Inverted oscillator

Yüce, C.; Kılıç, Ali Yavuz; Coruh, A.

doi:10.1088/0031-8949/74/1/014

Cited by 53 publications

(56 citation statements)

References 16 publications

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“…Here the constant µ must be chosen in such a way that the inside of the square root should be positive for all q. As an example, consider the following inverted harmonic potential: V R = −V 2 0 q 2 , where V 0 is a real number [42]. Therefore the imaginary part of the potential reads…”

Section: Self-accelerating Constant Intensity Wavesmentioning

confidence: 99%

Self-acceleration in non-Hermitian systems

Yüce

Turker

2017

Physics Letters A

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Section: Self-accelerating Constant Intensity Wavesmentioning

confidence: 99%

Self-acceleration in non-Hermitian systems

Yüce

Turker

2017

Physics Letters A

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“…We point out that the Hamiltonians (4), (10), (13), (14), (20), (21), (25) and (28) generated from SU SY QM -R are non-Hermitian because the imaginary unit accompanies the reflection operator. As in the case of the simplest inverted oscillator, whose eigenfunctions are not L 2 (R)-square integrable for an arbitrary energy E ∈ C [28,39,36], the Hamiltonians and their definite parity eigenfunctions reported in this paper result to be non-L 2 (R)-square integrable. As a consequence of the properties of the confluent hypergeometric function, equations (8), (16), (23), (27) and (30) show that the spectrum of our different Hamiltonians is complex.…”

Section: Supersymmetric Two-body Calogero -Type Modelmentioning

confidence: 54%

Non-Hermitian inverted harmonic oscillator-type Hamiltonians generated from supersymmetry with reflections

et al. 2019

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By modifying and generalizing known supersymmetric models we are able to find four different sets of one-dimensional Hamiltonians for the inverted harmonic oscillator. The first set of Hamiltonians is derived by extending the supersymmetric quantum mechanics with reflections to non-Hermitian supercharges. The second set is obtained by generalizing the supersymmetric quantum mechanics valid for non-Hermitian supercharges with the Dunkl derivative instead of d dx . Also, by changing the derivative d dx by the Dunkl derivative in the creation and annihilation-type operators of the standard inverted Harmonic oscillator H SIO = − 1 2 d 2 dx 2 − 1 2 x 2 , we generate the third set of Hamiltonians. The fourth set of Hamiltonians emerges by allowing a parameter of the supersymmetric two-body Calogero-type model to take imaginary values. The eigensolutions of definite parity for each set of Hamiltonians are given.

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“…During this interval the atoms temporarily experience an antitrapping potential (like in an inverted harmonic oscillator, with the possibility of cooling first noticed in the conclusions of Ref. [14]) leading to an accelerated spreading of the wave function, after which the trap is flipped back to allow regrouping, and desired cooling, of the wave function by t = t f .…”

Section: Squeezing In Frictionless Coolingmentioning

confidence: 98%

Squeezing and robustness of frictionless cooling strategies

2012

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Quantum control strategies that provide shortcuts to adiabaticity are increasingly considered in various contexts including atomic cooling. Recent studies have emphasized practical issues in order to reduce the gap between idealized models and actual ongoing implementations. We rephrase the cooling features in terms of a peculiar squeezing effect and use it to parametrize the robustness of frictionless cooling techniques with respect to noise-induced deviations from the ideal time-dependent trajectory for the trapping frequency. We finally discuss qualitative issues for the experimental implementation of this scheme using bichromatic optical traps and lattices, which seem especially suitable for cooling Fermi-Bose mixtures and for investigating equilibration of negative temperature states, respectively

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Inverted oscillator

Abstract: The inverted harmonic oscillator problem is investigated quantum mechanically. The exact wave function for the confined inverted oscillator is obtained and it is shown that the associated energy eigenvalues are discrete and it is given as a linear function of the quantum number n.

Cited by 53 publications

References 16 publications

Self-acceleration in non-Hermitian systems

Self-acceleration in non-Hermitian systems

Non-Hermitian inverted harmonic oscillator-type Hamiltonians generated from supersymmetry with reflections

Squeezing and robustness of frictionless cooling strategies

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