arXiv subjects

A. O. Bolivar

Publications and source records attributed to A. O. Bolivar.

9 recordsLinked to original sources

arXiv2017

Anomalous Brownian motion via linear Fokker-Planck equations

According to a traditional point of view Boltzmann entropy is intimately related to linear Fokker-Planck equations (Smoluchowski, Klein-Kramers, and Rayleigh equations) that describe a well-known nonequilibrium phenomenon: (normal) Brownian motion of a particle immersed in a thermal bath. Nevertheless, current researches have claimed that non-Boltzmann entropies (Tsallis and Renyi entropies, for instance) may give rise to anomalous Brownian motion through nonlinear Fokker-Planck equations. The novelty of the present article is to show that anomalous diffusion could be investigated within the framework of non-Markovian linear Fokker-Planck equations. So on the ground of this non-Markovian approach to Brownian motion, we find out anomalous diffusion characterized by the mean square displacement of a free particle and a harmonic oscillator in absence of inertial force as well as the mean square momentum of a free particle in presence of inertial force.

physics.gen-ph↗

arXiv2015

Non-Markovian quantum Brownian motion: a non-Hamiltonian approach

We generalize the classical theory of Brownian motion so as to reckon with non-Markovian effects on both Klein-Kramers and Smoluchowski equations. For a free particle and a harmonic oscillator, it is shown that such non-Markovian effects account for the differentiability of the Brownian trajectories as well as the breakdown of the energy equipartition of statistical mechanics at short times in some physical situations. This non-Markovian approach is also extended to look at anomalous diffusion. Next, we bring in the dynamical-quantization method for investigating open quantum systems, which does consist in quantizing the classical Brownian motion starting directly from our non-Markovian Klein-Kramers and Smoluchowski equations, without alluding to any model Hamiltonian. Accordingly, quantizing our non-Markovian Klein-Kramers in phase space gives rise to a non-Markovian quantum master equation in configuration space, whereas quantizing our non-Markovian Smoluchowski equation in configuration space leads to a non-Markovian quantum Smoluchowski equation in phase space. In addition, it is worth noticing that non-Markovian quantum Brownian motion takes place in presence of a generic environment (e.g. a non-thermal quantum fluid). As far as the special case of a heat bath comprising of quantum harmonic oscillators is concerned, a non-Markovian Caldeira-Leggett master equation and a thermal quantum Smoluchowski equation are derived and extended to bosonic and fermionic heat baths valid for all temperatures.

quant-ph↗

arXiv2010

The dynamical-quantization approach to open quantum systems

On the basis of the dynamical-quantization approach to open quantum systems, we can derive a non-Markovian Caldeira-Leggett quantum master equation as well as a non-Markovian quantum Smoluchowski equation in phase space. On the one hand, we solve our Caldeira-Leggett equation for the case of a quantum Brownian particle in a gravitational field. On the other hand, we solve our quantum Smoluchowski equation for a harmonic oscillator. In both physical situations we come up with the existence of a non-equilibrium thermal quantum force. Further, as a physical application of our quantum Smoluchowski equation we take up the phenomenon of escape rate of a non-inertial Brownian particle over a potential barrier. Key-words: Quantum Brownian motion; Non-Markovian effects; Caldeira-Leggett quantum master equation; Quantum Smoluchowski equation; Quantum tunneling

cond-mat.stat-mech↗

arXiv2010

Non-Markovian Caldeira--Leggett quantum master equation

We obtain a non-Markovian quantum master equation directly from the quantization of a non-Markovian Fokker-Planck equation describing the Brownian motion of a particle immersed in a generic environment (e.g. a non-thermal fluid). As far as the especial case of a heat bath comprising of quantum harmonic oscillators is concerned, we derive a non-Markovian Caldeira-Leggett master equation on the basis of which we work out the concept of non-equilibrium quantum thermal force exerted by the harmonic heat bath upon the Brownian motion of free particle. The classical limit (or dequantization process) of this sort of non-equilibrium quantum effect is scrutinized, as well.

cond-mat.stat-mech↗

arXiv2010

Time-dependent attractive thermal quantum force upon a Brownian free particle in the large friction regime

We quantize the Brownian motion undergone by a free particle in the absence of inertial force (the so-called large friction regime) as described by the diffusion equation early found out by Einstein in 1905. Accordingly, we are able to come up with a time-dependent attractive quantum force F(t) that acts upon the Brownian free particle as a result of quantum-mechanical thermal fluctuations of a heat bath consisting of a set of quantum harmonic oscillators having the same oscillation frequency /omega in thermodynamic equilibrium at temperature T. More specifically, at zero temperature we predict that the zero-point force is given by F^((T=0)) (t)=-[ω/(1+2\omegat)^(3/2)] \sqrt(γ/2), where γis the friction constant with dimensions of mass per time and /eta the Planck constant divided by 2π. For evolution times t~1/ω, ω~0^14 Hz, /gamma~10^(-10) kg/s, and /eta~10^(-34) m^2 kg/s, we find out F^((T=0)) ~10^(-8) N, which exhibits the same magnitude order as the Casimir electromagnetic quantum force, for instance. Thus, we reckon that novel quantum effects arising from our concept of time-dependent thermal quantum force F(t) may be borne out by some experimental set-up in nanotechnology.

cond-mat.stat-mech↗

arXiv2010

Dynamical quantization of the non-Markovian Smoluchowski equation and the quantum tunneling phenomenon

Based on the dynamical quantization method we derive a quantum phase-space non-Markovian Smoluchowski equation describing the non-inertial Brownian motion of a harmonic oscillator immersed in a generic environment. In the long-time regime we investigate the tunneling phenomenon by evaluating the quantum Kramers escape rate of a Brownian particle over a potential barrier. As far as a quantum thermal reservoir is concerned, it is found that our steady quantum Kramers rate may depend upon no friction constant in the strong friction domain. This preposterous feature may suggest the existence of non-dissipative quantum tunneling at the low-temperature range, including the zero temperature case. Lastly, we predict that our quantum escape rate non-exponentially decays on the edge of the breakdown of the dissipation-fluctuation relation.

cond-mat.stat-mech↗

arXiv2010

Non-Markovian Effects on the Brownian Motion of a Free Particle

Non-Markovian effects upon the Brownian movement of a free particle in the presence as well as in the absence of inertial force are investigated within the framework of Fokker-Planck equations (Rayleigh and Smoluchowski equations). More specifically, it is predicted that non-Markovian features can enhance the values of the mean square displacement and momentum, thereby assuring the mathematical property of differentiability of the these physically observable quantities.

cond-mat.stat-mech↗

arXiv2007

Quantization of the Smoluchowski equation and the problem of quantum tunneling at zero temperature

In this article we address the problem of quantum tunneling of a non-Markovian Brownian particle away from thermal equilibrium. We calculate the Kramers escape rate at low temperature (including the zero temperature case) in the Smoluchowski limit (strong friction regime). Our main findings are: (i) our quantum escape rate is valid far from the thermal equilibrium and is non-Markovian, but it becomes Markovian as the correlation time vanishes; (ii) at thermodynamic equilibrium we obtain a non-Markovian quantum rate that predicts a superfluidity phenomenon in the Markovian limit at low and zero temperatures.

nlin.CD↗

arXiv2007

Generalization of the classical Kramers rate for non-Markovian open systems out of equilibrium

We analyze the behavior of a Brownian particle moving in a double-well potential. The escape probability of this particle over the potential barrier from a metastable state toward another state is known as the Kramers problem. In this work we generalize Kramers' rate theory to the case of an environment always out of thermodynamic equilibrium reckoning with non-Markovian effects.

nlin.CD↗