Tunnelling time and tunnelling dynamics

Maji, Kaushik; Mondal, Chandan Kumar; Bhattacharyya, S. P.

doi:10.1080/01442350701619689

Cited by 22 publications

(13 citation statements)

References 58 publications

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“…PACS numbers: 03.65.Xp, 32.80.Fb In 1932, MacColl [1] studied the time which may be associated with the process of a particle approaching from far away a potential barrier of a height larger than the particle's energy and eventually tunneling through the barrier. Many efforts have been directed toward defining [2][3][4] and measuring [5][6][7][8][9] tunneling times. A related open problem is the question of how long it takes to ionize by tunneling through a binding potential.…”

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confidence: 99%

Ionization Time and Exit Momentum in Strong-Field Tunnel Ionization

et al. 2016

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Tunnel ionization belongs to the fundamental processes of atomic physics. The so-called two-step model, which describes the ionization as instantaneous tunneling at the electric field maximum and classical motion afterwards with zero exit momentum, is commonly employed to describe tunnel ionization in adiabatic regimes. In this contribution, we show by solving numerically the time-dependent Schrödinger equation in one dimension and employing a virtual detector at the tunnel exit that there is a nonvanishing positive time delay between the electric field maximum and the instant of ionization. Moreover, we find a nonzero exit momentum in the direction of the electric field. To extract proper tunneling times from asymptotic momentum distributions of ionized electrons, it is essential to incorporate the electron's initial momentum in the direction of the external electric field.

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confidence: 99%

Ionization Time and Exit Momentum in Strong-Field Tunnel Ionization

et al. 2016

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“…DE(t)s can help us in understanding the energetics of the processes. The tunneling time has been calculated by computing the average slope of the plot of hx(t)i against time to obtain average velocity hvi and dividing the idealized barrier width l 0 by hvi [28][29][30].…”

Section: Methodsmentioning

confidence: 99%

Tunneling time in fluctuating symmetric double wells: Suppression and enhancement of tunneling by spatial symmetry-preserving perturbations

Kar

Bhattacharyya

2011

Chemical Physics

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Section: Introductionmentioning

confidence: 99%

“…There are many existing definitions of tunneling probability in dynamic systems . According to Majii et al tunneling probability is defined as the probability of finding the particle in the right well when it is initially located in the left well . In a communication of Garashchuk et al tunneling probability in a double well is calculated in a semiclassical way by calculating the under barrier transmission probability by taking the energy eigenstates of the double well potential assuming Boltzmann distribution .…”

Section: Introductionmentioning

confidence: 99%

The effect of stochastic barrier fluctuation on semiclassical transmission probability and Shannon entropy of a symmetric double well potential

Naskar

Talukder

Ghosh

2018

Int J of Quantum Chemistry

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Stochastic fluctuation of barrier height and width of a symmetric double well plays a very significant role in the corresponding dynamics by increasing the semiclassical transmission probability and Shannon entropy of the system. The population of the system has been observed to be spread into several under barrier states starting from the W L or W R [W L;R 5 1 ffiffi 2 p W 1 6W 2 ð Þ , where W 1 and W 2 are the wave functions describing the two lowest degenerate states] in presence of the stochastic fluctuation. This distribution over several states is manifested by steady increase in Shannon entropy. However, any arbitrary value of the stochastic fluctuation cannot increase the populations of the upper energy states and consequently no gain in the net value of Shannon entropy results. There is an optimum frequency for which the Shannon entropy passes through a maximum, which is also found out in this work. We have also calculated the semiclassical WKB like transmission probability as a function of time and it is clear that the random fluctuation of barrier causes the transmission probability to increase to a significant amount. As the total energy of the system remains below the potential barrier, this transmission probability is equivalent to tunneling probability. It has been clearly shown that if the fluctuation is made to be periodic (without changing the frequency and magnitude of the fluctuation) it cannot effect any significant change in the overall dynamics. K E Y W O R D S barrier fluctuation, Hellmann-Feynman energy, Shannon entropy, TDFGH, transmission probability 1 | I N T R O D U C T I O N Quantum mechanical tunneling through a symmetric double well is an well studied area both in context of theoretical and experimentalresearch. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] Quantum mechanical tunneling plays crucial roles in low energy reactions in condensed phase where the potential energy surface is represented by a symmetric or asymmetric double well. [21][22][23][24][25][26][27][28] The effect of interaction of the particle trapped in a bistable potential with the environment can be mimicked by fluctuating the barrier height and width. As the interaction with the environment is mainly aperiodic and stochastic, one can model the system potential as a symmetric double well whose barrier parameters are getting continuously perturbed by a nonperiodic Gaussian like perturbation. This acts as a very useful model in describing H-atom tunneling in a number of chemical and biological systems. [6,7] There are many chemical systems which involve reaction at the surface which can be seen as a particle tunneling through a potential energy surface. [21][22][23] The potential energy surface obviously depends on the interactions among surface atoms or molecules with the moving gas molecules which are getting absorbed. So the potential energy surface has an explicit time dependence and this effect can be dressed into the fluctuating barrier model. Also many isomerization and tautomeriz...

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Tunnelling time and tunnelling dynamics

Cited by 22 publications

References 58 publications

Ionization Time and Exit Momentum in Strong-Field Tunnel Ionization

Ionization Time and Exit Momentum in Strong-Field Tunnel Ionization

Tunneling time in fluctuating symmetric double wells: Suppression and enhancement of tunneling by spatial symmetry-preserving perturbations

The effect of stochastic barrier fluctuation on semiclassical transmission probability and Shannon entropy of a symmetric double well potential

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