Resonances and adiabatic invariance in classical and quantum scattering theory

Jain, Sudhir R.

doi:10.1016/j.physleta.2004.12.014

Cited by 8 publications

(6 citation statements)

References 17 publications

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“…The outer resonances constitute extremely broad background in the density of states because of their quite high leakage and they should be take into account in the study of the trace formula in open cavity [22,33].…”

Section: Discussionmentioning

confidence: 99%

“…In Using BEM, we showed that the outer resonances universally exist as one group of QNMs in two-dimensional dielectric cavities irrespective of the geometry of cavity and, especially, exist as the nearly degenerate states in the slightly deformed cavity. The outer resonances constitute extremely broad background in the density of states because of their quite high leakage and they should be take into account in the study of the trace formula in open cavity [22,33].…”

Section: Discussionmentioning

confidence: 99%

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Outer resonances and effective potential analogy in two-dimensional dielectric cavities

et al. 2010

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Outer resonances are studied as one type of quasinormal modes in two-dimensional dielectric cavities with refractive index n > 1. The outer resonances can be verified as the resonances which survive only outside the cavity in the small opening limit of the dielectric disk. We have confirmed that the outer resonances universally exist in deformed cavities irrespective of the geometry of cavity and they split into nearly degenerate states in slightly deformed cavity. Also we have introduced an extended interpretation of the effective potential analogy for the outer resonances. Since most outer resonances in the dielectric cavities have quite high leakages, they would affect to the broad background in the density of states. But, for TE polarization case, relatively low-leaky outer resonances exist and it presents the possibility that they can interact with the inner resonances.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Outer resonances and effective potential analogy in two-dimensional dielectric cavities

et al. 2010

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“…on the right of the potential range, ±e i(−Knx−Ent/h) on the left of the potential range, (22) where the sign of the second line on the right-hand side depends on whether the solution is odd or even, we obtain…”

Section: Particle Number Conservationmentioning

confidence: 97%

Probabilistic interpretation of resonant states

2009

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We provide probabilistic interpretation of resonant states. We do this by showing that the integral of the modulus square of resonance wave functions (i.e., the conventional norm) over a properly expanding spatial domain is independent of time, and therefore leads to probability conservation. This is in contrast with the conventional employment of a bi-orthogonal basis that precludes probabilistic interpretation, since wave functions of resonant states diverge exponentially in space. On the other hand, resonant states decay exponentially in time, because momentum leaks out of the central scattering area. This momentum leakage is also the reason for the spatial exponential divergence of resonant state. It is by combining the opposite temporal and spatial behaviours of resonant states that we arrive at our probabilistic interpretation of these states. The physical need to normalize resonant wave functions over an expanding spatial domain arises because particles leak out of the region which contains the potential range and escape to infinity, and one has to include them in the total count of particles.

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“…In the comprehensive review [16] a number of definitions of the tunneling time have been given, among them the so-called phase time or group delay time and dwell time. The energy integral of timedelay, as shown in [17], is an adiabatic invariant in quantum scattering theory, and corresponds classically to an open image in phase space. It has long been considered that the two contributions of asymptotic phase times, the time spent in the barrier region and the self-interference delay during the approach to the barrier, may not be disentangled.…”

Section: Introductionmentioning

confidence: 99%