Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption

Fyodorov, Yan V.; Savin, Dmitry V.; Sommers, Hans-Jürgen

doi:10.1088/0305-4470/38/49/017

Cited by 281 publications

(543 citation statements)

References 118 publications

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“…To this end let us stress that statis- [25] or system of randomly interacting fermions [26]. As to the theoretical framework, it mainly relies on studying the relevant non-Hermitian RMT [13,14], understanding of which has substantially improved over the last two decades; see, e.g., Ref.[27] and references therein. Note that the spatial properties related to the associated bi-orthogonal eigenvectors are known to a much lesser extent [18,[28][29][30].…”

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Statistics of Resonance Width Shifts as a Signature of Eigenfunction Nonorthogonality

2012

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We consider an open (scattering) quantum system under the action of a perturbation of its closed counterpart. It is demonstrated that the resulting shift of resonance widths is a sensitive indicator of the nonorthogonality of resonance wavefunctions, being zero only if those were orthogonal. Focusing further on chaotic systems, we employ random matrix theory to introduce a new type of parametric statistics in open systems, and derive the distribution of the resonance width shifts in the regime of weak coupling to the continuum. PACS numbers: 05.45.Mt, 03.65.Nk, 05.60.Gg The classical question of how energy levels of a quantum system get shifted under the action of a perturbation kept attracting renewed attention during the last two decades, mostly due to the established universality of such a parametric motion for systems with chaotic dynamics or intrinsic disorder [1,2]. In particular, the distributions and correlation functions of parametric derivatives of energy levels ("level velocities") [1][2][3] and their second derivatives ("level curvatures") [4] were found explicitly using the methods of random matrix theory (RMT) [5], and also verified, e.g., in microwave billiard experiments [6]. The other reason for such an interest is the recent development of the fidelity concept as the measure of the susceptibility of internal dynamics to perturbations [7].Experimentally, the energy levels are mostly accessible by means of a scattering setup [8]. From such a viewpoint, parametric dependencies of scattering characteristics, like phase shifts and time delays [9], conductances [10] and S matrix elements [11] were under intensive study. As to the parental discrete energy levels, they are converted into the resonances with finite lifetimes, since the original closed system becomes open (unstable). Such resonances manifest themselves in the energy-dependent S matrix as its poles in the complex energy plane, and can be analytically described as the complex eigenvalues of an effective non-Hermitian Hamiltonian [12][13][14]. Notably, the corresponding eigenfunctions are not orthogonal in the conventional sense but rather form a biorthogonal system. Their nonorthogonality plays an important role in many applications, e.g., describing interference in neutral kaon systems [15], influencing branching ratios of nuclear cross sections [16], and yielding excess noise in open laser resonators [17,18]. It also features in decay laws of quantum chaotic systems [19] and in dissipative quantum chaotic maps [20].In such a context the question of parametric motion of resonances and associated resonance states in open systems arises very naturally, but to the best of our knowledge has never been properly addressed. Our goal here is to begin filling in that gap by considering universal statistics of the shifts in the resonance widths under a generic perturbation in chaotic systems. In particular, we will demonstrate that such shifts are a clear manifestation of eigenstate nonorthogonality, thus providing a promising way to probe this ...

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Statistics of Resonance Width Shifts as a Signature of Eigenfunction Nonorthogonality

2012

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“…When such systems become open through their coupling to continuum channels, their bound states acquire decay widths and become resonances, but they are still expected to exhibit universal statistics [4]. Examples are the conductance fluctuations in quantum dots [5] and the statistics of the indirect molecular photodissociation cross section [6,7].…”

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“…For a classically chaotic system, these statistics can be derived from random matrix theory. In recent years, such a random matrix approach has been successfully used to model the statistics of resonances [4] and cross-section fluctuations in the photodissociation of classically chaotic molecules [8,9,10,11,12,13]. A semiclassical treatment was discussed in Refs.…”

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Fano interference and cross-section fluctuations in molecular photodissociation

et al. 2006

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We derive an expression for the total photodissociation cross section of a molecule incorporating both indirect processes that proceed through excited resonances, and direct processes. We show that this cross section exhibits generalized Beutler-Fano line shapes in the limit of isolated resonances. Assuming that the closed system can be modeled by random matrix theory, we derive the statistical properties of the photodissociation cross section and find that they are significantly affected by the direct processes. We identify a unique signature of the direct processes in the cross-section distribution in the limit of isolated resonances.

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Experimental Realization of Anti‐Unitary Wave‐Chaotic Photonic Topological Insulator Graphs Showing Kramers Degeneracy and Symplectic Ensemble Statistics

Ma,

Anlage

2023

Advanced Optical Materials

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Working in analogy with topological insulators in condensed matter, photonic topological insulators (PTI) have been experimentally realized, and protected electromagnetic edge‐modes have been demonstrated in such systems. Moreover, PTI technology also emulates a synthetic spin‐1/2 degree of freedom (DOF) in the reflectionless topological modes. The spin‐1/2 DOF is carried by quantum valley Hall (QVH)/quantum spin Hall (QSH) interface modes created from the bianisotropic meta waveguide platform and realized both in simulation and experiment. The PTI setting is employed to build an ensemble of wave chaotic 1D metric graphs that display statistical properties consistent with Gaussian symplectic ensemble (GSE) statistics. The two critical ingredients required to create a physical system in the GSE universality class, the half‐integer‐spin DOF and preserved time‐reversal invariance, are clearly realized in the QVH/QSH interface modes. The anti‐unitary T‐operator is identified for the PTI Hamiltonian underlying the experimental realization. An ensemble of PTI‐edgemode metric graphs are proposed and experimentally demonstrated. Then, the Kramers degeneracy of eigenmodes of the PTI‐graph systems is demonstrated with both numerical and experimental studies. Further, spectral statistical studies of the edgemode graphs are studied, and good agreement with the GSE theoretical predictions is found. The PTI chaotic graph structures present an innovative and easily extendable platform for continued future investigation of GSE systems.

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Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption

Cited by 281 publications

References 118 publications

Statistics of Resonance Width Shifts as a Signature of Eigenfunction Nonorthogonality

Statistics of Resonance Width Shifts as a Signature of Eigenfunction Nonorthogonality

Fano interference and cross-section fluctuations in molecular photodissociation

Experimental Realization of Anti‐Unitary Wave‐Chaotic Photonic Topological Insulator Graphs Showing Kramers Degeneracy and Symplectic Ensemble Statistics

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