Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators

Fring, Andreas; Tenney, Rebecca

doi:10.1016/j.physleta.2020.126530

Cited by 21 publications

(40 citation statements)

References 30 publications

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“…for n ≥ 2. When eliminating the γs from these equations we are left with a differential equation entirely in g given by which is in precise agreement with the Dyson map we previously found in [24].…”

Section: The Unstable Anharmonic Quartic Oscillatorsupporting

confidence: 74%

Perturbative approach for strong and weakly coupled time-dependent non-Hermitian quantum systems

Fring,

Tenney

2020

Preprint

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We propose a perturbative approach to determine the time-dependent Dyson map and the metric operator associated with time-dependent non-Hermitian Hamiltonians. We apply the method to a pair of explicitly time-dependent two dimensional harmonic oscillators that are weakly coupled to each other in a PT-symmetric fashion and to the strongly coupled explicitly time-dependent negative quartic anharmonic oscillator potential. We demonstrate that once the perturbative Ansatz is set up the coupled differential equations resulting order by order may be solved recursively in a constructive manner, thus bypassing the need for making any guess for the Dyson map or the metric operator. Exploring the ambiguities in the solutions of the order by order differential equations naturally leads to a whole set of inequivalent solutions for the Dyson maps and metric operators implying different physical behaviour as demonstrated for the expectation values of the time-dependent energy operator.

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Section: The Unstable Anharmonic Quartic Oscillatorsupporting

confidence: 74%

Perturbative approach for strong and weakly coupled time-dependent non-Hermitian quantum systems

Fring,

Tenney

2020

Preprint

Self Cite

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“…We explore here the possibility of not terminating the procedure at this stage, but instead to use perturbative methods and then feed the approximated expressions back into the Lewis and Riesenfeld approach. Naturally one may also use other approximation methods at this point, such as the WKB approximation, which we explore elsewhere [34].…”

Section: Introductionmentioning

confidence: 99%

Time-independent approximations for time-dependent optical potentials

Fring

Tenney

2020

Eur. Phys. J. Plus

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We explore the possibility of modifying the Lewis-Riesenfeld method of invariants developed originally to find exact solutions for time-dependent quantum mechanical systems for the situation in which an exact invariant can be constructed, but the subsequently resulting time-independent eigenvalue system is not solvable exactly. We propose to carry out this step in an approximate fashion, such as employing standard time-independent perturbation theory or the WKB approximation, and feeding the resulting approximated expressions back into the time-dependent scheme. We illustrate the quality of this approach by contrasting an exactly solvable solution to one obtained with a perturbatively carried out second step for two types of explicitly time-dependent optical potentials.

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“…In this paper we presented, for the first time, time-dependent solutions for the Dyson map and metric operator for the non-Hermitian Jaynes-Cummings Hamiltonian. Until [43], time-dependent solutions to other models have always relied on the existence of a closed algebra in order to form an ansatz [44,45,28,46], however this was not possible for the JC Hamiltonian. In this paper, we formed an ansatz for the timedependent Dyson map by taking inspiration from the time-independent case (which we solved starting from perturbation theory).…”

Section: Discussionmentioning

confidence: 99%

Exotic entanglement for non-Hermitian Jaynes-Cummings Hamiltonians

Frith

2020

Preprint

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We provide the first solution of a time-dependent metric operator for the non-Hermitian Jaynes-Cummings Hamiltonian. We use this solution to calculate the entanglement between two identical isolated such Hamiltonians. The presence of a non-Hermitian interaction term leads to a spontaneously broken PT -symmetric regime which manifests itself in the exotic time-evolution of entanglement. When the symmetry is broken, oscillatory modes transition into decay. As such that there is a drastic difference in behaviour between the broken and unbroken regimes.

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Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators

Cited by 21 publications

References 30 publications

Perturbative approach for strong and weakly coupled time-dependent non-Hermitian quantum systems

Perturbative approach for strong and weakly coupled time-dependent non-Hermitian quantum systems

Time-independent approximations for time-dependent optical potentials

Exotic entanglement for non-Hermitian Jaynes-Cummings Hamiltonians

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