Coherent states with complex frequency

Papaloucas, L. C.

doi:10.1007/bf02726738

Cited by 4 publications

(2 citation statements)

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“…Simple harmonic oscillators with complex angular frequencies have also been studied in the context of squeezed states [26], coherent states [27], tunneling phenomenon in non-hermitian theory [28] and resonant states [29]. In general, the eigenvalues for the above cases are complex and the time-evolution is non-unitary.…”

Section: A Simple Harmonic Oscillatormentioning

confidence: 99%

“…It is worth mentioning here that simple harmonic oscillators with complex angular frequencies appear in the description of electromagnetic pulse propagation in a free-electron laser [25]. Simple harmonic oscillators with complex angular frequencies have also been studied in the context of squeezed states [26], coherent states [27], tunneling phenomenon in non-Hermitian theory [28] and resonant states [29]. In general, the eigenvalues for the above cases are complex and the time evolution is non-unitary.…”

Section: Simple Harmonic Oscillatormentioning

confidence: 99%

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On the construction of a pseudo-Hermitian quantum system with a pre-determined metric in the Hilbert space

Ghosh¹

2010

J. Phys. A: Math. Theor.

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A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum system in terms of operators those are hermitian with respect to a pre-determined positive definite metric in the Hilbert space. Appropriate combinations of these operators result in a large number of pseudo-hermitian quantum systems admitting entirely real spectra and unitary time evolution. The examples considered include simple harmonic oscillators with complex angular frequencies, Stark(Zeeman) effect with non-hermitian interaction, non-hermitian general quadratic form of N boson(fermion) operators, symmetric and asymmetric XXZ spin-chain in complex magnetic field, non-hermitian Haldane-Shastry spin-chain and LipkinMeshkov-Glick model.

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Section: A Simple Harmonic Oscillatormentioning

confidence: 99%

Section: Simple Harmonic Oscillatormentioning

confidence: 99%

On the construction of a pseudo-Hermitian quantum system with a pre-determined metric in the Hilbert space

Ghosh¹

2010

J. Phys. A: Math. Theor.

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Squeezing in the SU(1,1) Group

Aliaga

Crespo

Proto

1991

Instabilities and Nonequilibrium Structures III

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E(2)-symmetric two-mode sheared states

Kim

Yeh

1992

Journal of Mathematical Physics

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It is noted that the symmetry of two-mode squeezed states of light is governed by the group Sp(4) that is locally isomorphic to O(3,2). This group has subgroups that are locally isomorphic to the two-dimensional Euclidean group. Two-mode states having the E(2) symmetry are constructed. The translation-like transformations of this symmetry group shear the Wigner distribution function defined over the four-dimensional phase space consisting of two pairs of canonical variables. Sheared states are constructed in the Schrödinger picture of quantum mechanics and in the Fock space for photon numbers. It is shown that the Wigner phase-space picture is a convenient representation of quantum mechanics for calculating measurable quantities of the sheared states.

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Coherent states with complex frequency

Cited by 4 publications

References 10 publications

On the construction of a pseudo-Hermitian quantum system with a pre-determined metric in the Hilbert space

On the construction of a pseudo-Hermitian quantum system with a pre-determined metric in the Hilbert space

Squeezing in the SU(1,1) Group

E(2)-symmetric two-mode sheared states

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