Effect of external fluctuations on the Fréedericksz transition in an analogue simulator

The influence of multiplicative external fluctuations (noise) on the phenomenological equation describing the Fréedericksz transition has been studied by means of an electronic analogue simulator. Measurements were made of the stationary probability density for a wide range of fluctuation intensities and correlation times, for both dichotomous and Gaussianly distributed noise. For dichotomous forcing, the resultant phase diagrams at particular values of the field intensity parameter were found to be in satisfactory agreement with exact theoretical predictions by Horsthemkeet al. In the (physically more realistic) case of Gaussian fluctuations, for which no theory is currently available, the results obtained were distinctively different. A physically motivated discussion is given to account for the interesting differences and similarities of behavior found for the two types of external noise.     

Analog simulation of a simple system with state-dependent diffusion

We have constructed an electronic simulator of a simple bistable system driven by noise, whose intensity is determined by the instantaneous value of the coordinate. We observe that the most probable state of the system can be reversed by altering the noise intensity only in the neighborhood of the barrier, an effect pointed out by Landauer many years ago in the context of discussions on entropy-related stability criteria for nonequilibrium systems. We compare detailed measurements on the system with the recent white noise calculations of Landauer and van Kampen. The system also has interesting possibilities for tests of contemporary colored noise theory which we illustrate with an example.     

Critical Analyses of Order Parameter and Phase Transitions at High Density in Gross-Neveu Model

By critical analyses of the order parameter of symmetry breaking, we have researched the phase transitionsat high density in D = 2 and D = 3 Gross-Neveu (GN) model and shown that the gap equation obeyed by the dynamicalfermion mass has the same effectivenesss as the effective potentials for such analyses of all the second order and somespecial first order phase transitions. In the meantime we also further ironed out a theoretical divergence and proventhat in D = 3 GN model a first order phase transition does occur in the case of zero temperature and finite chemicalpotential.     

Critical Analyses of Order Parameter and Phase Transitions at High Density in Gross－Neveu Model

By critical analyses of the order parameter of symmetry breaking, we have researched the phase transitions at high density in D = 2 and D = 3 Gross-Neveu (GN) model and shown that the gap equation obeyed by the dynamical fermion mass has the same effectivenesss as the effective potentials for such analyses of all the second order and some specJal first order phase transitions. In the meantime we also further ironed out a theoretical divergence and proven that in D = 3 GN model a first order phase transition does occur in the case of zero temperature and finite chemical potential.     

Problems of the electronic structure of nonmetals in a wide energy region of fundamental absorption (review)

The article surveys the main unsolved problems of the electronic structure of nonmetals in a wide energy region of fundamental absorption. Udmurtia State University, 71, Krasnogeroiskaya Str., Izhevsk, 426034, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 3, pp. 299–315, May–June, 1999.