Unitary equivalence and phase properties of the quantum parametric and generalized harmonic oscillators

Maamache, M.; Provost, Jean‐Pierre; Vallée, G.

doi:10.1103/physreva.59.1777

Cited by 23 publications

(24 citation statements)

References 13 publications

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“…(2). Notice that this Hamiltonian is actually the same as that of the parametric harmonic oscillator treated by Maamache et al [11]. It is proved that parametric harmonic oscillator is unitarily equivalent to a generalized time-dependent harmonic oscillator [11].…”

Section: Hamiltonian Dynamics Of Fieldsmentioning

confidence: 64%

Quantum Analysis of a Modified Caldirola-Kanai Oscillator Model for Electromagnetic Fields in Time-Varying Plasma

Choi¹,

Lakehal²,

Maamache³

et al. 2014

PIER Letters

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Abstract-Quantum properties of a modified Caldirola-Kanai oscillator model for propagating electromagnetic fields in a plasma medium are investigated using invariant operator method. As a modification, ordinary exponential function in the Hamiltonian is replaced with a modified exponential function, so-called the q-exponential function. The system described in terms of q-exponential function exhibits nonextensivity. Characteristics of the quantized fields, such as quantum electromagnetic energy, quadrature fluctuations, and uncertainty relations are analyzed in detail in the Fock state, regarding the q-exponential function. We confirmed, from their illustrations, that these quantities oscillate with time in some cases. It is shown from the expectation value of energy operator that quantum energy of radiation fields dissipates with time, like a classical energy, on account of the existence of non-negligible conductivity in media.

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Section: Hamiltonian Dynamics Of Fieldsmentioning

confidence: 64%

Quantum Analysis of a Modified Caldirola-Kanai Oscillator Model for Electromagnetic Fields in Time-Varying Plasma

Choi¹,

Lakehal²,

Maamache³

et al. 2014

PIER Letters

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show abstract

“…Then, using Eqs. (20), (21), (25) and (35) we find that the coherent states for the oscillator described by the Hamiltonian (1) are given by…”

Section: Coherent Statesmentioning

confidence: 96%

“…They have mainly considered the following oscillators [1][2][3][4]11,13,[15][16][17][18][19][20][21][22][23][24][25] : (1) damped oscillators; (2) oscillators with time-dependent mass and/or frequency; (3) generalized oscillator with time-dependent parameters; (4) generalized nonstationary forced oscillators; (5) damped harmonic oscillator with time-dependent mass and frequency and (6) time-dependent oscillators with an inverse quadratic potential. However, the generalized harmonic oscillator with time-dependent mass and frequency subjected to a friction force proportional to its velocity is barely mentioned.…”

Section: Introductionmentioning

confidence: 99%

Coherent states and geometric phases of a generalized damped harmonic oscillator with time-dependent mass and frequency

Pedrosa

Lima

2014

Int. J. Mod. Phys. B

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In this paper, we study the generalized harmonic oscillator with arbitrary timedependent mass and frequency subjected to a linear velocity-dependent frictional force from classical and quantum points of view. We obtain the solution of the classical equation of motion of this system for some particular cases and derive an equation of motion that describes three different systems. Furthermore, with the help of the quantum invariant method and using quadratic invariants we solve analytically and exactly the time-dependent Schrödinger equation for this system. Afterwards, we construct coherent states for the quantized system and employ them to investigate some of the system's quantum properties such as quantum fluctuations of the coordinate and the momentum as well as the corresponding uncertainty product. In addition, we derive the geometric, dynamical and Berry phases for this nonstationary system. Finally, we evaluate the dynamical and Berry phases for three special cases and surprisingly find identical expressions for the dynamical phase and the same formulae for the Berry's phase.

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“…For instance, particular recent interest has been devoted to systems in which evolution originates geometric contributions [1][2][3][4][5][6]. One of these, the generalized harmonic oscillator has invoked much attention to study the nonadiabatic geometric phase for various quantum states, such as Gaussian, number, squeezed or coherent states, which can be found exactly [7][8][9][10]. Recently, the geometric phase for a cyclic wave packet solution of the generalized harmonic oscillator and its relation…”

mentioning

confidence: 99%

“…Let us consider the classical equation (9). The main property of this evolution is that is linear and area preserving.…”

mentioning

confidence: 99%

Evolution of Gaussian wave packet and nonadiabatic geometrical phase for the time-dependent singular oscillator

Maamache¹,

Bekkar²

2003

J. Phys. A: Math. Gen.

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The geometrical phase of a time-dependent singular oscillator is obtained in the framework of Gaussian wave packet. It is shown by a simple geometrical approach that the geometrical phase is connected to the classical Explicitly time-dependent problems present special difficulties in classical and quantum mechanics. However, they deserve detailed study because very interesting properties emerge when, even for simple linear systems, some parameters are allowed to vary with time. For instance, particular recent interest has been devoted to systems in which evolution originates geometric contributions [1][2][3][4][5][6]. One of these, the generalized harmonic oscillator has invoked much attention to study the nonadiabatic geometric phase for various quantum states, such as Gaussian, number, squeezed or coherent states, which can be found exactly [7][8][9][10]. Recently, the geometric phase for a cyclic wave packet solution of the generalized harmonic oscillator and its relation

show abstract

Unitary equivalence and phase properties of the quantum parametric and generalized harmonic oscillators

Cited by 23 publications

References 13 publications

Quantum Analysis of a Modified Caldirola-Kanai Oscillator Model for Electromagnetic Fields in Time-Varying Plasma

Quantum Analysis of a Modified Caldirola-Kanai Oscillator Model for Electromagnetic Fields in Time-Varying Plasma

Coherent states and geometric phases of a generalized damped harmonic oscillator with time-dependent mass and frequency

Evolution of Gaussian wave packet and nonadiabatic geometrical phase for the time-dependent singular oscillator

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