arXiv subjects

Serge Shpyrko

Publications and source records attributed to Serge Shpyrko.

7 recordsLinked to original sources

arXiv2010

Quantum phase crossover and chaos in generalized Jahn-Teller lattice model

The generalized multispin Jahn-Teller model on a finite lattice or formally equivalent Dicke model extended to two long-wavelength coherent bosons of different frequencies is shown to exhibit a crossover between the polaron-modified "quasi-normal" and the squeezed "radiation" domains. We investigate effects of two kinds of interfering fluctuations on the phase crossover and on statistical characteristics of boson complex spectra: (i) Fluctuations in the electron subsystem- finite-size quantum fluctuations- are responsible for the dephasing of the coherence in the radiation domain and for the moderate occupation of the excited states in the normal domain. In the quasiclassical limit, radiation phase implies existence of a coherent acoustic super-radiant phase. (ii) Level-spacing fluctuations in excited boson level subsystem with strong level repulsions. Related probability distributions are shown to be non-universally spread between the limiting universal Wigner-Dyson and Poisson distributions. We proved that the difference in boson frequencies is responsible for reaching the most stochastic limit of the Wigner-Dyson distribution. Instanton lattice as a sequence of tunneling events in the most chaotic radiation domain exhibits maximal number of level-avoidings (repulsions). The non-universality of the distributions is caused by boson correlations which compete the level repulsions.

cond-mat.quant-gas↗

arXiv2007

Stochastic storage models and noise-induced phase transitions

The most frequently used in physical application diffusive (based on the Fokker-Planck equation) model leans upon the assumption of small jumps of a macroscopic variable for each given realization of the stochastic process. This imposes restrictions on the description of the phase transition problem where the system is to overcome some finite potential barrier, or systems with finite size where the fluctuations are comparable with the size of a system. We suggest a complementary stochastic description of physical systems based on the mathematical stochastic storage model with basic notions of random input and output into a system. It reproduces statistical distributions typical for noise-induced phase transitions (e.g. Verhulst model) for the simplest (up to linear) forms of the escape function. We consider a generalization of the stochastic model based on the series development of the kinetic potential. On the contrast to Gaussian processes in which the development in series over a small parameter characterizing the jump value is assumed [Stratonovich R.L., Nonlinear Nonequilibrium Thermodynamics, Springer Series in Synergetics, vol.59, Springer Verlag, 1994], we propose a series expansion directly suitable for storage models and introduce the kinetic potential generalizing them.

cond-mat.stat-mech↗

arXiv2006

Incipience of quantum chaos in the Jahn-Teller model

We studied complex spectra of a two-level electron system coupled to two phonon (vibron) modes represented by the E$\otimes$e Jahn-Teller model. For particular rotation quantum numbers we found a coexistence of up to three regions of the spectra, (i) the dimerized region of long-range ordered (extended) pairs of oscillating levels, (ii) the short-range-ordered (localized) "kink lattice" of avoiding levels, and (iii) the intermediate region of kink nucleation with variable range of ordering. This structure appears above a certain critical line as a function of interaction strength. The level clustering and level avoiding generic patterns reflect themselves in several intermittent regions between up to three branches of spectral entropies. Linear scaling behavior of the widths of level curvature probability distributions provides the conventionally adopted indication for the presence of quantum chaos. Level spacing probability distributions show peculiarities of the partial (for fixed quantum angular momentum) as well as of the cumulative (all angular momenta) case. The clustering of levels with two and three dominant spacings at fixed angular momenta causes notable deviations of the cumulative distributions from the Poissonian one.

cond-mat.other↗

arXiv2006

Quantum chaotic patterns in the E x (b_1+b_2) Jahn-Teller model

We study statistical properties of excited levels of the E x (b_1+b_2) Jahn-Teller model. The multitude of avoided crossings of energy levels is generally claimed to be a testimony of quantum chaos. We found that apart from two limiting cases (E x e and Holstein model) the distribution of nearest-neighbor spacings is rather stable as to the change of parameters and different from the Wigner one. This limiting distribution assumably shows scaling ~$\sqrt{S}$ at small S and resembles the semi-Poisson law P(S)= 4S \exp (-2 S) at S> 1. The latter is believed to be universal and characteristic, e.g., at the transition between metal and insulator phases.

cond-mat.other↗

arXiv2005

Reaction Enhanced Diffusion in Spherical Membranes

The reversible reactions like A+B <-> C in the many-component diffusive system affect the diffusive properties of the constituents. The effective conjugation of irreversible processes of different dimensionality takes place due to the stationarity in the system and can lead to essential increase of the resulting diffusive fluxes. The exact equations for the spatial concentration profiles of the components are difficult to treat analytically. We solve approximately the equations for the concentration profiles of the reaction-diffusion components in the spherical geometry in the application to the problem of the enhanced oxygen transfer through a biological membrane and to the mathematically similar problem of surface diffusion in a solid body. In the latter case the spherical geometry can be an adequate tool for describing the surface of a real solid body which can be modeled as a fractal object formed of sequences of spherical surfaces with different radii.

cond-mat.other↗

arXiv1999

Kinks in the discrete sine-Gordon model with Kac-Baker long-range interactions

We study effects of Kac-Baker long-range dispersive interaction (LRI) between particles on kink properties in the discrete sine-Gordon model. We show that the kink width increases indefinitely as the range of LRI grows only in the case of strong interparticle coupling. On the contrary, the kink becomes intrinsically localized if the coupling is under some critical value. Correspondingly, the Peierls-Nabarro barrier vanishes as the range of LRI increases for supercritical values of the coupling but remains finite for subcritical values. We demonstrate that LRI essentially transforms the internal dynamics of the kinks, specifically creating their internal localized and quasilocalized modes. We also show that moving kinks radiate plane waves due to break of the Lorentz invariance by LRI.

cond-mat.soft↗

arXiv1999

Interplay of disorder and nonlinearity in Klein-Gordon models: Immobile kinks

We consider Klein-Gordon models with a $δ$-correlated spatial disorder. We show that the properties of immobile kinks exhibit strong dependence on the assumptions as to their statistical distribution over the minima of the effective random potential. Namely, there exists a crossover from monotonically increasing (when a kink occupies the deepest potential well) to the non-monotonic (at equiprobable distribution of kinks over the potential minima) dependence of the average kink width as a function of the disorder intensity. We show also that the same crossover may take place with changing size of the system.

cond-mat.dis-nn↗