We consider a two-photon quantum model of radiation-matter interaction between a single two-level atom and a degenerate bimodal high-Q cavity field. Within this tripartite system the explicit construction of two collective radiation modes, one of whi
ch freely evolving and the other one quadratically coupled to the matter subsystem, is reported. Meaning and advantages of such a decoupling treatment are carefully discussed.
In this paper we study in a Hilbert space a homogeneous linear second order difference equation with nonconstant and noncommuting operator coefficients. We build its exact resolutive formula consisting in the explicit non-iterative expression of a ge
neric term of the unknown sequence of vectors of the Hilbert space. Some non-trivial applications are reported with the aim of showing the usefulness and the broad applicability of our result.
The dynamical behavior of a star network of spins, wherein each of N decoupled spins interact with a central spin through non uniform Heisenberg XX interaction is exactly studied. The time-dependent Schrodinger equation of the spin system model is so
lved starting from an arbitrary initial state. The resulting solution is analyzed and briefly discussed.
Quadratic matrix equations occur in a variety of applications. In this paper we introduce new permutationally invariant functions of two solvents of the n quadratic matrix equation X^2- L1X - L0 = 0, playing the role of the two elementary symmetric f
unctions of the two roots of a quadratic scalar equation. Our results rely on the connection existing between the QME and the theory of linear second order difference equations with noncommutative coefficients. An application of our results to a simple physical problem is briefly discussed.
The detailed construction of the general solution of a second order non-homogenous linear operatordifference equation is presented. The wide applicability of such an equation as well as the usefulness of its resolutive formula is shown by studying so
me applications belonging to different mathematical contexts.
The exact dynamics of a disordered spin star system, describing a central spin coupled to N distinguishable and non interacting spins 1/2, is reported. Exploiting their interaction with the central single spin system, we present possible conditional
schemes for the generation of W-like states, as well as of well-defined angular momentum states, of the N uncoupled spins. We provide in addition a way to estimate the coupling intensity between each of the N spins and the central one. Finally the feasibility of our procedure is briefly discussed.
The exact solution of a Cauchy problem related to a linear second-order difference equation with constant noncommutative coefficients is reported.
