Formation of the internal structure of solids under severe action

On the example of a particular problem, the theory of vacancies, a new form of kinetic equations symmetrically incorporation the internal and free energies has been derived. The dynamical nature of irreversible phenomena at formation and motion of defects (dislocations) has been analyzed by a computer experiment. The obtained particular results are extended into a thermodynamic identity involving the law of conservation of energy at interaction with an environment (the 1st law of thermodynamics) and the law of energy transformation into internal degree of freedom (relaxation). The identity is compared with the analogous Jarzynski identity. The approach is illustrated by simulation of processes during severe plastic deformation, the Rybin kinetic equation for this case has been derived.Comment: 9 pages, 5 figure

Synchrotron radiography and x-ray topography studies of hexagonal habitus SiC bulk crystals

Phase-sensitive synchrotron radiation (SR) radiography was combined with x-ray diffraction topography to study structural defects of SiC crystals. The particular bulk SiC crystals examined had a low micropipe density and a hexagonal habitus composed of prismatic, pyramidal, and basal faces well developed. X-ray diffraction topography images of the sliced (0001) wafers, which were formed due to the complex lattice distortions associated with defective boundaries, demonstrated the existence of two-dimensional defective boundaries in the radial direction, normal to the (0001) planes. In particular, those parallel to the 〈1120〉 directions extended rather far from the seed. On the other hand, by phase-sensitive SR radiography the effect of micropipe collection was detected. Micropipes grouped mostly in the vicinities of the defective boundaries but rarely appeared between groups. Some general remarks about possible reasons for the development of such peculiar defect structures were mad

Diagonalization of an Integrable Discretization of the Repulsive Delta Bose Gas on the Circle

We introduce an integrable lattice discretization of the quantum system of n bosonic particles on a ring interacting pairwise via repulsive delta potentials. The corresponding (finite-dimensional) spectral problem of the integrable lattice model is solved by means of the Bethe Ansatz method. The resulting eigenfunctions turn out to be given by specializations of the Hall-Littlewood polynomials. In the continuum limit the solution of the repulsive delta Bose gas due to Lieb and Liniger is recovered, including the orthogonality of the Bethe wave functions first proved by Dorlas (extending previous work of C.N. Yang and C.P. Yang).Comment: 25 pages, LaTe

Ordering of Energy Levels in Heisenberg Models and Applications

In a recent paper we conjectured that for ferromagnetic Heisenberg models the smallest eigenvalues in the invariant subspaces of fixed total spin are monotone decreasing as a function of the total spin and called this property ferromagnetic ordering of energy levels (FOEL). We have proved this conjecture for the Heisenberg model with arbitrary spins and coupling constants on a chain. In this paper we give a pedagogical introduction to this result and also discuss some extensions and implications. The latter include the property that the relaxation time of symmetric simple exclusion processes on a graph for which FOEL can be proved, equals the relaxation time of a random walk on the same graph. This equality of relaxation times is known as Aldous' Conjecture.Comment: 20 pages, contribution for the proceedings of QMATH9, Giens, September 200

Tunable Lyapunov exponent in inverse magnetic billiards

The stability properties of the classical trajectories of charged particles are investigated in a two dimensional stadium-shaped inverse magnetic domain, where the magnetic field is zero inside the stadium domain and constant outside. In the case of infinite magnetic field the dynamics of the system is the same as in the Bunimovich billiard, i.e., ergodic and mixing. However, for weaker magnetic fields the phase space becomes mixed and the chaotic part gradually shrinks. The numerical measurements of the Lyapunov exponent (performed with a novel method) and the integrable/chaotic phase space volume ratio show that both quantities can be smoothly tuned by varying the external magnetic field. A possible experimental realization of the arrangement is also discussed.Comment: 4 pages, 6 figure

Level spacing distribution of pseudointegrable billiard

In this paper, we examine the level spacing distribution $P(S)$ of the rectangular billiard with a single point-like scatterer, which is known as pseudointegrable. It is shown that the observed $P(S)$ is a new type, which is quite different from the previous conclusion. Even in the strong coupling limit, the Poisson-like behavior rather than Wigner-like is seen for $S>1$, although the level repulsion still remains in the small $S$ region. The difference from the previous works is analyzed in detail.Comment: 11 pages, REVTeX file, 3 PostScript Figure

Semiclassical approach to discrete symmetries in quantum chaos

We use semiclassical methods to evaluate the spectral two-point correlation function of quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these systems can be divided into subspectra that are associated to irreducible representations of the corresponding symmetry group. We show that for (spinless) time reversal invariant systems the statistics inside these subspectra depend on the type of irreducible representation. For real representations the spectral statistics agree with those of the Gaussian Orthogonal Ensemble (GOE) of Random Matrix Theory (RMT), whereas complex representations correspond to the Gaussian Unitary Ensemble (GUE). For systems without time reversal invariance all subspectra show GUE statistics. There are no correlations between non-degenerate subspectra. Our techniques generalize recent developments in the semiclassical approach to quantum chaos allowing one to obtain full agreement with the two-point correlation function predicted by RMT, including oscillatory contributions.Comment: 26 pages, 8 Figure

Level statistics and eigenfunctions of pseudointegrable systems: dependence on energy and genus number

We study the level statistics (second half moment $I_0$ and rigidity $\Delta_3$) and the eigenfunctions of pseudointegrable systems with rough boundaries of different genus numbers $g$. We find that the levels form energy intervals with a characteristic behavior of the level statistics and the eigenfunctions in each interval. At low enough energies, the boundary roughness is not resolved and accordingly, the eigenfunctions are quite regular functions and the level statistics shows Poisson-like behavior. At higher energies, the level statistics of most systems moves from Poisson-like towards Wigner-like behavior with increasing $g$. Investigating the wavefunctions, we find many chaotic functions that can be described as a random superposition of regular wavefunctions. The amplitude distribution $P(\psi)$ of these chaotic functions was found to be Gaussian with the typical value of the localization volume $V_{\rm{loc}}\approx 0.33$. For systems with periodic boundaries we find several additional energy regimes, where $I_0$ is relatively close to the Poisson-limit. In these regimes, the eigenfunctions are either regular or localized functions, where $P(\psi)$ is close to the distribution of a sine or cosine function in the first case and strongly peaked in the second case. Also an interesting intermediate case between chaotic and localized eigenfunctions appears

Synchrotron radiography and x-ray topography studies of hexagonal habitus SiC bulk crystals

Phase-sensitive synchrotron radiation (SR) radiography was combined with x-ray diffraction topography to study structural defects of SiC crystals. The particular bulk SiC crystals examined had a low micropipe density and a hexagonal habitus composed of prismatic, pyramidal, and basal faces well developed. X-ray diffraction topography images of the sliced (0001) wafers, which were formed due to the complex lattice distortions associated with defective boundaries, demonstrated the existence of two-dimensional defective boundaries in the radial direction, normal to the (0001) planes. In particular, those parallel to the directions extended rather far from the seed. On the other hand, by phase-sensitive SR radiography the effect of micropipe collection was detected. Micropipes grouped mostly in the vicinities of the defective boundaries but rarely appeared between groups. Some general remarks about possible reasons for the development of such peculiar defect structures were made

Inhibition of rhythmic neural spiking by noise: the occurrence of a minimum in activity with increasing noise

The effects of noise on neuronal dynamical systems are of much current interest. Here, we investigate noise-induced changes in the rhythmic firing activity of single Hodgkin–Huxley neurons. With additive input current, there is, in the absence of noise, a critical mean value µ = µc above which sustained periodic firing occurs. With initial conditions as resting values, for a range of values of the mean µ near the critical value, we have found that the firing rate is greatly reduced by noise, even of quite small amplitudes. Furthermore, the firing rate may undergo a pronounced minimum as the noise increases. This behavior has the opposite character to stochastic resonance and coherence resonance. We found that these phenomena occurred even when the initial conditions were chosen randomly or when the noise was switched on at a random time, indicating the robustness of the results. We also examined the effects of conductance-based noise on Hodgkin–Huxley neurons and obtained similar results, leading to the conclusion that the phenomena occur across a wide range of neuronal dynamical systems. Further, these phenomena will occur in diverse applications where a stable limit cycle coexists with a stable focus