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International Journal of Quantum Chemistry

Effects of thermal modulation on tunneling through a fluctuating barrier in presence of bichromatic electromagnetic field

Aparna Saha, Pranab Sarkar

Published Jan 1, 2005• 1 citation
Publisher

Abstract

Abstract The effects of thermal modulation on the tunneling dynamics of a particle moving in a bistable potential with a fluctuating barrier in the presence of bichromatic electromagnetic field are examined. This study brings to light various interesting features. While rate constant increases steadily with increasing fluctuation strength, a stochastic resonance‐like behavior is exhibited when tunneling rate is plotted as a function of barrier fluctuation frequency. The tunneling rate constant decreases with the increase in the differences of the strength of the two electric fields; on the other hand, it displays a maxima when plotted as a function of the ratio of the frequencies of the two fields. When the rate constant is plotted as a function of temperature, it increases and eventually settles down to a saturation value. We have also studied the effect of the phase difference between the two electric fields on the tunneling behavior in the presence of thermal modulation. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

DOI
10.1002/qua.20516

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Abstract The effects of thermal modulation on the tunneling dynamics of a particle moving in a bistable potential with a fluctuating barrier in the presence of bichromatic electromagnetic field are examined. This study brings to light various interesting features. While rate constant increases steadily with increasing fluctuation strength, a stochastic resonance‐like behavior is exhibited when tunneling rate is plotted as a function of barrier fluctuation frequency. The tunneling rate constant decreases with the increase in the differences of the strength of the two electric fields; on the other hand, it displays a maxima when plotted as a function of the ratio of the frequencies of the two fields. When the rate constant is plotted as a function of temperature, it increases and eventually settles down to a saturation value. We have also studied the effect of the phase difference between the two electric fields on the tunneling behavior in the presence of thermal modulation. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
Abstract The tunneling dynamics of a particle moving in a bistable potential with fluctuating barrier is studied. For barriers fluctuating randomly in time we show by exact numerical calculation the significant effect of barrier fluctuation on the tunneling behavior of the particle. At nonzero temperatures the computed tunneling rate constant passes through a maximum when plotted against fluctuation frequency. The resonant frequency (at which the maximum appears) slowly decreases with increase in temperature and attains a constant value at higher temperature and it increases linearly with increase in barrier height of the potential. Another important observation is that in presence of barrier fluctuation the dependence of tunneling rate constant on temperature is strongly guided by the barrier fluctuation frequency. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 280–285, 2003
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We make a brief review of the Kramers escape rate theory for the probabilistic motion of a particle in a potential well U(x), and under the influence of classical fluctuation forces. The Kramers theory is extended in order to take into account the action of the thermal and zero-point random electromagnetic fields on a charged particle. The result is physically relevant because we get a non null escape rate over the potential barrier at low temperatures (T -> 0). It is found that, even if the mean energy is much smaller than the barrier height, the classical particle can escape from the potential well due to the action of the zero-point fluctuating fields. These stochastic effects can be used to give a classical interpretation to some quantum tunneling phenomena. Relevant experimental data are used to illustrate the theoretical results.
Abstract 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 or [ , where and 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.
Usually one finds that dissipation tends to make a quantum system more classical in nature. In this paper we study the effect of momentum dissipation on a quantum system. The momentum of the particle is coupled bilinearly to the momenta of a harmonic oscillator heat bath. For a harmonic oscillator system we find that the position and momentum variances for momentum coupling are respectively identical to momentum and position variances for spatial friction. This implies that momentum coupling leads to an increase in the fluctuations in position as the temperature is lowered, exactly the opposite of the classical like localization of the oscillator, found with spatial friction. For a parabolic barrier, momentum coupling causes an {\it increase} in the unstable normal mode barrier frequency, as compared to the lowering of the barrier frequency in the presence of purely spatial coupling. This increase in the frequency leads to an enhancement of the thermal tunneling flux, which below the crossover temperature becomes exponentially large. The crossover temperature between tunneling and thermal activation {\it increases} with momentum friction so that quantum effects in the escape are relevant at higher temperatures.
We generalize the phenomenon of forced stochastic synchronization into the quantum domain within the framework of a paradigmatic spin‐boson model (tunneling charge, or flipping spin 1/2 coupled to an environment) which is driven by an external periodic rectangular field. The overdamped regime of dissipative quantum tunneling is studied. Thermal noise assisted synchronization of a very high quality is shown to occur in a broad range of temperatures, driving strengths and frequencies, if the external driving frequency exceeds the zero‐temperature limit of dissipative tunneling rate, the dissipation strength exceeds a critical value, and the driving is sufficiently strong. A simple criterion for such stochastic synchronization is established. Both the similarities and the profound differences with the akin phenomenon of quantum stochastic resonance are outlined.