994 research outputs found
Short-time critical dynamics of the three-dimensional systems with long-range correlated disorder
Monte Carlo simulations of the short-time dynamic behavior are reported for
three-dimensional Ising and XY models with long-range correlated disorder at
criticality, in the case corresponding to linear defects. The static and
dynamic critical exponents are determined for systems starting separately from
ordered and disordered initial states. The obtained values of the exponents are
in a good agreement with results of the field-theoretic description of the
critical behavior of these models in the two-loop approximation and with our
results of Monte Carlo simulations of three-dimensional Ising model in
equilibrium state.Comment: 24 RevTeX pages, 12 figure
Nonequilibrium work distribution of a quantum harmonic oscillator
We analytically calculate the work distribution of a quantum harmonic
oscillator with arbitrary time-dependent angular frequency. We provide detailed
expressions for the work probability density for adiabatic and nonadiabatic
processes, in the limit of low and high temperature. We further verify the
validity of the quantum Jarzynski equalityComment: 6 pages, 3 figure
Comments on dihedral and supersymmetric extensions of a family of Hamiltonians on a plane
For any odd , a connection is established between the dihedral and
supersymmetric extensions of the Tremblay-Turbiner-Winternitz Hamiltonians
on a plane. For this purpose, the elements of the dihedral group
are realized in terms of two independent pairs of fermionic creation and
annihilation operators and some interesting trigonometric identities are
demonstrated.Comment: 10 pages, no figure, acknowledgments added, references completed,
published versio
The influence of long-range correlated defects on critical ultrasound propagation in solids
The effect of long-range correlated quenched structural defects on the
critical ultrasound attenuation and sound velocity dispersion is studied for
three-dimensional Ising-like systems. A field-theoretical description of the
dynamic critical effects of ultrasound propagation in solids is performed with
allowance for both fluctuation and relaxation attenuation mechanisms. The
temperature and frequency dependences of the dynamical scaling functions of the
ultrasound critical characteristics are calculated in a two-loop approximation
for different values of the correlation parameter of the Weinrib-Halperin
model with long-range correlated defects. The asymptotic behavior of the
dynamical scaling functions in hydrodynamic and critical regions is separated.
The influence of long-range correlated disorder on the asymptotic behavior of
the critical ultrasonic anomalies is discussed.Comment: 12 RevTeX pages, 3 figure
Defining integrals over connections in the discretized gravitational functional integral
Integration over connection type variables in the path integral for the
discrete form of the first order formulation of general relativity theory is
studied. The result (a generalized function of the rest of variables of the
type of tetrad or elementary areas) can be defined through its moments, i. e.
integrals of it with the area tensor monomials. In our previous paper these
moments have been defined by deforming integration contours in the complex
plane as if we had passed to an Euclidean-like region. In the present paper we
define and evaluate the moments in the genuine Minkowsky region. The
distribution of interest resulting from these moments in this non-positively
defined region contains the divergences. We prove that the latter contribute
only to the singular (\dfun like) part of this distribution with support in the
non-physical region of the complex plane of area tensors while in the physical
region this distribution (usual function) confirms that defined in our previous
paper which decays exponentially at large areas. Besides that, we evaluate the
basic integrals over which the integral over connections in the general path
integral can be expanded.Comment: 18 page
Non-relativistic limit of multidimensional gravity: exact solutions and applications
It is found the exact solution of the Poisson equation for the
multidimensional space with topology . This
solution describes smooth transition from the newtonian behavior for
distances bigger than periods of tori (the extra dimension sizes) to
multidimensional behavior in opposite limit. In the case of
one extra dimension , the gravitational potential is expressed via compact
and elegant formula. These exact solutions are applied to some practical
problems to get the gravitational potentials for considered configurations.
Found potentials are used to calculate the acceleration for point masses and
gravitational self-energy.It is proposed models where the test masses are
smeared over some (or all) extra dimensions. In 10-dimensional spacetime with 3
smeared extra dimensions, it is shown that the size of 3 rest extra dimensions
can be enlarged up to submillimeter for the case of 1TeV fundamental Planck
scale . In the models where all extra dimensions are smeared, the
gravitational potential exactly coincides with the newtonian one regardless of
size of the extra dimensions. Nevertheless, the hierarchy problem can be solved
in these models.Comment: LaTex file, 18 pages, 4 figure
Critical behavior of disordered systems with replica symmetry breaking
A field-theoretic description of the critical behavior of weakly disordered
systems with a -component order parameter is given. For systems of an
arbitrary dimension in the range from three to four, a renormalization group
analysis of the effective replica Hamiltonian of the model with an interaction
potential without replica symmetry is given in the two-loop approximation. For
the case of the one-step replica symmetry breaking, fixed points of the
renormalization group equations are found using the Pade-Borel summing
technique. For every value , the threshold dimensions of the system that
separate the regions of different types of the critical behavior are found by
analyzing those fixed points. Specific features of the critical behavior
determined by the replica symmetry breaking are described. The results are
compared with those obtained by the -expansion and the scope of the
method applicability is determined.Comment: 18 pages, 2 figure
Relaxational dynamics in 3D randomly diluted Ising models
We study the purely relaxational dynamics (model A) at criticality in
three-dimensional disordered Ising systems whose static critical behaviour
belongs to the randomly diluted Ising universality class. We consider the
site-diluted and bond-diluted Ising models, and the +- J Ising model along the
paramagnetic-ferromagnetic transition line. We perform Monte Carlo simulations
at the critical point using the Metropolis algorithm and study the dynamic
behaviour in equilibrium at various values of the disorder parameter. The
results provide a robust evidence of the existence of a unique model-A dynamic
universality class which describes the relaxational critical dynamics in all
considered models. In particular, the analysis of the size-dependence of
suitably defined autocorrelation times at the critical point provides the
estimate z=2.35(2) for the universal dynamic critical exponent. We also study
the off-equilibrium relaxational dynamics following a quench from T=\infty to
T=T_c. In agreement with the field-theory scenario, the analysis of the
off-equilibrium dynamic critical behavior gives an estimate of z that is
perfectly consistent with the equilibrium estimate z=2.35(2).Comment: 38 page
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