Whispering gallery modes in open quantum billiards

Nazmitdinov, R. G.; Pichugin, K. N.; Rotter, I.; Šeba, P.

doi:10.1103/physreve.64.056214

Cited by 41 publications

(76 citation statements)

References 19 publications

(26 reference statements)

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“…For transport through open chaotic systems, classical ergodicity clearly has to be established faster than the lifetime of an electron in the system. Accordingly, the dynamics should not allow for too many short, nonergodic classical scattering trajectories going straight through the cavity, or hitting its boundary only very few times [25]. This requires that the inverse Lyapunov exponent λ −1 and the typical time τ B between bounces off the confinement are much smaller than the dwell time τ D , hence λ −1 , τ B ≪ τ D .…”

Section: Introductionmentioning

confidence: 99%

Quantum-to-classical correspondence in open chaotic systems

Schomerus¹,

Jacquod²

2005

J. Phys. A: Math. Gen.

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Abstract. We review properties of open chaotic mesoscopic systems with a finite Ehrenfest time τ E . The Ehrenfest time separates a short-time regime of the quantum dynamics, where wave packets closely follow the deterministic classical motion, from a long-time regime of fully-developed wave chaos. For a vanishing Ehrenfest time the quantum systems display a degree of universality which is well described by randommatrix theory. In the semiclassical limit, τ E becomes parametrically larger than the scattering time off the boundaries and the dwell time in the system. This results in the emergence of an increasing number of deterministic transport and escape modes, which induce strong deviations from random-matrix universality. We discuss these deviations for a variety of physical phenomena, including shot noise, conductance fluctuations, decay of quasibound states, and the mesoscopic proximity effect in Andreev billiards.

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Section: Introductionmentioning

confidence: 99%

Quantum-to-classical correspondence in open chaotic systems

Schomerus¹,

Jacquod²

2005

J. Phys. A: Math. Gen.

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“…Theoretical and experimental studies on open microwave cavities and also on quantum dots at low energy have shown that the individual properties of the states and their matching to the wave functions of the environment play an important role, indeed [8,9,[15][16][17][18]. Analytical considerations show that level repulsion as well as level clustering may appear.…”

Section: Introductionmentioning

confidence: 99%

“…The role of the matching of the wave functions for the dynamics of the system is studied further in [17]. Here, some special states are shown to accumulate the total coupling strength between system and environment which is expressed by the sum of the widths of all states lying in the energy region considered.…”

Section: Introductionmentioning

confidence: 99%

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Conductance of open quantum billiards and classical trajectories

et al. 2002

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We analyse the transport phenomena of 2D quantum billiards with convex boundary of different shape. The quantum mechanical analysis is performed by means of the poles of the S matrix while the classical analysis is based on the motion of a free particle inside the cavity along trajectories with a different number of bounces at the boundary. The value of the conductance depends on the manner the leads are attached to the cavity. The Fourier transform of the transmission amplitudes is compared with the length of the classical paths. There is good agreement between classical and quantum mechanical results when the conductance is achieved mainly by special short-lived states such as whispering gallery modes (WGM) and bouncing ball modes (BBM). In these cases, also the localization of the wave functions agrees with the picture of the classical paths. The S matrix is calculated classically and compared with the transmission coefficients of the quantum mechanical calculations for five modes in each lead. The number of modes coupled to the special states is effectively reduced.

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“…Both time scales are well separated from one another. A theoretical example are the shortlived whispering gallery modes in a small microwave cavity with convex boundary which coexist with many long-lived states, for details see [20][21][22]. An experimental example are the isobaric analogue resonances in medium -mass nuclei.…”

Section: Resonance Trapping and Dynamical Phase Transitionsmentioning

confidence: 99%

Dynamical Phase Transitions in Quantum Systems

Rotter¹

2010

JMP

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Many years ago Bohr characterized the fundamental differences between the two extreme cases of quantum mechanical many-body problems known at that time: between the compound states in nuclei at extremely high level density and the shell-model states in atoms at low level density. It is shown in the present paper that the compound nucleus states at high level density are the result of a dynamical phase transition due to which they have lost any spectroscopic relation to the individual states of the nucleus. The last ones are shell-model states which are of the same type as the shell-model states in atoms. Mathematically, dynamical phase transitions are caused by singular (exceptional) points at which the trajectories of the eigenvalues of the non-Hermitian Hamilton operator cross. In the neighborhood of these singular points, the phases of the eigenfunctions are not rigid. It is possible therefore that some eigenfunctions of the system align to the scattering wavefunctions of the environment by decoupling (trapping) the remaining ones from the environment. In the Schrödinger equation, nonlinear terms appear in the neighborhood of the singular points.

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Whispering gallery modes in open quantum billiards

Cited by 41 publications

References 19 publications

Quantum-to-classical correspondence in open chaotic systems

Quantum-to-classical correspondence in open chaotic systems

Conductance of open quantum billiards and classical trajectories

Dynamical Phase Transitions in Quantum Systems

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