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

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

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

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

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

Vacuum polarization in a cosmic string spacetime induced by flat boundary

In this paper we analyze the vacuum expectation values of the field squared and the energy-momentum tensor associated to a massive scalar field in a higher dimensional cosmic string spacetime, obeying Dirichlet or Neumann boundary conditions on the surface orthogonal to the string.Comment: 12 pages, 5 figures, talk presented at the 8th Alexander Friedmann International Seminar on Gravitation and Cosmology, in Rio de Janeiro, Brazi

Spectral signatures of magnetic Bloch oscillations in one-dimensional easy-axis ferromagnets

Domain walls in a one-dimensional gapped easy-axis ferromagnet can exhibit Bloch oscillations in an applied magnetic field. We investigate how exchange couplings modify this behavior within an approximation based on noninteracting domain-wall bound states. In particular, we obtain analytical results for the spectrum and the dynamic structure factor, and show where in momentum space to expect equidistant energy levels, the Wannier-Zeeman ladder, which is the spectral signature of magnetic Bloch oscillations. We compare our results to previous calculations employing a single domain-wall approximation, and make predictions relevant for the material $CoCl2\cdot2H2O$.Comment: 12 pages, 14 figure