmed in a realistic case by applying the dissipation model to study the current-voltage data in a Al/Al 2 O 3 /Al solid state junction at various temperatures.The friction coefficient for Al 2 O 3 as a function of temperature is presented. It is found to decrease with increasing temperature.

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“…In particular, dissipative tunnelling through a parabolic repeller has been studied via quantum Langevin equation [54], in resistively shunted Josephson junctions, and using the CK [55] and Kostin [47] approaches. Investigation of dissipative tunnelling times through different approaches have attracted many researchers [56][57][58][59][60]. Thus, Baskoutas and Jannussis [61] and Papadopoulos [55], Tokieda and Hagino [62] have considered similar theoretical frameworks.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Bohmian and Scaled Trajectories

Mousavi

Miret‐Artés

2022

Found Phys

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In this review we deal with open (dissipative and stochastic) quantum systems within the Bohmian mechanics framework which has the advantage to provide a clear picture of quantum phenomena in terms of trajectories, originally in configuration space. The gradual decoherence process is studied from linear and nonlinear Schrödinger equations through Bohmian trajectories as well as by using the so-called quantumclassical transition differential equation through scaled trajectories. This transition is governed by a continuous parameter, the transition parameter, covering these two extreme open dynamical regimes. Thus, two sources of decoherence of different nature are going to be considered. Several examples will be presented and discussed in order to illustrate the corresponding theory behind each case, namely: the so-called Brownian-Bohmian motion leading to quantum diffusion coefficients, dissipative diffraction in time, dissipative tunnelling for a parabolic barrier under the presence of an electric field and stochastic early arrivals for the same type of barrier. In order to simplify the notations and physical discussion, the theoretical developments will be carried out in one dimension throughout all this wok. One of the main goals is to analyze the gradual decoherence process existing in these open dynamical regimes in terms of trajectories, leading to a more intuitive way of understanding the underlying physics in order to gain new insights.

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The effect of dissipation on quantum transmission resonance

Cited by 4 publications

References 24 publications

Stochastic Bohmian mechanics within the Schrödinger-Langevin framework: A trajectory analysis of wave-packet dynamics in a fluctuative-dissipative medium

Stochastic Bohmian mechanics within the Schrödinger-Langevin framework: A trajectory analysis of wave-packet dynamics in a fluctuative-dissipative medium

Time in dissipative tunneling: Subtleties and applications

Stochastic Bohmian and Scaled Trajectories

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