Asymptotic dynamics of three-dimensional bipolar ultrashort electromagnetic pulses in an array of semiconductor carbon nanotubes.

We study the propagation of three-dimensional bipolar ultrashort electromagnetic pulses in an array of semiconductor carbon nanotubes at times much longer than the pulse duration, yet still shorter than the relaxation time in the system. The interaction of the electromagnetic field with the electronic subsystem of the medium is described by means of Maxwell's equations, taking into account the field inhomogeneity along the nanotube axis beyond the approximation of slowly varying amplitudes and phases. A model is proposed for the analysis of the dynamics of an electromagnetic pulse in the form of an effective equation for the vector potential of the field. Our numerical analysis demonstrates the possibility of a satisfactory description of the evolution of the pulse field at large times by means of a three-dimensional generalization of the sine-Gordon and double sine-Gordon equations.

Activation processes with memory.

We propose a mathematical treatment of the activated processes governed by stochastic Langevin dynamics with a colored random force, corresponding to a noise generated by an Ornstein-Uhlenbeck process. Such non-Markovian dynamics take place in a variety of chemical and biological systems. Using the path integral approach, we constructed the conditional probability for passing between two stationary states in configurational space. Our relations can be used for Monte Carlo sampling of evolution trajectories for systems with many degrees of freedom as well as for determining the reaction coordinate used in transition state theory. On the basis of our relation for a conditional probability, we generalize the method of determining the most probable path to the case of colored random force. Using the simple three-hole potential, we examine numerically the effect of nonzero correlation time (memory) on the evolution of the most probable path for a finite temperature.

Relaxation time hierarchy in a two-component quasiparticle gas.

A quasiparticle description of various condensed media is a very popular tool in the study of their transport and thermodynamic properties. I present here a microscopic theory for the description of diffusion processes in a two-component gas of quasiparticles with arbitrary dispersion law and statistics. In particular, I analyze the role of interaction within each subsystem (i.e., between identical quasiparticles) in relaxation of the whole system. The approach for solving such kinetic problems allows one to study the most important limiting cases and to clarify their physical sense. Classical results for diffusion coefficients of light particles in a massive gas (Lorentz model) and of massive particles in a light gas (Rayleigh model) are obtained directly from the general solution without using artificial approaches, as was done earlier. This provides a possibility to generalize these popular models on quasiparticle systems.