Nonclassicality of photon-added squeezed vacuum and its decoherence in thermal environment

We study the nonclassicality of photon-added squeezed vacuum (PASV) and its decoherence in thermal environment in terms of the sub-Poissonian statistics and the negativity of Wigner function (WF). By converting the PASV to a squeezed Hermite polynomial excitation state, we derive a compact expression for the normalization factor of m-PASV, which is an m-order Legendre polynomial of squeezing parameter r. We also derive the explicit expression of WF of m-PASV and find the negative region of WF in phase space. We show that there is an upper bound value of r for this state to exhibit sub-Poissonian statistics increasing as m increases. Then we derive the explicit analytical expression of time evolution of WF of m-PASV in the thermal channel and discuss the loss of nonclassicality using the negativity of WF. The threshold value of decay time is presented for the single PASV.Comment: 14 pages and 7 figure

Statistical correlations of an anyon liquid at low temperatures

Using a proposed generalization of the pair distribution function for a gas of non-interacting particles obeying fractional exclusion statistics in arbitrary dimensionality, we derive the statistical correlations in the asymptotic limit of vanishing or low temperature. While Friedel-like oscillations are present in nearly all non-bosonic cases at T=0, they are characterized by exponential damping at low temperature. We discuss the dependence of these features on dimensionality and on the value of the statistical parameter alpha.Comment: to appear in Phys. Chem. Liquid

Water entry of a body which moves in more than six degrees of freedom

The water entry of a three-dimensional smooth body into initially calm water is examined. The body can move freely in its 6 d.f. and may also change its shape over time. During the early stage of penetration, the shape of the body is approximated by a surface of double curvature and the radii of curvature may vary over time. Hydrodynamic loads are calculated by the Wagner theory. It is shown that the water entry problem with arbitrary kinematics of the body motion, can be reduced to the vertical entry problem with a modified vertical displacement of the body and an elliptic region of contact between the liquid and the body surface. Low pressure occurrence is determined; this occurrence can precede the appearance of cavitation effects. Hydrodynamic forces are analysed for a rigid ellipsoid entering the water with 3 d.f. Experimental results with an oblique impact of elliptic paraboloid confirm the theoretical findings. The theoretical developments are detailed in this paper, while an application of the model is described in electronic supplementary materials

Scheme to measure squeezing and phase properties of a harmonic oscillator

We propose a simple scheme to measure squeezing and phase properties of a harmonic oscillator. We treat in particular the case of a the field, but the scheme may be easily realized in ion traps. It is based on integral transforms of measured atomic properties as atoms exit a cavity. We show that by measuring atomic polarizations it is possible, after a given integration, to measure several properties of the field.Comment: Presented at XI Central European Workshop on Quantum Optics, Trieste, Italy, 18-20 July, 200

Logarithmic interaction under periodic boundary conditions: Closed form formulas for energy and forces

A method is given to obtain closed form formulas for the energy and forces for an aggregate of charges interacting via a logarithmic interaction under periodic boundary conditions. The work done here is a generalization of Glasser's results [M. L. Glasser, J. Math. Phys. 15, 188 (1974)] and is obtained with a different and simpler method than that by Stremler [M. A. Stremler, J. Math. Phys. 45, 3584 (2004)]. The simplicity of the formulas derived here makes them extremely convenient in a computer simulation

Class of invariants for the 2D time-dependent Landau problem and harmonic oscillator in a magnetic field

We consider an isotropic two dimensional harmonic oscillator with arbitrarily time-dependent mass $M(t)$ and frequency $\Omega(t)$ in an arbitrarily time-dependent magnetic field $B(t)$. We determine two commuting invariant observables (in the sense of Lewis and Riesenfeld) $L,I$ in terms of some solution of an auxiliary ordinary differential equation and an orthonormal basis of the Hilbert space consisting of joint eigenvectors $\phi_\lambda$ of $L,I$. We then determine time-dependent phases $\alpha_\lambda(t)$ such that the $\psi_\lambda(t)=e^{i\alpha_\lambda}\phi_\lambda$ are solutions of the time-dependent Schr\"odinger equation and make up an orthonormal basis of the Hilbert space. These results apply, in particular to a two dimensional Landau problem with time-dependent $M,B$, which is obtained from the above just by setting $\Omega(t) \equiv 0$. By a mere redefinition of the parameters, these results can be applied also to the analogous models on the canonical non-commutative plane.Comment: 13 pages, 3 references adde

Polarizations and differential calculus in affine spaces

Within the framework of mappings between affine spaces, the notion of $n$-th polarization of a function will lead to an intrinsic characterization of polynomial functions. We prove that the characteristic features of derivations, such as linearity, iterability, Leibniz and chain rules, are shared -- at the finite level -- by the polarization operators. We give these results by means of explicit general formulae, which are valid at any order $n$, and are based on combinatorial identities. The infinitesimal limits of the $n$-th polarizations of a function will yield its $n$-th derivatives (without resorting to the usual recursive definition), and the above mentioned properties will be recovered directly in the limit. Polynomial functions will allow us to produce a coordinate free version of Taylor's formula

Three-dimensional water impact at normal incidence to a blunt structure

The three-dimensional (3D) water impact onto a blunt structure with a spreading rectangular contact region is studied. The structure is mounted on a flat rigid plane with the impermeable curved surface of the structure perpendicular to the plane. Before impact, the water region is a rectangular domain of finite thickness bounded from below by the rigid plane and above by the flat free surface. The front free surface of the water region is vertical, representing the front of an advancing steep wave. The water region is initially advancing towards the structure at a constant uniform speed. We are concerned with the slamming loads acting on the surface of the structure during the initial stage of water impact. Air, gravity and surface tension are neglected. The problem is analysed by using some ideas of pressure-impulse theory, but including the time-dependence of the wetted area of the structure. The flow caused by the impact is 3D and incompressible. The distribution of the pressure-impulse (the time-integral of pressure) over the surface of the structure is analysed and compared with the distributions provided by strip theories. The total impulse exerted on the structure during the impact stage is evaluated and compared with numerical and experimental predictions. An example calculation is presented of water impact onto a vertical rigid cylinder. Three-dimensional effects on the slamming loads are of main concern in this study

Yukawa potentials in systems with partial periodic boundary conditions II : Lekner sums for quasi-two dimensional systems

Yukawa potentials may be long ranged when the Debye screening length is large. In computer simulations, such long ranged potentials have to be taken into account with convenient algorithms to avoid systematic bias in the sampling of the phase space. Recently, we have provided Ewald sums for quasi-two dimensional systems with Yukawa interaction potentials [M. Mazars, {\it J. Chem. Phys.}, {\bf 126}, 056101 (2007) and M. Mazars, {\it Mol. Phys.}, Paper I]. Sometimes, Lekner sums are used as an alternative to Ewald sums for Coulomb systems. In the present work, we derive the Lekner sums for quasi-two dimensional systems with Yukawa interaction potentials and we give some numerical tests for pratical implementations. The main result of this paper is to outline that Lekner sums cannot be considered as an alternative to Ewald sums for Yukawa potentials. As a conclusion to this work : Lekner sums should not be used for quasi-two dimensional systems with Yukawa interaction potentials.Comment: 25 pages, 5 figures and 1 tabl

Hard Thermal Loops in the n-Dimensional phi3 Theory

We derive a closed-form result for the leading thermal contributions which appear in the n-dimensional phi3 theory at high temperature. These contributions become local only in the long wavelength and in the static limits, being given by different expressions in these two limits.Comment: 3 pages, one figure. To be published in the Brazilian Journal of Physic