Spectroscopic properties of large open quantum-chaotic cavities with and without separated time scales

Bulgakov, Evgeny N.; Rotter, I.

doi:10.1103/physreve.73.066222

Cited by 4 publications

(1 citation statement)

References 27 publications

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“…Autonomous systems are much richer than maps as they display an additional, even more ubiquitous phenomenon related to quantum-to-classical correspondence, namely, the formation of resonance chains encountered in various systems such as quantum cavities with large openings [34,35], dielectric microresonators with low index materials [36,37,38,39,40], and models of mathematical interest such as convex co-compact surfaces (Schottky surfaces) [28]). The simplest resonance chains are supported by a single ballistic trajectory, resulting in a sequence of states in close analogy to those of a particle in a one-dimensional box with leaking walls [41].…”

Section: Introductionmentioning

confidence: 99%

Formation and interaction of resonance chains in the open three-disk system

et al. 2014

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In ballistic open quantum systems, one often observes that the resonances in the complex-energy plane form a clear chain structure. Taking the open three-disk system as a paradigmatic model system, we investigate how this chain structure is reflected in the resonance states and how it is connected to the underlying classical dynamics. Using an efficient scattering approach, we observe that resonance states along one chain are clearly correlated, while resonance states of different chains show an anticorrelation. Studying the phase-space representations of the resonance states, we find that their localization in phase space oscillates between different regions of the classical trapped set as one moves along the chains, and that these oscillations are connected to a modulation of the resonance spacing. A single resonance chain is thus not a WKB quantization of a single periodic orbit, but the structure of several oscillating chains arises from the interaction of several periodic orbits. We illuminate the physical mechanism behind these findings by combining the semiclassical cycle expansion with a quantum graph model.

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Section: Introductionmentioning

confidence: 99%

Formation and interaction of resonance chains in the open three-disk system

et al. 2014

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A non-Hermitian Hamilton operator and the physics of open quantum systems

Rotter

2009

J. Phys. A: Math. Theor.

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785

1,040

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A powerful method for the description of open quantum systems is the Feshbach projection operator (FPO) technique. In this formalism, the whole function space is divided into two subspaces that are coupled with one another. One of the subspaces contains the wave functions localized in a certain finite region while the continuum of extended scattering wave functions is involved in the other subspace. The Hamilton operator of the whole system is Hermitian, that of the localized part is, however, non-Hermitian. This non-Hermitian Hamilton operator H eff represents the core of the FPO method in present-day studies. It gives a unified description of discrete and resonance states. Furthermore, it contains the time operator. The eigenvalues z λ and eigenfunctions φ λ of H eff are an important ingredient of the S matrix. They are energy dependent. The phases of the φ λ are, generally, nonrigid. Most interesting physical effects are caused by the branch points in the complex plane. On the one hand, they cause the avoided level crossings that appear as level repulsion or widths bifurcation in approaching the branch points under different conditions. On the other hand, observable values are usually enhanced and accelerated in the vicinity of the branch points. In most cases, the theory is time asymmetric. An exception are the PT symmetric bound states in the continuum appearing in space symmetric systems due to the avoided level crossing phenomenon in the complex plane. In the paper, the peculiarities of the FPO method are considered and three typical phenomena are sketched: (i) the unified description of decay and scattering processes, (ii) the appearance of bound states in the continuum and (iii) the spectroscopic reordering processes characteristic of the regime with overlapping resonances.

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Spin chaos manifestation in a driven quantum billiard with spin-orbit coupling

et al. 2013

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The coupling of orbital and spin degrees of freedom is the source of many interesting phenomena. Here, we study the electron dynamics in a quantum billiard driven by a periodic electric field-a mesoscopic rectangular quantum dot-with spin-orbit coupling. We find that the spatial and temporal profiles of the observables demonstrate the transition to chaotic dynamics with qualitative modifications of the power spectra and patterns of probability and spin density. The time dependence of the wavefunctions and spin density indicates spin-charge separation seen in the decay of the spin-charge density correlators. Experimental verification of this spin chaos effect can lead to a better understanding of the interplay between spin and spatial degrees of freedom in mesoscopic systems.

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Spectroscopic properties of large open quantum-chaotic cavities with and without separated time scales

Cited by 4 publications

References 27 publications

Formation and interaction of resonance chains in the open three-disk system

Formation and interaction of resonance chains in the open three-disk system

A non-Hermitian Hamilton operator and the physics of open quantum systems

Spin chaos manifestation in a driven quantum billiard with spin-orbit coupling

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