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PubMed2000

Reaction-controlled diffusion

The dynamics of a coupled two-component nonequilibrium system is examined by means of continuum field theory representing the corresponding master equation. Particles of species A may perform hopping processes only when particles of different type B are present in their environment. Species B is subject to diffusion-limited reactions. If the density of B particles attains a finite asymptotic value (active state), the A species displays normal diffusion. On the other hand, if the B density decays algebraically approximately t(-alpha) at long times (inactive state), the effective attractive A-B interaction is weakened. The combination of B decay and activated A hopping processes gives rise to anomalous diffusion, with mean-square displacement (A)(t)(2)> approximately t(1-alpha) for alpha<1. Such algebraic subdiffusive behavior ensues for nth-order B annihilation reactions (nB-->) with n>/=3, and n=2 for d<2. The mean-square displacement of the A particles grows only logarithmically with time in the case of B pair annihilation (n=2) and d>/=2 dimensions. For radioactive B decay (n=1), the A particles remain localized. If the A particles may hop spontaneously as well, or if additional random forces are present, the A-B coupling becomes irrelevant, and conventional diffusion is recovered in the long-time limit.

Journal Article↗
PubMed2000

Path-integral formulation of stochastic processes for exclusive particle systems

We present a systematic formalism to derive a path-integral formulation for hard-core particle systems far from equilibrium. Writing the master equation for a stochastic process of the system in terms of the annihilation and creation operators with mixed commutation relations, we find the Kramers-Moyal coefficients for the corresponding Fokker-Planck equation (FPE), and the stochastic differential equation (SDE) is derived by connecting these coefficients in the FPE to those in the SDE. Finally, the SDE is mapped onto field theory using the path integral, giving the field-theoretic action, which may be analyzed by the renormalization group method. We apply this formalism to a two-species reaction-diffusion system with drift, finding a universal decay exponent for the long-time behavior of the average concentration of particles in arbitrary dimension.

Journal Article↗
PubMed2000

Analytic results for scaling function and moments for a different type of avalanche in the bak-sneppen evolution model

Starting from the master equation for the hierarchical structure of avalanches of a different kind within the frame of the Bak-Sneppen evolution model, we derive the exact formula of the scaling function describing the probability distribution of avalanches. The scaling function displays features required by the scaling ansatz and verified by simulations. Using the scaling function we investigate the avalanche moment, denoted by (Delta&fmacr;). It is found that for any non-negative integer k, (Delta&fmacr;) diverges as Delta&fmacr;(-k), which gives an infinite group of exact critical exponents. Simulation outcomes of avalanche moments with k=1,2,3, are found to be consistent with the corresponding analytical results.

Journal Article↗
PubMed2000

Mean-field stochastic theory for species-rich assembled communities.

A dynamical model of an ecological community is analyzed within a "mean-field approximation" in which one of the species interacts with the combination of all of the other species in the community. Within this approximation the model may be formulated as a master equation describing a one-step stochastic process. The stationary distribution is obtained in closed form, and is shown to reduce to a log-series or log-normal distribution, depending on the values that the parameters describing the model take on. A hyperbolic relationship between the connectance of the matrix of interspecies interactions and the average number of species exists for a range of parameter values. The time evolution of the model at short and intermediate times is analyzed using van Kampen's approximation, which is valid when the number of individuals in the community is large. Good agreement with numerical simulations is found. The large time behavior, and the approach to the stationary state, is obtained by solving the equation for the generating function of the probability distribution. The analytical results which follow from the analysis are also in good agreement with direct simulations of the model.

Biophysical Phenomena↗
PubMed2000

Driven electron transfer in an environment with slow and fast degrees of freedom.

Driven electron transfer in a polar medium with slow and fast degrees of freedom is studied in the framework of a spin-boson Hamiltonian. Evolution dynamics is rigorously found when omega(s)(c)/(Gamma(a))sqrt[E(rs)/kT]<<1, where omega(s)(c) is the Debye cutoff frequency in the spectral function for the slow modes, E(rs) is the reorganization energy of slow degrees of freedom, and Gamma(-1)(a) is the reaction time dependent on the laser intensity parameter a=muE(0)/Planck's over 2piomega. Here omega and E0 are the frequency and the amplitude of a cw electric field, and mu is the electron dipole moment difference between the initial and final states. The master equation is derived for an arbitrary driving force affecting both the transition matrix element and the potential energy. For a cw electric field, the time dependent probability of staying at the product state, P1(t), is shown to be strongly dependent on the field intensity parameter a: P1(a,t) approximately (Gamma(m(1),m(2))t)(-E(rf)/E(rs)) or P1(a,t) approximately (Gamma(m(0))t)(-E(rf)/E(rs)), double or single resonances, respectively. Here E(rf) is the reorganization energy of fast degrees of freedom, Gamma(m(1),m(2)) approximately J(2)(m(1))(a)+J(2)(m(2))(a), and Gamma(m(0)) approximately J(2)(m(0))(a), where J(a) is a Bessel function. By changing the parameter a, one is able to manipulate the rate and direction of the reaction. When J(2)(m(0))(a) is close to zero the reaction is slow. Hence, slow modes turn out to be fast. This changes the character of the evolution dynamics from non- to mono- exponential decay, respectively. For the double resonance, the equilibrium constant is studied with the field intensity. It is shown that the reaction is almost insensitive to temperature. However, it strongly depends on the reaction heat, which provides a condition for the resonance.

Journal Article↗
PubMed2001

Nonlocal thermodynamic equilibrium self-consistent average-atom model for plasma physics.

A time-dependent collisional-radiative average-atom model is presented to study statistical properties of highly charged ion plasmas in off-equilibrium conditions. The time evolution of electron populations and the electron covariance matrix is obtained as approximate solutions of a master equation. Atomic structure is described either with a screened-hydrogenic model including l splitting, or by calculating one-electron states in a self-consistent average-atom potential. Collisional and radiative excitation/deexcitation and ionization/recombination rates, as well as autoionization and dielectronic recombination rates, are formulated within the average-configuration framework. Local thermodynamic equilibrium is obtained as a specific steady-state solution. The influence of atomic structure and the role of autoionization and dielectronic recombination processes are studied by calculating steady-state average ionization and ionization variance of hot plasmas with or without radiation field.

Journal Article↗
PubMed2001

Nonequilibrium steady-state circulation and heat dissipation functional.

A nonequilibrium steady-state (NESS), different from an equilibrium, is sustained by circular balance rather than detailed balance. The circular fluxes are driven by energy input and heat dissipation, accompanied by a positive entropy production. Based on a Master equation formalism for NESS, we show the circulation is intimately related to the recently studied Gallavotti-Cohen symmetry of heat dissipation functional, which in turn suggests a Boltzmann's formulalike relation between rate constants and energy in NESS. Expanding this unifying view on NESS to diffusion is discussed.

Journal Article↗
PubMed2001

Dynamical aspects of an adiabatic piston.

Dynamical aspects of an adiabatic piston are investigated, based on the mass ratio expansion of the master equation for the piston velocity distribution function. Simple theory for piston motion and relaxation of an ideal gas in a cylinder turns out to reproduce our numerical experiments quantitatively.

Journal Article↗
PubMed2001

Dynamics of the spin-boson Hamiltonian by the projection operator technique: applications to electron transfer reactions.

A perturbative treatment developed by using the projection operator technique is provided to find dynamics of the spin-boson Hamiltonian in the second order approximation of the subsystem-bath interaction. In the framework of the generalized master equations and in the Markovian approximation it leads to the Redfield/Bloch-type equations. The treatment can be applied to both fast and slow bath cases; in this paper we consider the fast bath case. The relaxation times, energy splitting, and bath-induced renormalization effect of the coherence frequency are discussed and applied to a Lorentzian-Ohmic fast bath. A good agreement between our results and those obtained by the path-integral formalism is obtained. The treatment is applied to electron transfer reactions to test the possibility of apparition of the electronic coherence in certain photosynthetic reaction centers.

Journal Article↗
PubMed2001

Quantum effects after decoherence in a quenched phase transition.

We study a quantum mechanical toy model that mimics some features of a quenched phase transition. Both by virtue of a time-dependent Hamiltonian or by changing the temperature of the bath we are able to show that even after classicalization has been reached, the system may display quantum behavior again. We explain this behavior in terms of simple nonlinear analysis and estimate relevant time scales that match the results of numerical simulations of the master equation. This opens new possibilities both in the study of quantum effects in nonequilibrium phase transitions and in general time-dependent problems where quantum effects may be relevant even after decoherence has been completed.

Journal Article↗
PubMed2002

Exactly solved dynamics for an infinite-range spin system. II. Antiferromagnetic interactions.

In a previous paper [E. Milotti, Phys. Rev. E 63, 026116 (2001)]. I have shown how to derive both thermodynamical and dynamical properties of an infinite-range Ising spin system with binary ferromagnetic interactions from the master equation for magnetization obtained from a simple spin dynamics. The same method can be adapted to different spin interactions: here I discuss the case of antiferromagnetic interactions. This model permits a study of the static properties of the antiferromagnetic lattice, and it displays very clearly the differences between the antiferromagnetic and the ferromagnetic case with long-range interactions. The dynamical behavior of the antiferromagnetic system is simpler, and the magnetization always relaxes exponentially.

Journal Article↗
PubMed2002

Constant bond breakup probability model for reversible aggregation processes.

Reversible aggregation processes were simulated for systems of freely diffusing sticky particles. Reversibility was introduced by allowing that all bonds in the system may break with a given probability per time interval. In order to describe the kinetics of such aggregation-fragmentation processes, a fragmentation kernel was developed and then used together with the Brownian aggregation kernel for solving the corresponding kinetic master equation. The deduced fragmentation kernel considers a single characteristic lifetime for all bonds and accounts for the cluster morphology by averaging over all possible configurations for clusters of a given size. It became evident that the simulated cluster-size distributions could be described only when an additional fragmentation effectiveness was considered. Doing so, the stochastic solutions were in good agreement with the simulated data.

Journal Article↗
PubMed2002

Reply to "comment on 'Monte Carlo simulations for a Lotka-type model with reactant surface diffusion and interactions' ".

We reply to the Comment by Zhdanov [preceding paper, Phys. Rev. E 65, blacksquare, square, filled (2002)] on our recent paper [G. Zvejnieks and V. N. Kuzovkov, Phys. Rev. E 63, 051104 (2001)]. We demonstrate that our quite different viewpoints result, in fact, entirely from nonunique definitions of the master equation, which has nothing to do with neglecting important physical principles, as Zhdanov claims.

Journal Article↗
PubMed2002

Quantum refrigeration cycles using spin-1/2 systems as the working substance.

The cycle model of a quantum refrigerator composed of two isothermal and two isomagnetic field processes is established. The working substance in the cycle consists of many noninteracting spin-1/2 systems. The performance of the cycle is investigated, based on the quantum master equation and semigroup approach. The general expressions of several important performance parameters, such as the coefficient of performance, cooling rate, and power input, are given. Especially, the case at high temperatures is analyzed in detail. The results obtained are further generalized and discussed, so that they may be directly used to describe the performance of the quantum refrigerator using spin-J systems as the working substance. Finally, the optimum characteristics of the quantum Carnot refrigerator are derived simply.

Journal Article↗
PubMed2002

Separation quality of a geometric ratchet.

We consider an experimentally relevant model of a geometric ratchet in which particles undergo drift and diffusive motion in a two-dimensional periodic array of obstacles, and which is used for the continuous separation of particles subject to different forces. The macroscopic drift velocity and diffusion tensor are calculated by a Monte Carlo simulation and by a master-equation approach, using the corresponding microscopic quantities and the shape of the obstacles as input. We define a measure of separation quality and investigate its dependence on the applied force and the shape of the obstacles.

Journal Article↗
PubMed2002

Classical kinetical Bose gas.

An autocatalytic reaction combined with spontaneous creation and annihilation processes of particles are studied in a quantum formalism of the master equation in a lattice gas representation with unrestricted occupancy. In case the system is activated by a linear coupling to a heat bath the problem can be solved exactly and the stationary particle density follows the Bose distribution. The relation to spin-flip processes with a restricted occupancy is discussed. Different from those processes the relaxation time and the density fluctuation increase in the high-temperature limit. On a small scale the mutual interaction between the particles is relevant. While in case of a repulsive interaction the stationary solution becomes unstable against short wavelength fluctuations, an attractive interaction leads to an instability for long wavelength fluctuations. The system decays in domains, the size of which can be estimated as a function of temperature and interaction strength. The model is also appropriate to study the growth of open bacterial colonies under the influence of a competitive interaction between the species.

Journal Article↗
PubMed2002

Density matrix negativity for two oscillators in an Agarwal bath.

A system of two harmonic oscillators is placed in an Agarwal bath. The resulting quantum master equations are studied with the help of quantum characteristic functions. The density matrix positivity is investigated in view of the recent interest in searching for a sound quantum dissipation theory. An analytical criterion is derived for density matrix negativity for two uncoupled oscillators. It is found that, for an initial two-oscillator squeezed state with a real squeezing parameter s, density matrix negativity occurs for two uncoupled oscillators at temperatures lower than Planck's over 2 pi omega/(k(B) ln coth/s/) with omega the oscillator frequency and k(B) the Boltzmann factor. As a by-product an analytical expression is also obtained for determining the quantum separability of two uncoupled oscillators. The effects of interoscillator coupling on density matrix negativity are discussed.

Journal Article↗
PubMed2002

Stepwise structure of Lyapunov spectra for many-particle systems using a random matrix dynamics.

The structure of the Lyapunov spectra for the many-particle systems with a random interaction between the particles is discussed. The dynamics of the tangent space is expressed as a master equation, which leads to a formula that connects the positive Lyapunov exponents and the time correlations of the particle interaction matrix. Applying this formula to one- and two-dimensional models we investigate the stepwise structure of the Lyapunov spectra that appear in the region of small positive Lyapunov exponents. Long range interactions lead to a clear separation of the Lyapunov spectra into a part exhibiting stepwise structure and a part changing smoothly. The part of the Lyapunov spectrum containing the stepwise structure is clearly distinguished by a wave-like structure in the eigenstates of the particle interaction matrix. The two-dimensional model has the same step widths as found numerically in a deterministic chaotic system of many hard disks.

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