相关论文: (p,q)-Deformations and (p,q)-Vector Coherent State…

In this work we study the validity of the rotating wave approximation of an ideal system composed of two harmonic oscillators evolving with a quadratic Hamiltonian and arbitrarily strong interaction. We prove its validity for arbitrary…

A class of shape-invariant bound-state problems which represent transitions in a two-level system introduced earlier are generalized to include arbitrary energy splittings between the two levels. We show that the coupled-channel…

We revisit the mathematical formulation of the famous Jaynes-Cummings-Paul Hamiltonian, which describes the interaction of a two-level atom with a single mode of an electromagnetic cavity reservoir. We rigorously show that under the…

A scheme is proposed which allows to obtain special $q$-oscillator models whose characteristic feature consists in possessing two differing pairs of degenerate energy levels. The method uses the model of two-parameter deformed…

By using a wave packet approach, this paper reviews the Jaynes-Cummings model with and without the rotating wave approximation in a non-standard way. This gives new insight, not only of the two models themselves, but of the rotating wave…

q-Deformed harmonic oscillator algebra for real and root of unity values of the deformation parameter is discussed by using an extension of the number concept proposed by Gauss, namely the Q-numbers. A study of the reducibility of the Fock…

In this paper, the 2+1 Dirac-Moshinsky oscillator (2+1 DMO) coupled to an external isospin field is mapped onto the Jaynes-Cummings model (JCM), which describes the interaction between two two-level systems and a quantum single-mode field.…

In this paper, we discuss the compatibility between the rotating-wave and the adiabatic approximations for controlled quantum systems. Although the paper focuses on applications to two-level quantum systems, the main results apply in higher…

In the q-deformed theory the perturbation approach can be expressed in terms of two pairs of undeformed position and momentum operators. There are two configuration spaces. Correspondingly there are two q-perturbation Hamiltonians, one…

The interaction of qubits with quantized modes of electromagnetic fields has been largely addressed in the quantum optics literature under the rotating wave approximation (RWA), where rapid oscillating terms in the qubit-mode interaction…

In this paper, the Higgs-like approach is used to analyze the quantum dynamics of a harmonic oscillator constrained on a circle. We obtain the Hamiltonian of this system as a function of the Cartesian coordinate of the tangent line through…

In the recent years a generalization $H=p^2 +x^2(ix)^\epsilon$ of the harmonic oscillator using a complex deformation was investigated, where \epsilon\ is a real parameter. Here, we will consider the most simple case: \epsilon even and x…

The Jaynes-Cummings model is solved with the raising and lowering (shift) operators by using the matrix-diagonalizing technique. Bell nonlocality is also found present ubiquitously in the excitations states of the model.

Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schroedinger type. In contrast to the standard harmonic oscillators such systems exhibit a continuous…

We present, for the isospectral family of oscillator Hamiltonians, a systematic procedure for constructing raising and lowering operators satisfying any prescribed `distorted' Heisenberg algebra (including the $q$-generalization). This is…

Dynamical systems associated with a q-deformed two dimensional phase space are studied as effective dynamical systems described by ordinary variables. In quantum theory, the momentum operator in such a deformed phase space becomes a…

We follow a generalized kinematic approach to compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models, which provide a fully quantum description for a two-level system interacting with a single mode of…

Relation between Bopp-Kubo formulation and Weyl-Wigner-Moyal symbol calculus, and non-commutative geometry interpretation of the phase space representation of quantum mechanics are studied. Harmonic oscillator in phase space via creation…

Quantum--mechanical operators corresponding to canonical momentum and position of a point--like particle, which follow from the quantum field theory in the general Riemannian space-time, satisfy generally to a deformation of the canonical…

Calder\'on-Zygmund decompositions of functions have been used to prove weak-type (1,1) boundedness of singular integral operators. In many examples, the decomposition is done with respect to a family of balls that corresponds to some family…