M. A. Jivulescu

Non-Markovian dynamics of a single electron spin coupled to a nuclear spin bath

We apply the time-convolutionless (TCL) projection operator technique to the model of a central spin, which is coupled to a spin bath via nonuniform Heisenberg interaction. The second-order results of the TCL method for the coherences and populations of the central spin are determined analytically and compared to numerical simulations of the full von Neumann equation of the total system. The TCL approach is found to yield an excellent approximation in the strong field regime for the description of both the short-time dynamics and the long time behavior.

Elementary symmetric functions of two solvents of a quadratic matrix equation

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 functions 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.

Exact treatment of linear difference equations with noncommutative coefficients

The exact solution of a Cauchy problem related to a linear second-order difference equation with constant noncommutative coefficients is reported. Copyright

Exact dynamics of XX central spin models

The dynamical behavior of a star network of spins, wherein each N decoupled spin interacts with a central spin through non-uniform Heisenberg XX interaction, is exactly studied. The time-dependent Schrodinger equation of the spin system model is solved starting from an arbitrary initial state. The resulting solution is analyzed and briefly discussed.

Dynamical behaviour of an XX central spin model through Bethe ansatz techniques

Following the Bethe ansazt procedure the exact dynamics of an XX central spin model is revealed. Particular initial conditions are analyzed and the consequent time evolution is compared with the exact solution obtained by solving the time-dependent Schrudinger equation. The interest towards spin systems and in particular central spin systems, is motivated by the recent developments in more applicative contexts.

Riccati equation-based generalization of Dawson's integral function

A new generalization of Dawsons integral function based on the link between a Riccati nonlinear differential equation and a second-order ordinary differential equation is reported. The MacLaurin expansion of this generalized function is built up and to this end an explicit formula for a generic cofactor of a triangular matrix is deduced. Copyright

Unitary decoupling treatment of a quadratic bimodal cavity quantum electrodynamics model

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 which is freely evolving and the other one quadratically coupled to the matter subsystem, is reported. The meaning and advantages of such a decoupling treatment are carefully discussed.

ELECTROMAGNETIC CONTROL OF DYNAMICAL LOCALIZATION CONDITIONS IN 1D LATTICES WITH LONG-RANGE INTERSITE INTERACTIONS

In this paper we investigate the possibility of controlling dynamical localization conditions for a charged particle confined in a 1D lattice biased with a dc-bichromatic field and long-range intersite interactions. We derive the quasi-energy spectrum of the system proving that the tunneling dynamics of the particle can be destroyed provided that the parameters of the external irradiating electric field are properly chosen.

W-like states of N uncoupled spins 1/2

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.

W-like states of \(\bf N\) uncoupled spins \(\frac{\mbox{\sffamily\bfseries\fontsize{11}{12}\selectfont 1}}{\mbox{\sffamily\bfseries\fontsize{11}{12}\selectfont 2}}\)

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.