COHERENT STATES AND SCHWINGER MODELS FOR PSEUDO GENERALIZATION OF THE HEISENBERG ALGEBRA

We show that the non-Hermitian Hamiltonians of the simple harmonic oscillator with [Formula: see text] and [Formula: see text] symmetries involve a pseudo generalization of the Heisenberg algebra via two pairs of creation and annihilation operators which are [Formula: see text]-pseudo-Hermiticity and [Formula: see text]-anti-pseudo-Hermiticity of each other. The non-unitary Heisenberg algebra is represented by each of the pair of the operators in two different ways. Consequently, the coherent and the squeezed coherent states are calculated in two different approaches. Moreover, it is shown that the approach of Schwinger to construct the su(2), su(1, 1) and sp(4, ℝ) unitary algebras is promoted so that unitary algebras with more linearly dependent number of generators are made.

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COHERENT STATE OF α-DEFORMED WEYL–HEISENBERG ALGEBRA

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s021988781350014x ◽

2013 ◽

Vol 10 (05) ◽

pp. 1350014 ◽

Cited By ~ 8

Author(s):

SH. DEHDASHTI ◽

A. MAHDIFAR ◽

R. ROKNIZADEH

Keyword(s):

Coherent State ◽

Harmonic Oscillator ◽

Coherent States ◽

Heisenberg Algebra ◽

Statistical Properties ◽

Potential Well ◽

Mandel Parameter ◽

Boson Realization ◽

Deformed Algebra

At first, we introduce α-deformed algebra as a kind of generalization of the Weyl–Heisenberg algebra so that we get the su(2)- and su(1, 1)-algebras whenever α has specific values. After that, we construct coherent states of this algebra. Third, a realization of this algebra is given in the system of a harmonic oscillator confined at the center of a potential well. Then, we introduce two-boson realization of the α-deformed Weyl–Heisenberg algebra and use this representation to write α-deformed coherent states in terms of the two modes number states. Following these points, we consider mean number of excitations (we call them in general photons) and Mandel parameter as statistical properties of the α-deformed coherent states. Finally, the Fubini–Study metric is calculated for the α-coherent states manifold.

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QUANTUM MECHANICAL COHERENT STATES OF THE HARMONIC OSCILLATOR AND THE GENERALIZED UNCERTAINTY PRINCIPLE

International Journal of Quantum Information ◽

10.1142/s0219749905001468 ◽

2005 ◽

Vol 03 (04) ◽

pp. 623-632 ◽

Cited By ~ 18

Author(s):

KOUROSH NOZARI ◽

TAHEREH AZIZI

Keyword(s):

Quantum Mechanics ◽

Harmonic Oscillator ◽

Uncertainty Principle ◽

Coherent States ◽

Equations Of Motion ◽

Generalized Uncertainty Principle ◽

Quantum Mechanical ◽

Simple Harmonic Oscillator ◽

Definition Of ◽

Ordinary Quantum

In this paper, dynamics and quantum mechanical coherent states of a simple harmonic oscillator are considered in the framework of the Generalized Uncertainty Principle (GUP). Equations of motion for the simple harmonic oscillator are derived and some of their new implications are discussed. Then, coherent states of the harmonic oscillator in the case of the GUP are compared with the relative situation in ordinary quantum mechanics. It is shown that in the framework of GUP there is no considerable difference in definition of coherent states relative to ordinary quantum mechanics. But, considering expectation values and variances of some operators, based on quantum gravitational arguments, one concludes that although it is possible to have complete coherency and vanishing broadening in usual quantum mechanics, gravitational induced uncertainty destroys complete coherency in quantum gravity and it is not possible to have a monochromatic ray in principle.

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Harmonic Oscillators with Nonlinear Damping

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127417300373 ◽

2017 ◽

Vol 27 (11) ◽

pp. 1730037 ◽

Cited By ~ 8

Author(s):

J. C. Sprott ◽

W. G. Hoover

Keyword(s):

Dynamical Systems ◽

Harmonic Oscillator ◽

Strange Attractor ◽

Nonlinear Damping ◽

Harmonic Oscillators ◽

Coexisting Attractors ◽

Simple Harmonic Oscillator ◽

Interesting Behavior

Dynamical systems with special properties are continually being proposed and studied. Many of these systems are variants of the simple harmonic oscillator with nonlinear damping. This paper characterizes these systems as a hierarchy of increasingly complicated equations with correspondingly interesting behavior, including coexisting attractors, chaos in the absence of equilibria, and strange attractor/repellor pairs.

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Propagator for the simple harmonic oscillator

American Journal of Physics ◽

10.1119/1.19003 ◽

1998 ◽

Vol 66 (11) ◽

pp. 1022-1024 ◽

Cited By ~ 14

Author(s):

Nora S. Thornber ◽

Edwin F. Taylor

Keyword(s):

Harmonic Oscillator ◽

Simple Harmonic Oscillator

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NON-HERMITIAN OSCILLATOR-LIKE HAMILTONIANS AND λ-COHERENT STATES REVISITED

Modern Physics Letters A ◽

10.1142/s021773230100295x ◽

2001 ◽

Vol 16 (02) ◽

pp. 91-98 ◽

Cited By ~ 9

Author(s):

JULES BECKERS ◽

NATHALIE DEBERGH ◽

JOSÉ F. CARIÑENA ◽

GIUSEPPE MARMO

Keyword(s):

Harmonic Oscillator ◽

Hilbert Spaces ◽

Coherent States ◽

Scalar Product ◽

Points Of View ◽

Usual Scalar ◽

Usual Scalar Product

Previous λ-deformed non-Hermitian Hamiltonians with respect to the usual scalar product of Hilbert spaces dealing with harmonic oscillator-like developments are (re)considered with respect to a new scalar product in order to take into account their property of self-adjointness. The corresponding deformed λ-states lead to new families of coherent states according to the DOCS, AOCS and MUCS points of view.

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(ANTI)COMMUTATIVITY OF THE HARMONIC CREATION AND ANNIHILATION OPERATORS

International Journal of Modern Physics B ◽

10.1142/s0217979206034327 ◽

2006 ◽

Vol 20 (11n13) ◽

pp. 1808-1818

Author(s):

S. KUWATA ◽

A. MARUMOTO

Keyword(s):

Irreducible Representation ◽

Harmonic Oscillator ◽

Linear Algebra ◽

Commutation Relation ◽

Complex Number ◽

Single Mode ◽

Equation Of Motion ◽

Sufficient Condition ◽

Special Linear ◽

Creation And Annihilation Operators

It is known that para-particles, together with fermions and bosons, of a single mode can be described as an irreducible representation of the Lie (super) algebra 𝔰𝔩2(ℂ) (2-dimensional special linear algebra over the complex number ℂ), that is, they satisfy the equation of motion of a harmonic oscillator. Under the equation of motion of a harmonic oscillator, we obtain the set of the commutation relations which is isomorphic to the irreducible representation, to find that the equation of motion, conversely, can be derived from the commutation relation only for the case of either fermion or boson. If Nature admits of the existence of such a sufficient condition for the equation of motion of a harmonic oscillator, no para-particle can be allowed.

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