Global versus Local Billiard Level Dynamics: The Limits of Universality

Barth, Michael; Kuhl, Ulrich; Stöckmann, H.‐J.

doi:10.1103/physrevlett.82.2026

Cited by 54 publications

(62 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Several studies support that, in general, the elements of ∂H/∂X have themselves also Gaussian random entries (see, for instance, Ref. 16 and references therein). We choose their variance to be (λ/M X c ) 2 .…”

Section: Pumping Currentsmentioning

confidence: 99%

Statistical fluctuations of pumping and rectification currents in quantum dots

2004

View full text Add to dashboard Cite

We investigate the statistical fluctuations of currents in chaotic quantum dots induced by pumping and rectification at finite temperature and in the presence of dephasing. In open quantum dots, dc currents can be generated by the action of two equal-frequency ac gate voltages. The adiabatic regime occurs when the driving frequency is smaller than the electron inverse dwell time. Using numerical simulations complemented by semiclassical calculations, we consider both limits of small and large number of propagating channels in the leads when time-reversal symmetry is fully broken. We find that at intermediate temperature regimes, namely, kBT < ∼ ∆, where ∆ is the mean singleparticle level spacing, thermal smearing suppresses the current amplitude more effectively than dephasing. Motivated by recent theoretical and experimental works, we also study the statistics of rectified currents in the presence of a parallel, Zeeman splitting, magnetic field.

show abstract

Section: Pumping Currentsmentioning

confidence: 99%

Statistical fluctuations of pumping and rectification currents in quantum dots

2004

View full text Add to dashboard Cite

show abstract

“…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].…”

mentioning

confidence: 99%

“…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].…”

mentioning

confidence: 99%

Statistics of Resonance Width Shifts as a Signature of Eigenfunction Nonorthogonality

2012

View full text Add to dashboard Cite

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 ...

show abstract

“…We obtain a sharp peak atε = 0 which is similar to the result of the microwave experiment for the case when the local level dynamics are concerned. [13] This non-Gaussian behavior suggests that the wave functions for the scattering quasiparticles in this regime is still localized. [12] …”

Section: Universality In Level Velocity Distributionmentioning

confidence: 99%

“…[9][10][11][12] For the quantum chaotic systems, there are experimental studies of the microwave billiards where the Gaussian distribution of level velocities has been observed. [13] The motivation of the current study is to investigate the universal behavior of the level velocities for low energy excitation spectra inside a moving vortex core dragged through a layered superconductor over a wide region from moderately clean to dirty phase. In the presence of disorder, the Hamiltonian for the scattering quasi-particles between the excitation levels inside the vortex core becomes the Lie algebra Sp(2N), and it belongs to the class C of the classification of the Atland-Zirnbauer.…”

Section: Introductionmentioning

confidence: 99%

Vortex dissipation and level dynamics for layered superconductors with impurities

Fujita¹

2001

Phys. Rev. B

View full text Add to dashboard Cite

We study parametric level statistics of the discretized excitation spectra inside a moving vortex core in layered superconductors with impurities. The universal conductivity is evaluated numerically for the various values of rescaled vortex velocities κ from the clean case to the dirty limit case. The random matrix theoretical prediction is verified numerically in the large κ regime. On the contrary in the low velocity regime, we observe σ xx ∝ κ 2/3 which is consistent with the theoretical result for the super-clean case, where the energy dissipation is due to the Landau-Zener transition which takes place at the points called "avoided crossing".

show abstract

Global versus Local Billiard Level Dynamics: The Limits of Universality

Cited by 54 publications

References 24 publications

Statistical fluctuations of pumping and rectification currents in quantum dots

Statistical fluctuations of pumping and rectification currents in quantum dots

Statistics of Resonance Width Shifts as a Signature of Eigenfunction Nonorthogonality

Vortex dissipation and level dynamics for layered superconductors with impurities

Contact Info

Product

Resources

About