Related papers: Collapse and revivals for the binomial field distr…
Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets, with applications in algebraic geometry and beyond. We have previously reported on an implementation of CAD in Maple which offers…
A method is described which allows to evaluate efficiently a polynomial in a (possibly trivial) extension of the finite field of its coefficients. Its complexity is shown to be lower than that of standard techniques when the degree of the…
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…
In two dimensions, we consider the problem of reconstructing a vector field from partial knowledge of its zeroth and first moment ray transforms. Different from existing works the data is known on a subset of lines, namely the ones…
The method of perturbative expansion of master equation is employed to study the dissipative properties of system and of atom in the two-photon Jaynes-Cummings model (JCM) with degenerate atomic levels. The numerical results show that the…
The collapse and revival of quantum states appear in diverse areas of physics. In quantum optics the occurrence of such a phenomena in the evolution of an atomic state, interacting with a light field initially in a coherent state, was…
Within a simple quantization scheme, observables for a large class of finite dimensional time reparametrization invariant systems may be constructed by integration over the manifold of time labels. This procedure is shown to produce a…
In many field theoretical models one has to resum two- and four-legged subdiagrams in order to determine their behaviour. In this article we present a novel formalism which does this in a nice way. It is based on the central limit theorem…
The interpolation-regression approximation is a powerful tool in numerical analysis for reconstructing functions defined on square or triangular domains from their evaluations at a regular set of nodes. The importance of this technique lies…
To construct flexible nonlinear predictive distributions, the paper introduces a family of softplus function based regression models that convolve, stack, or combine both operations by convolving countably infinite stacked gamma…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
A well known description of superradiance from pointlike collections of many atoms involves the dissipative motion of a large spin. The pertinent ``superradiance master equation'' allows for a formally exact solution which we subject to a…
By using extended bosonic coherent states, the solution to the Jaynes-Cummings model without the rotating-wave approximation can be mapped to that of a polynomial equation with a single variable. The solutions to this polynomial equation…
We further study the stochastic model discussed in Ref.[2] in which positive and negative particles diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and…
The resonant interaction between two two-level atoms and m- electromagnetic modes in a cavity is considered. Entanglement dynamics between two atoms is examined. In particular we compare dynamical variations for different cavity modes as…
We examine doing probabilistic descent over manifolds implicitly defined by a set of polynomials with rational coefficients. The system of polynomials is assumed to be triangularized. An application of Whitney's embedding theorem allows us…
In this paper we provide a microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses. We single out both the differences with the phenomenological master equation used in the literature and the…
In this paper, we describe some interesting properties of a non-Hermitian Jaynes-Cummings model. For this particular model, it is known that the Hilbert space can be described by infinitely-many two-dimensional invariant (closed) subspaces,…
The applicability of the highly idealized secondary infall model to `realistic' initial conditions is investigated. The collapse of proto-halos seeded by $3\sigma$ density perturbations to an Einstein--de Sitter universe is studied here for…
It has been proposed that Randall-Sundrum models can be holographically described by a regularized (broken) conformal field theory. We analyze the foundations of this duality using a regularized version of the AdS/CFT correspondence. We…