scholarly journals Generalized coherent states for solvable quantum systems with degenerate discrete spectra and their nonclassical properties

2011 ◽  
Vol 390 (7) ◽  
pp. 1381-1392 ◽  
Author(s):  
G.R. Honarasa ◽  
M.K. Tavassoly ◽  
M. Hatami ◽  
R. Roknizadeh
Keyword(s):  
Coherent States ◽  
Quantum Systems ◽  
Nonclassical Properties ◽  
Generalized Coherent States ◽  
Solvable Quantum ◽  
Discrete Spectra

VECTOR COHERENT STATES AND NON-ABELIAN GAUGE STRUCTURES IN QUANTUM MECHANICS

1990 ◽  
Vol 05 (22) ◽  
pp. 4311-4331 ◽  
Author(s):  
G. GIAVARINI ◽  
E. ONOFRI
Keyword(s):  
Quantum Mechanics ◽  
Lie Group ◽  
Coherent States ◽  
Quantum Systems ◽  
Semisimple Lie Group ◽  
Abelian Gauge ◽  
Geometric Properties ◽  
Generalized Coherent States ◽  
Abelian Case ◽  
Vector Coherent States

We set the general formalism for calculating Berry's phase in quantum systems with Hamiltonian belonging to the algebra of a semisimple Lie group of any rank in the framework of generalized coherent states. Within this approach the geometric properties of Berry's connection are also studied, both in the Abelian and non-Abelian cases. In particular we call attention to the non-Abelian case where we make use of a vectorial generalization of coherent states. In this respect a thorough and self-contained exposition of the formalism of vector coherent states is given. The specific examples of the groups SU(3) and Sp(2) are worked out in detail.

scholarly journals ON A GENERAL FORMALISM OF NONLINEAR CHARGE COHERENT STATES, THEIR QUANTUM STATISTICS AND NONCLASSICAL PROPERTIES

2010 ◽  
Vol 25 (17) ◽  
pp. 3481-3504 ◽  
Author(s):  
F. EFTEKHARI ◽  
M. K. TAVASSOLY
Keyword(s):  
Coherent States ◽  
Nonclassical States ◽  
Mandel Parameter ◽  
Physical Systems ◽  
Nonclassical Properties ◽  
Deformed Algebra ◽  
Solvable Quantum ◽  
Antibunching Effect ◽  
Quantum Statistical ◽  
Special Case

In this paper, we will present a general formalism for constructing the nonlinear charge coherent states which in special case lead to the standard charge coherent states. The su Q(1, 1) algebra as a nonlinear deformed algebra realization of the introduced states is established. In addition, the corresponding even and odd nonlinear charge coherent states have also been introduced. The formalism has the potentiality to be applied to systems either with known "nonlinearity function" f(n) or solvable quantum system with known "discrete nondegenerate spectrum" en. As some physical appearances, a few known physical systems in the two mentioned categories have been considered. Finally, since the construction of nonclassical states is a central topic of quantum optics, nonclassical features and quantum statistical properties of the introduced states have been investigated by evaluating single- and two-mode squeezing, su (1, 1)-squeezing, Mandel parameter and antibunching effect (via g-correlation function) as well as some of their generalized forms we have introduced in the present paper.

scholarly journals Time and classical equations of motion from quantum entanglement via the Page and Wootters mechanism with generalized coherent states

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Caterina Foti ◽  
Alessandro Coppo ◽  
Giulio Barni ◽  
Alessandro Cuccoli ◽  
Paola Verrucchi
Keyword(s):  
Classical Limit ◽  
Coherent States ◽  
Equations Of Motion ◽  
Quantum Systems ◽  
Physical Systems ◽  
Quantum Time ◽  
First Case ◽  
Hamilton Equations ◽  
Generalized Coherent States ◽  
Evolving System

AbstractWe draw a picture of physical systems that allows us to recognize what “time” is by requiring consistency with the way that time enters the fundamental laws of Physics. Elements of the picture are two non-interacting and yet entangled quantum systems, one of which acting as a clock. The setting is based on the Page and Wootters mechanism, with tools from large-N quantum approaches. Starting from an overall quantum description, we first take the classical limit of the clock only, and then of the clock and the evolving system altogether; we thus derive the Schrödinger equation in the first case, and the Hamilton equations of motion in the second. This work shows that there is not a “quantum time”, possibly opposed to a “classical” one; there is only one time, and it is a manifestation of entanglement.

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