0000000000170982
AUTHOR
Demosthenes Ellinas
showing 3 related works from this author
Anharmonicity deformation and curvature in supersymmetric potentials
1994
An algebraic description of the class of 1D supersymmetric shape invariant potentials is investigated in terms of the shape-invariant-potential (SIP) deformed algebra, the generators of which act both on the dynamical variable and on the parameters of the potentials. The phase space geometry associated with SIP's is studied by means of a coherent state (SIP-CS) path integral and the ray metric of the SIP-CS manifold. The anharmonicity of SIP's results in a inhomogeneous phase space manifold with one Killing vector and with a modified symplectic Kahler structure, and it induces a non constant curvature into the generalized phase space. Analogous results from the phase space geometry of someq…
Motion of the wave-function zeros in spin-boson systems.
1995
In the analytic Bargmann representation associated with the harmonic oscillator and spin coherent states, the wave functions considered as consisting of entire complex functions can be factorized in terms of their zeros in a unique way. The Schr\"odinger equation of motion for the wave function is turned to a system of equations for the zeros of the wave function. The motion of these zeros as a nonlinear flow of points is studied and interpreted for linear and nonlinear bosonic and spin Hamiltonians. Attention is given to the study of the zeros of the Jaynes-Cummings model and to its finite analog. Numerical solutions are derived and dicussed.
On the representation theory of quantum Heisenberg group and algebra
1994
We show that the quantum Heisenberg groupH q (1) and its *-Hopf algebra structure can be obtained by means of contraction from quantumSU q (2) group. Its dual Hopf algebra is the quantum Heisenberg algebraU q (h(1)). We derive left and right regular representations forU q (h(1)) as acting on its dualH q (1). Imposing conditions on the right representation, the left representation is reduced to an irreducible holomorphic representation with an associated quantum coherent state. Realized in the Bargmann-Hilbert space of analytic functions the unitarity of regular representation is also shown. By duality, left and right regular representations for quantum Heisenberg group with the quantum Heis…