78 research outputs found
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
Geometry of Schroedinger Space-Times II: Particle and Field Probes of the Causal Structure
We continue our study of the global properties of the z=2 Schroedinger
space-time. In particular, we provide a codimension 2 isometric embedding which
naturally gives rise to the previously introduced global coordinates.
Furthermore, we study the causal structure by probing the space-time with point
particles as well as with scalar fields. We show that, even though there is no
global time function in the technical sense (Schroedinger space-time being
non-distinguishing), the time coordinate of the global Schroedinger coordinate
system is, in a precise way, the closest one can get to having such a time
function. In spite of this and the corresponding strongly Galilean and almost
pathological causal structure of this space-time, it is nevertheless possible
to define a Hilbert space of normalisable scalar modes with a well-defined
time-evolution. We also discuss how the Galilean causal structure is reflected
and encoded in the scalar Wightman functions and the bulk-to-bulk propagator.Comment: 32 page
A Feynman integral in Lifshitz-point and Lorentz-violating theories in R<sup>D</sup> âš R<i><sup>m</sup></i>
We evaluate a 1-loop, 2-point, massless Feynman integral ID,m(p,q) relevant for perturbative field theoretic calculations in strongly anisotropic d=D+m dimensional spaces given by the direct sum RD âš Rm . Our results are valid in the whole convergence region of the integral for generic (noninteger) codimensions D and m. We obtain series expansions of ID,m(p,q) in terms of powers of the variable X:=4p2/q4, where p=|p|, q=|q|, p Đ RD, q Đ Rm, and in terms of generalised hypergeometric functions 3F2(âX), when X<1. These are subsequently analytically continued to the complementary region Xâ„1. The asymptotic expansion in inverse powers of X1/2 is derived. The correctness of the results is supported by agreement with previously known special cases and extensive numerical calculations
A unified matrix approach to the representation of Appell polynomials
In this paper, we propose a unified approach to matrix representations of different types of Appell polynomials. This approach is based on the creation matrix â a special matrix which has only the natural numbers as entries and is closely related to the well-known Pascal matrix. By this means, we stress the arithmetical origins of Appell polynomials. The approach also allows to derive, in a simplified way, the properties of Appell polynomials by using only matrix operations
On a new class of summation formulas involving the generalized hypergeometric F 2 2 polynomial
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