Squeezed states and Helmholtz spectra

Delgado, Francisco; Mielnik, Bogdan; Reyes, M.

doi:10.1016/s0375-9601(97)00882-7

Cited by 14 publications

(8 citation statements)

References 28 publications

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“…The description of the radiative phenomena in quantum field theories (QFT) involves some intuitive dealings with perturbative divergences. Some of them depart from some basic bound state Hamiltonian H 0 which defines the initial 40) and (42). All remaining separatrix branches (the 'blue ones') host (41) and (43).…”

Section: The Non-perturbative Aspectsmentioning

confidence: 99%

Ion traps: some semiclassical observations

Mielnik

Ramirez²

2010

Phys. Scr.

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The unitary evolution operators generated by periodically varying elastic potentials including the Mathieu case are studied. The evolution operations in the stability areas of the Strutt diagram admit effective (Floquet) Hamiltonians generalizing the orthodox oscillators. The points on the separatrices represent two exceptional types of unitary operations, imitating (in a soft way) the results of the sudden δ-like kicks of the elastic potential, or the distorted free evolution (in accelerated, slowed down or even negative time). In all domains the dynamical phenomena illustrate a non-trivial relation between the micro- and macroscopic motion scales.

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Section: The Non-perturbative Aspectsmentioning

confidence: 99%

Ion traps: some semiclassical observations

Mielnik

Ramirez²

2010

Phys. Scr.

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“…Luckily among the integrable cases are the so-called quadratic Hamiltonians that attracted substantial attention over the years in view of their great importance to many advanced quantum problems. Examples can be found in quantum and physical optics [34], [74], [114], [116], physics of lasers and masers [128], [142], [131], [148], molecular spectroscopy [41], quantum chemistry, quantization of mechanical systems [31], [45], [46], [47], [50], [75], [77] and Hamiltonian cosmology [9], [51], [52], [58], [64], [114], [124], [125], [126]. They include coherent states [95], [96], [97], [74] and Berry's phase [7], [8], [18], [57], [84], [105], asymptotic and numerical methods [54], [68], [78], [103], [107], charged particle traps [94] and motion in uniform magnetic fields [26], [29], [39],…”

Section: An Introductionmentioning

confidence: 99%

Quantum integrals of motion for variable quadratic Hamiltonians

2010

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We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the timedependent Schrödinger equation with variable quadraticHamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.

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“…, s = e −λ do not resemble the standard evolution operations; yet both can be induced by time-dependent magnetic fields [68][69][70][71]. In general, in a well-equipped laboratory, the quantum mechanical systems (of positive energy) are completely manipulable [72][73][74] (in spite of the 'difficult' configurations [75,76]), a fact of considerable interest for quantum control computing [77,78].…”

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confidence: 99%