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 $k$, a connection is established between the dihedral and supersymmetric extensions of the Tremblay-Turbiner-Winternitz Hamiltonians $H_k$ on a plane. For this purpose, the elements of the dihedral group $D_{2k}$ 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 $a$ 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 $M_{3+d}=\mathbb{R}^3\times T^d$. This solution describes smooth transition from the newtonian behavior $1/r_3$ for distances bigger than periods of tori (the extra dimension sizes) to multidimensional behavior $1/r^{1+d}_{3+d}$ in opposite limit. In the case of one extra dimension $d=1$, 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 $M_{Pl(10)}$. 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 $p$-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 $p$, 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 $\epsilon$-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