Related papers: Phase operators, phase states and vector phase sta…
It is shown that each one of the Lie algebras su(1,1) and su(2) determine the spectrum of the radial oscillator. States that share the same orbital angular momentum are used to construct the representation spaces of the non-compact Lie…
The Schwinger oscillator operator representation of SU(3), studied in a previous paper from the representation theory point of view, is analysed to discuss the intimate relationships between standard oscillator coherent state systems and…
We define the quadratic algebra su(2)_{\alpha} which is a one-parameter deformation of the Lie algebra su(2) extended by a parity operator. The odd-dimensional representations of su(2) (with representation label j, a positive integer) can…
We construct a class of generalized phase coherent states indexed by points of the unit circle and depending on three positive parameters "gamma","alpha" and "epsilon" by replacing the labelling coefficients of the canonical coherent states…
We use coherent states as trial states for a variational approach to study a system of a finite number of three-level atoms interacting in a dipolar approximation with a one-mode electromagnetic field. The atoms are treated as…
We develop a comprehensive theory of phase for finite-dimensional quantum systems. The only physical requirement we impose is that phase is complementary to amplitude. To implement this complementarity we use the notion of mutually unbiased…
A unified approach to the analysis of quantum phase transitions in some different Curie-Weiss models is proposed such that they are treated and analyzed under the same general scheme. This approach takes three steps: balancing the quantum…
We examine the dynamics of an ensemble of phase oscillators that are divided in $k$ sets, with time-delayed coupling interactions {\em only} between oscillators in different sets or partitions. The network of interactions thus form a…
The SU(1,1) coherent states for a relativistic model of the linear singular oscillator are considered. The corresponding partition function is evaluated. The path integral for the transition amplitude between SU(1,1) coherent states is…
We introduce the concept of algebra eigenstates which are defined for an arbitrary Lie group as eigenstates of elements of the corresponding complex Lie algebra. We show that this concept unifies different definitions of coherent states…
We define quantum phase in terms of inverses of annihilation and creation operators. We show that like Susskind - Glogower phase operators, the measured phase operators and the unitary phase operators can be defined in terms of the inverse…
The $SU(2,2)$-harmonic oscillator on the phase space ${\cal A}(2,2)= {SU(2,2)}/{S(U(2)\times U(2))}$ is quantized using the coherent states. The quantum Hamiltonian is the Toeplitz operator corresponding to the square of the distance with…
It is shown that a SU(1,1) algebra may be used to provide a unified description of the simple hamonic oscillator and the angular momentum algebras and a class of other semi-infinite algebras. A normal ordered representation of a Unitary…
A periodic linear graph operator acts on states (functions) defined on the vertices of a graph equipped with a free translation action. Fourier transform with respect to the translation group reveals the central spectral objects, Bloch and…
By utilization of three elementary vector operators as position, angular momentum and their cross product, a simple realization of gl(2,c) Lie algebra on sphere are constructed. The coherent states based on this algebra can then be…
We define a new algebra, which can formally be considered as a ${\cal C}{\cal P}$ deformed $\mathfrak{su}(2)$ Lie algebra. Then, we present a one-dimensional quantum oscillator model, of which the wavefunctions of even and odd states are…
We construct a calculus for generalized $\mathbf{SG}$ Fourier integral operators, extending known results to a broader class of symbols of $\mathbf{SG}$ type. In particular, we do not require that the phase functions are homogeneous. We…
We consider an extension of the real Lie algebra $\mathfrak{su}(2)$ by introducing a parity operator $P$ and a parameter $c$. This extended algebra is isomorphic to the Bannai-Ito algebra with two parameters equal to zero. For this algebra…
We study characteristic aspects of the geometric phase which is associated with the generalized coherent states. This is determined by special orbits in the parameter space defining the coherent state, which is obtained as a solution of the…
Requirements of a conjugate operator are emphasized, especially in its role in uncertainty relations.It is argued that in many contexts it is necessary to extend the Hilbert space in order to define a conjugate operator as in gauge…