Effect of structural defects on anomalous ultrasound propagation in solids during second-order phase transitions

The effect of structural defects on the critical ultrasound attenuation and ultrasound velocity dispersion in Ising-like three-dimensional systems is studied. A field-theoretical description of the dynamic effects of acoustic-wave propagation in solids during phase transitions is performed with allowance for both fluctuation and relaxation attenuation mechanisms. The temperature and frequency dependences of the scaling functions of the attenuation coefficient and the ultrasound velocity dispersion are calculated in a two-loop approximation for pure and structurally disordered systems, and their asymptotic behavior in hydrodynamic and critical regions is separated. As compared to a pure system, the presence of structural defects in it is shown to cause a stronger increase in the sound attenuation coefficient and the sound velocity dispersion even in the hydrodynamic region as the critical temperature is reached. As compared to pure analogs, structurally disordered systems should exhibit stronger temperature and frequency dependences of the acoustic characteristics in the critical region.Comment: 7 RevTeX pages, 4 figure

A probabilistic approach to some results by Nieto and Truax

In this paper, we reconsider some results by Nieto and Truax about generating functions for arbitrary order coherent and squeezed states. These results were obtained using the exponential of the Laplacian operator; more elaborated operational identities were used by Dattoli et al. \cite{Dattoli} to extend these results. In this note, we show that the operational approach can be replaced by a purely probabilistic approach, in the sense that the exponential of derivatives operators can be identified with equivalent expectation operators. This approach brings new insight about the kinks between operational and probabilistic calculus.Comment: 2nd versio

Spontaneous generation of the Nambu --Jona-Lazinio interaction in quantum chromodynamics with two light quarks

In QCD with two light quarks with application of Bogolubov quasi-averages approach a possibility of spontaneous generation of an effective interaction, leading to the Nambu -- Jona-Lazinio model, is studied. Compensation equations for form-factor of the interaction is shown to have the non-trivial solution leading to theory with two parameters: average low-energy value of $\alpha_s$ and dimensional parameter $f_\pi$. All other parameters: the current and the constituent quark masses, the quark condensate, mass of $\pi$ meson, mass of $\sigma$ meson and its width are expressed in terms of the two initial parameters in satisfactory correspondence to experimental phenomenology. The results being obtained allow to state an applicability of the approach in the low-energy hadron physics and promising possibilities of its applications to other problems.Comment: 16 pages, 1 table, 3 figure

Polymers in long-range-correlated disorder

We study the scaling properties of polymers in a d-dimensional medium with quenched defects that have power law correlations ~r^{-a} for large separations r. This type of disorder is known to be relevant for magnetic phase transitions. We find strong evidence that this is true also for the polymer case. Applying the field-theoretical renormalization group approach we perform calculations both in a double expansion in epsilon=4-d and delta=4-a up to the 1-loop order and secondly in a fixed dimension (d=3) approach up to the 2-loop approximation for different fixed values of the correlation parameter, 2=<a=<3. In the latter case the numerical results need appropriate resummation. We find that the asymptotic behavior of self-avoiding walks in three dimensions and long-range-correlated disorder is governed by a set of separate exponents. In particular, we give estimates for the 'nu' and 'gamma' exponents as well as for the correction-to-scaling exponent 'omega'. The latter exponent is also calculated for the general m-vector model with m=1,2,3.Comment: 13 pages, 5 figure

Obliquely propagating electromagnetic waves in magnetized kappa plasmas

Velocity distribution functions (VDFs) that exhibit a power-law dependence on the high-energy tail have been the subject of intense research by the plasma physics community. Such functions, known as kappa or superthermal distributions, have been found to provide a better fitting to the VDFs measured by spacecraft in the solar wind. One of the problems that is being addressed on this new light is the temperature anisotropy of solar wind protons and electrons. In the literature, the general treatment for waves excited by (bi-)Maxwellian plasmas is well-established. However, for kappa distributions, the wave characteristics have been studied mostly for the limiting cases of purely parallel or perpendicular propagation, relative to the ambient magnetic field. Contributions to the general case of obliquely-propagating electromagnetic waves have been scarcely reported so far. The absence of a general treatment prevents a complete analysis of the wave-particle interaction in kappa plasmas, since some instabilities can operate simultaneously both in the parallel and oblique directions. In a recent work, Gaelzer and Ziebell [J. Geophys. Res. 119, 9334 (2014)] obtained expressions for the dielectric tensor and dispersion relations for the low-frequency, quasi-perpendicular dispersive Alfv\'en waves resulting from a kappa VDF. In the present work, the formalism introduced by Ref. 1 is generalized for the general case of electrostatic and/or electromagnetic waves propagating in a kappa plasma in any frequency range and for arbitrary angles. An isotropic distribution is considered, but the methods used here can be easily applied to more general anisotropic distributions, such as the bi-kappa or product-bi-kappa.Comment: Accepted for publication in Physics of Plasmas; added references for section

The Partition Function and Level Density for Yang-Mills-Higgs Quantum Mechanics

We calculate the partition function $Z(t)$ and the asymptotic integrated level density $N(E)$ for Yang-Mills-Higgs Quantum Mechanics for two and three dimensions ($n = 2, 3$). Due to the infinite volume of the phase space $\Gamma$ on energy shell for $n= 2$, it is not possible to disentangle completely the coupled oscillators ($x^2 y^2$-model) from the Higgs sector. The situation is different for $n = 3$ for which $\Gamma$ is finite. The transition from order to chaos in these systems is expressed by the corresponding transitions in $Z(t)$ and $N(E)$, analogous to the transitions in adjacent level spacing distribution from Poisson distribution to Wigner-Dyson distribution. We also discuss a related system with quartic coupled oscillators and two dimensional quartic free oscillators for which, contrary to YMHQM, both coupling constants are dimensionless.Comment: 10 pages, LaTeX; minor changes; version accepted for publication as a Letter in J. Phys.

Monte Carlo Simulation of a Random-Field Ising Antiferromagnet

Phase transitions in the three-dimensional diluted Ising antiferromagnet in an applied magnetic field are analyzed numerically. It is found that random magnetic field in a system with spin concentration below a certain threshold induces a crossover from second-order phase transition to first-order transition to a new phase characterized by a spin-glass ground state and metastable energy states at finite temperatures.Comment: 10 pages, 11 figure

Universal Parametric Correlations of Eigenvalues of Random Matrix Ensemble

Eigenvalue correlations of random matrix ensembles as a function of an external perturbation are investigated vis the Dyson Brownian Motion Model in the situation where the level density has a hard edge singularity. By solving a linearized hydrodynamical equation, a universal dependence of the density-density correlator on the external field is found. As an application we obtain a formula for the variance of linear statistics with the parametric dependence exhibited as a Laplace transform.Comment: 23 pages, late

Phase Transition in a Model with Non-Compact Symmetry on Bethe Lattice and the Replica Limit

We solve $O(n,1)$ nonlinear vector model on Bethe lattice and show that it exhibits a transition from ordered to disordered state for $0 \leq n < 1$. If the replica limit $n\to 0$ is taken carefully, the model is shown to reduce to the corresponding supersymmetric model. The latter was introduced by Zirnbauer as a toy model for the Anderson localization transition. We argue thus that the non-compact replica models describe correctly the Anderson transition features. This should be contrasted to their failure in the case of the level correlation problem.Comment: 21 pages, REVTEX, 2 Postscript figures, uses epsf styl

On vacuum-vacuum amplitude and Bogoliubov coefficients

Even if the electromagnetic field does not create pairs, virtual pairs lead to the appearance of a phase in vacuum-vacuum amplitude. This makes it necessary to distinguish the in- and out-solutions even when it is commonly assumed that there is only one complete set of solutions as, for example, in the case of a constant magnetic field. Then in- and out-solutions differ only by a phase factor which is in essence the Bogoliubov coefficient. The propagator in terms of in- and out-states takes the same form as the one for pair creating fields. The transition amplitude for an electron to go from an initial in-state to out-state is equal to unity (in diagonal representation). This is in agreement with Pauli principal: if in the field there is an electron with given (conserved) set of quantum numbers, virtual pair cannot appear in this state. So even the phase of transition amplitude remains unaffected by the field. We show how one may redefine the phases of Bogoliubov coefficients in order to express the vacuum-vacuum amplitude through them.Comment: 20pages, no figures, some typos corrected, minor improvement