98 research outputs found
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
and dimensional parameter . All other parameters: the current and the
constituent quark masses, the quark condensate, mass of meson, mass of
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 and the asymptotic integrated
level density for Yang-Mills-Higgs Quantum Mechanics for two and three
dimensions (). Due to the infinite volume of the phase space
on energy shell for , it is not possible to disentangle completely the
coupled oscillators (-model) from the Higgs sector. The situation is
different for for which is finite. The transition from order
to chaos in these systems is expressed by the corresponding transitions in
and , 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 nonlinear vector model on Bethe lattice and show that it
exhibits a transition from ordered to disordered state for . If
the replica limit 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
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