On the quantum langevin equation

The quantum Langevin equation is the Heisenberg equation of motion for the (operator) coordinate of a Brownian particle coupled to a heat bath. We give an elementary derivation of this equation for a simple coupled-oscillator model of the heat bath.Deceased.     

Analytical solution of a multidimensional Langevin equation at high friction limits and probability passing over a two-dimensional saddle

The analytical solution of a multidimensional Langevin equation at the overdamping limit is obtained and the probability of particles passing over a two-dimensional saddle point is discussed. These results may break a path for studying further the fusion in superheavy elements synthesis.     

The complex langevin equation and Monte Carlo simulations of actions with static charges

We explore the possibilities of using the complex Langevin equation to Monte Carlo generate configurations of gauge theories with static charges present in the action. Successful results are obtained for systems that possess nontrivial saddle-point (classical) solutions. For that reason the algorithm works impressively for two-dimensional U(1) in the entire β-range whereas for three- and four-dimensional U(1) the applicability is limited to the weak coupling regime (large β). The method fails completely for SU(2) and SU(3).     

Analytical solution of a multidimensional Langevin equation at high friction limits and probability passing over a two-dimensional saddle

The analytical solution of a multidimensional Langevin equation at the overdamping limit is obtained and the probability of particles passing over a two-dimensional saddle point is discussed. These results may break a path for studying further the fusion in superheavy elements synthesis.     

Nonstationarity induced by long-time noise correlations in the langevin equation

We solve the generalized Langevin equation driven by a stochastic force with a power-law autocorrelation function. A stationary Markov process has been applied as a model of the noise. However, the resulting velocity variance does not stabilize but diminishes with time. It is shown that algebraic distributions can induce such effects. Results are compared to those obtained with a deterministic random force. Consequences for the diffusion process are also discussed.     

Stochastic derivation of the chiral anomaly based on the generalized langevin equation

A generalized Langevin equation for fermion field is first derived within the framework of the stochastic quantization. Based on it, the chiral anomaly is derived directly from the stationary property of the pseudoscalar density. This approach is convenient to observe the quantum origin of anomalies. The conservation law of the vector current is also derived in a similar way.     

Master equation with two times: Diffusion in external field

The master equation for diffusion involving two times applies to the problem of diffusion in a time-dependent (in general inhomogeneous) external field. We consider the case of the quasi Fokker-Planck approximation, when the probability transition function for diffusion (PTD-function) does not possess a long tail in coordinate space and can be expanded as the function of instantaneous displacements. For relatively weak external field the linear expansion of the PTD function leads to a simple generalization of diffusion equation, containing the retardation factors.     

Diffusion described with quantum Langevin equation in tilted periodic potential

In this paper, diffusion behavior of Brownian particles moving in a 1D periodic potential landscape has been theoretically investigated by using the general quantum Langevin equation. At first, in the condition of weak disorder, some anomalous diffusive behaviors have been revealed in the process. Then, two types of mean square displacement, ensemble averaged and time averaged mean square displacement, have been investigated in a long time, and the weak ergodicity breaking phenomenon has been revealed. It is shown that the general quantum Langevin equation can exhibit some novel details of the experimental diffusion process.     

Diffusion of particles over strongly anisotropic surface with traps

We investigate surface diffusion in a system of particles adsorbed on a two-dimensional strongly anisotropic lattice. There are two kinds of the lattice sites - ordinary sites and deep traps. Particles adsorbed in the ordinary sites can migrate over the surface, but particles adsorbed in traps are immobile. These particles do not move over the surface and they obstacle also the mobile particles migration (surface defects). Using kinetic Monte Carlo simulations we obtained coverage dependencies of the tracer, jump, and chemical diffusion coefficients. The coefficients are rather sensitive to the defect concentration. Even small admixture of the defects decreases drastically the fast diffusion. The effect is rather specific: strong dependence of the pre-exponential factor on the defect concentration and almost independent activation energy. The defect influence on the slow diffusion is weak. It results in strong decreasing of the surface diffusion anisotropy with the defect concentration. Such unusual behavior of the diffusion coefficients was observed in many experimental investigations of the surface diffusion of lithium, cesium, potassium, and strontium over strongly anisotropic W(1 1 2) and Mo(1 1 2) planes. It was shown that this specific behavior arises exclusively due to the surface anisotropy, and does not depend on the lateral interaction between the particles.     

Invariant power law distribution of langevin systems with colored multiplicative noise

The random multiplicative process is studied for the case of a colored multiplicative noise with exponentially decreasing autocorrelation function. We observe the power law exponent of probability distribution in a statistically steady state numerically to clarify the effect of finite correlation time. The renormalization procedure is applied to derive the power law exponent theoretically. The power law exponent is inversely proportional to the autocorrelation time of the multiplicative noise.     

Combining a langevin description of heavy-ion induced fission including neutron evaporation with the statistical model

A model is developed which combines dynamical (Langevin-) calculations with the Kramers modified statistical model in order to describe heavy-ion induced fission including neutron evaporation. In the example of the¹⁹F+¹⁸¹Ta collision, the energy dependence of fission probabilities, neutron multiplicities and (H.I.,xn)-cross sections is calculated and a fair agreement with the data is achieved with a reduced friction parameter ofβ=3^*10²¹sec^?1. We pay particular attention to the angular momentum dependence of the fusion-fission process.     

Diffusion approximations of the two dimensional master equation

The effects of rotational energy transfer on unimolecular dissociation are assessed using a two-dimensional master equation approach. The collision operator for such a system can be very large, and approximations are sought that reduce the size of the matrix that has to be stored. The density of states of the vibrational energy is large for most molecules and can be treated as virtually continuous. As a consequence, motion in vibrational energy space can be treated using a diffusion equation approach. This reduces the storage requirements greatly and increases the speed at which diagonalization occurs. Results are presented for the dissociation of ethane and methane.     

Orientational and fluctuation polarizations of langevin dipoles in a random electric field

The polarization and dielectric susceptibility of polar regions composed of Langevin microdipoles in a random electric field are considered. It is shown that the polarization of this system has orientational and fluctuation components in addition to the conventional phonon contribution. Both components diverge when the amplitude of the random field tends to zero but can be stabilized in finite internal fields. The orientational susceptibility does not depend on the external field if its amplitude is smaller than the amplitude of the random field and rapidly decreases in the opposite case. The field dependence of the fluctuation susceptibility exhibits a maximum. With an increase in the field, the fluctuation susceptibility quadratically increases as const + AE² in weak fields and decreases as E^?1/2 in strong fields. The equation of state takes the form P² ～ E in relatively strong fields (as compared to the internal field) and P ～ E in weak fields.     

Diffusion of particles over triangular inhomogeneous lattice with two non-equivalent sites

We investigate the diffusion of particles adsorbed on a triangular lattice with deep and shallow sites. It is shown that the character of the particle migration depends substantially on the relative jump rates from the deep and shallow sites. The site inhomogeneity imposes specific correlation betweeen successive jumps: particles perform pairs of slow and fast jumps. General analytical expressions have been derived for the chemical and jump diffusion coefficients. We have calculated coverage dependencies of the diffusion coefficients and some thermodynamic quantities for different lateral interactions between the particles. The analytical data have been compared with the numerical data obtained by kinetic Monte Carlo simulations. The agreement between the results obtained by these quite different approaches is found to be very satisfactory.     

Rotation of magnetization in unison and langevin equations for a large spin

A single-domain ferromagnetic particle is represented as a large spin (model of rotation in unison) whose stochastic dynamics is derived from a spin-boson Hamiltonian. It is shown in the Markovian limit that thermal equilibrium exists provided that the fluctuation-dissipation theorem is supplemented by a symmetry constraint which for bilinear anisotropic and nonlinear (magnetoelastic) spin-bath coupling can only be satisfied in the underdamped limit. Only for bilinear isotropic coupling (Gilbert's theory) is it satisfied identically for arbitrary damping strength. Uniaxial and cubic symmetries are considered. For a model uniaxial crystal the thermal decay rate of M and the thermal enhancement of the macroscopic quantum tunneling rate are calculated for Gilbert and magnetoelastic dissipative couplings and compared. The effects of memory are discussed.     

Diffusion of tin over clean silicon surfaces

Diffusion of tin over the (111), (100), and (110) silicon surfaces has been studied by Auger electron spectroscopy and low-energy electron diffraction. The diffusion mechanisms have been established, and the temperature dependences of the diffusion coefficients have been obtained.     

Coronal holes with a saddle structure as deduced from Yohkoh observations

Saddle structures are seen in some images of the Sun in the soft X-rays obtained by Yohkoh mission. At the center of any such structure, there is a small coronal hole having the outlines of an astroid or a cross. The coronal saddles occur in magnetic configurations with a high degree of symmetry (quadrupoles). Comparison with the models shows that open field lines cannot be modeled using only the source surface.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 10, pp. 1275–1279, October, 1996.This work was supported in part by the Russian Foundation for Fundamental Research under Grant No. 93-02-15112.