Squeezed coherent states for gravitational well in noncommutative space

Patra, Pinaki; Saha, Jyoti Prasad; Biswas, Kalpana

doi:10.1007/s12648-020-01962-6

Cited by 5 publications

(3 citation statements)

References 130 publications

(148 reference statements)

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“…Using the representation (9) together with the condition ( 16), one can easily calculate the mean values in (18), with ζ given in (14). Thus, the general solution from (18), reads…”

Section: B Time-dependent Ss Via Para-bose Number Statesmentioning

confidence: 99%

“…There is a wide range of publications in the literature that seeks to generalize CS to be able to describe systems in addition to the harmonic oscillator, such as the time-dependent quadratic systems [9,10], systems with a given Lie group [11,12], some non-trivial generalizations [13], and squeezed coherent states (SCS) [14,15]. On the other hand, CS can be generalized by considering deformations in the canonical commutation relation and thus allow us to study a wide range of relevant problems, such as, for instance, the implications of the gravitational effects in quantum mechanics [16][17][18], or even in q-and f-deformed oscillators study which is applied, mainly, to quantum optics [19][20][21]. Thus, our contribution in this field will be through the construction of CS via Wigner-Heisenberg algebra.…”

Section: Introductionmentioning

confidence: 99%

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Generalized para-Bose coherent states

Pereira¹,

Lemos²,

Brito³

2022

Preprint

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In this paper, we construct integrals of motion in a para-Bose formulation for a general timedependent quadratic Hamiltonian, which, in its turn, commutes with the reflection operator. In this context, we obtain generalizations for the squeezed vacuum states (SS) and coherent states (CS) in terms of the Wigner parameter. Furthermore, we show that there is a positive completeness relation for the SS owing to the Wigner parameter. In the study of the probability transition, we found that the displacement parameter acts as a transition parameter by allowing access to odd states, while the Wigner parameter controls the dispersion of the distribution.

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“…Using the representation (9) together with the condition ( 16), one can easily calculate the mean values in (18), with ζ given in (14). Thus, the general solution from (18), reads…”

Section: B Time-dependent Ss Via Para-bose Number Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalized para-Bose coherent states

Pereira¹,

Lemos²,

Brito³

2022

Preprint

View full text Add to dashboard Cite

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“…LRIM for various classes of TDSE had been studied extensively in the literature. Such as the harmonic oscillators, a particle moving in a time-dependent electromagnetic field, and a particle moving in non-commutative (NC) space with timedependent NC parameters have been solved with the help of LRIM [59][60][61][62][63]. M Maamache et al constructed a class of Lewis-Riesenfeld invariant operators (LRIO) for a free particle with TDEM [56].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of free time-dependent effective mass

Patra¹,

Chowdhury²,

Jana³

2022

Preprint

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The consensus is that an object with a large mass will not manifest quantum behavior. Therefore, we expect that the quantumness of a time-dependent effective mass (TDEM) will erase after a long time when the mass profile continuously grows with time. However, the present article depicts that the Wigner quasi-probability distribution (WQD) will manifest an entanglement behavior forever for two spatially separated free TDEMs.The time-dependent Schrödinger equation for a free particle with TDEM has been solved with the help of the Lewis-Riesenfeld phase space invariant method. WQD for the system of two identical TDEMs with quadratically increasing mass profiles shows that the particles are never separated.In particular, their reminiscent is present at the origin of the phase-space forever.

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On the two-dimensional time-dependent anisotropic harmonic oscillator in a magnetic field

Patra¹

2023

Journal of Mathematical Physics

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A charged harmonic oscillator in a magnetic field, Landau problems, and an oscillator in a noncommutative space share the same mathematical structure in their Hamiltonians. We have considered a two-dimensional anisotropic harmonic oscillator with arbitrarily time-dependent parameters (effective mass and frequencies), placed in an arbitrarily time-dependent magnetic field. A class of quadratic invariant operators (in the sense of Lewis and Riesenfeld) have been constructed. The invariant operators (Î) have been reduced to a simplified representative form by a linear canonical transformation [the group Sp(4,R)]. An orthonormal basis of the Hilbert space consisting of the eigenvectors of Î is obtained. In order to obtain the solutions of the time-dependent Schrödinger equation corresponding to the system, both the geometric and dynamical phase-factors are constructed. A generalized Peres–Horodecki separability criterion (Simon’s criterion) for the ground state corresponding to our system has been demonstrated.

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Squeezed coherent states for gravitational well in noncommutative space

Cited by 5 publications

References 130 publications

Generalized para-Bose coherent states

Generalized para-Bose coherent states

Dynamics of free time-dependent effective mass

On the two-dimensional time-dependent anisotropic harmonic oscillator in a magnetic field

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