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

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

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

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

Critical Behaviour of 3D Systems with Long-Range Correlated Quenched Defects

A field-theoretic description of the critical behaviour of systems with quenched defects obeying a power law correlations $\sim |{\bf x}|^{-a}$ for large separations ${\bf x}$ is given. Directly for three-dimensional systems and different values of correlation parameter $2\leq a \leq 3$ a renormalization analysis of scaling function in the two-loop approximation is carried out, and the fixed points corresponding to stability of the various types of critical behaviour are identified. The obtained results essentially differ from results evaluated by double $\epsilon, \delta$ - expansion. The critical exponents in the two-loop approximation are calculated with the use of the Pade-Borel summation technique.Comment: Submitted to J. Phys. A, Letter to Editor 9 pages, 4 figure