Longest Relaxation Time of Relaxation Processes for Classical and Quantum Brownian Motion in a Potential: Escape Rate Theory Approach

Coffey, W. T.; Kalmykov, Yuri P.; Титов, С. В.; Dowling, William J.

doi:10.1002/9781118571767.ch3

Cited by 3 publications

(7 citation statements)

References 205 publications

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“…While the classical theory of the Brownian motion (based either on the Langevin equation or on its accompanying Fokker–Planck equation) is well-established and is still the subject of discussions, a rigorous derivation and corresponding analysis for quantum systems is lacking as the formulation of dissipation in quantum mechanics is more complicated than that of classical one. ,,− However, in many cases, a theory of dissipation based on the classical Brownian motion is often inadequate (and also inappropriate) especially at low temperatures because it ignores quantum effects. Quantum molecular dynamics with dissipation (relevant to many processes in chemistry, physics, and biology) is a long-standing theoretical challenge.…”

Section: Introductionmentioning

confidence: 99%

Quantum Stochastic Dynamics in the Presence of a Time-Periodic Rapidly Oscillating Potential: Nonadiabatic Escape Rate

Shit

Chattopadhyay

Chaudhuri³

2013

J. Phys. Chem. A

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Escape from a metastable state in the presence of a high-frequency field (where the driving becomes nonadiabatic) underlies a broad range of phenomena of physics and chemistry, and thus its understanding is of paramount importance. We study the problem of intermediate-to-high-damping escape from a metastable state of a dissipative system driven by a rapidly oscillating field, one of the most important classes of nonequilibrium systems, in a broad range of field driving frequencies (ω) and amplitudes (a). We construct a Langevin equation using quantum gauge transformation in the light of Floquet theorem and exploiting a systematic perturbative expansion in powers of 1/ω using "Kapitza-Landau time window". The quantum dynamics in a high-frequency field are found to be described by an effective time-independent potential. The temperature dependence of escape rate and the change of its form with varying parameters of the field have been analyzed. It may decrease upon increasing the temperature which is contingent on the effects of intricate interplay between external modulation and dissipation. The crossover temperature between tunnelling and thermal hopping increases with an increase in external modulation so that quantum effects in the escape are relevant at higher temperatures. These observations are uncommon and counterintuitive and, therefore, of considerable interest. Our results might be valuable for the exploration of the dynamics of cold atoms in electromagnetic fields.

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Section: Introductionmentioning

confidence: 99%

Quantum Stochastic Dynamics in the Presence of a Time-Periodic Rapidly Oscillating Potential: Nonadiabatic Escape Rate

Shit

Chattopadhyay

Chaudhuri³

2013

J. Phys. Chem. A

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“…In order to illustrate this it will be necessary to summarize the main features of the calculation of the Kramers VLD rate. In so doing the opportunity will be taken to briefly describe how the Kramers result may be extended to all values of the dissipation of the particle to its surrounding heat bath because in general the calculations (see [3]) are not readily accessible and crucially depend on the Kramers oscillation concept.…”

Section: Introductionmentioning

confidence: 99%

High-Frequency Resonance Absorption as Evidence for Oscillation in a Well Before Escape from a Metastable State in the Kramers Energy Controlled Diffusion Model

Coffey¹,

Kalmykov²,

Titov³

et al. 2012

NATO Science for Peace and Security Series B: Physics and Biophysics

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A variety of disparate physical systems which are modeled in terms of their relaxation behavior by the Brownian motion in a potential and its extensions to anomalous diffusion exhibit slow overbarrier relaxation accompanied by relatively fast relaxation due to exponential decays in the potential wells and high frequency resonance absorption due to small oscillations about the minima of the wells. It is argued that the high frequency resonant process provides abundant evidence for the Kramers concept of oscillations in a potential well of particles with energy equal to the separatrix energy before escape as both are simply limiting cases of the same family of librational dynamical processes in a well.

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“…Very frequently, a system far away from equilibrium does not relax to a thermodynamic equilibrium state with a BG distribution, but might asymptotically approach a stationary nonequilibrium state with power-law distribution. In this situation, the Maxwellian distribution (4) should be replaced by the power-law one (2). In nonextensive statistical mechanics, the power-law distribution (2) can be derived using the extremization of Tsallis entropy [5].…”

Section: The Power-law Collision Theorymentioning

confidence: 99%

“…There have been various reaction rate theories that have been developed to calculate reaction rate coefficients, among which the collision theory is an old and foundational one [1]. Other reaction rate theories, such as transition state theory, Kramers rate theory, and unimolecular rate theory, all borrow the idea from the collision theory [1][2][3]. More important, analysis of the collision phenomena plays a central role in almost all investigations of structures of matters on microscopic scale.…”

Section: Introductionmentioning

confidence: 99%

“…A lot of theoretical and experimental works have shown that power-law distributions are quite common in the physical, chemical, biological and technical processes taking place in complex systems (see [4] and the references therein). In a reacting system, particles escape over the barrier would result in a perturbation about the Maxwell-Boltzmann distribution in the well [2]. Here we can introduce the power-law distribution in nonextensive statistical mechanics [5].…”

Section: Introductionmentioning

confidence: 99%

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The collision theory reaction rate coefficient for power-law distributions

Yin

2014

Physica A: Statistical Mechanics and its Applications

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Abstract:The collision theory for power-law distributions and a generalized collision theory rate coefficient is studied when the reactions take place in nonequilibrium systems with power-law distributions. We obtain the power-law rate coefficient and by numerical analyses we show a very strong dependence of the rate coefficient on the power-law parameter. We find that the power-law collision theory can successfully overcome the two difficulties of Lindemann-Christiansen mechanism. We take three reactions as examples to calculate the pre-exponential factor and yield the values that can be exactly in agreement with those measured in the experimental studies.

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Longest Relaxation Time of Relaxation Processes for Classical and Quantum Brownian Motion in a Potential: Escape Rate Theory Approach

Cited by 3 publications

References 205 publications

Quantum Stochastic Dynamics in the Presence of a Time-Periodic Rapidly Oscillating Potential: Nonadiabatic Escape Rate

Quantum Stochastic Dynamics in the Presence of a Time-Periodic Rapidly Oscillating Potential: Nonadiabatic Escape Rate

High-Frequency Resonance Absorption as Evidence for Oscillation in a Well Before Escape from a Metastable State in the Kramers Energy Controlled Diffusion Model

The collision theory reaction rate coefficient for power-law distributions

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