arXiv subjects

H. Schomerus

Publications and source records attributed to H. Schomerus.

At least 37 records · Page 2Linked to original sources

arXiv2007

A model for chaotic dielectric microresonators

We develop a random-matrix model of two-dimensional dielectric resonators which combines internal wave chaos with the deterministic Fresnel laws for reflection and refraction at the interfaces. The model is used to investigate the statistics of the laser threshold and line width (lifetime and Petermann factor of the resonances) when the resonator is filled with an active medium. The laser threshold decreases for increasing refractive index $n$ and is smaller for TM polarization than for TE polarization, but is almost independent of the number of out-coupling modes $N$. The Petermann factor in the line width of the longest-living resonance also decreases for increasing $n$ and scales as $\sqrt{N}$, but is less sensitive to polarization. For resonances of intermediate lifetime, the Petermann factor scales linearly with $N$. These qualitative parametric dependencies are consistent with the random-matrix theory of resonators with small openings. However, for a small refractive index where the resonators are very open, the details of the statistics become non-universal. This is demonstrated by comparison with a particular dynamical model.

physics.optics↗

arXiv2007

Analytical Analysis of Single-Photon Correlations Emitted by Disordered Semiconductor Heterostructures

In a recent publication [Phys. Rev. Lett. 97, 227402 (2006), cond-mat/0611411], it has been demonstrated numerically that a long-range disorder potential in semiconductor quantum wells can be reconstructed reliably via single-photon interferometry of spontaneously emitted light. In the present paper, a simplified analytical model of independent two-level systems is presented in order to study the reconstruction procedure in more detail. With the help of this model, the measured photon correlations can be calculated analytically and the influence of parameters such as the disorder length scale, the wavelength of the used light, or the spotsize can be investigated systematically. Furthermore, the relation between the proposed angle-resolved single-photon correlations and the disorder potential can be understood and the measured signal is expected to be closely related to the characteristic strength and length scale of the disorder.

cond-mat.dis-nn↗

arXiv2006

Long-time signatures of short-time dynamics in decaying quantum-chaotic systems

We analyze the decay of classically chaotic quantum systems in the presence of fast ballistic escape routes on the Ehrenfest time scale. For a continuous excitation process, the form factor of the decay cross section deviates from the universal random-matrix result on the Heisenberg time scale, i.e. for times much larger than the time for ballistic escape. We derive an exact analytical description and compare our results with numerical simulations for a dynamical model.

nlin.CD↗

arXiv2005

Non-universality of Anderson localization in short-range correlated disorder

We provide an analytic theory of Anderson localization on a lattice with a weak short-range correlated disordered potential. Contrary to the general belief we demonstrate that even next-neighbor statistical correlations in the potential can give rise to strong anomalies in the localization length and the density of states, and to the complete violation of single parameter scaling. Such anomalies originate in additional symmetries of the lattice model in the limit of weak disorder. The results of numerical simulations are in full agreement with our theory, with no adjustable parameters.

cond-mat.dis-nn↗

arXiv2004

Exponential sensitivity to dephasing of electrical conduction through a quantum dot

According to random-matrix theory, interference effects in the conductance of a ballistic chaotic quantum dot should vanish $\propto(τ_ϕ/τ_{D})^{p}$ when the dephasing time $τ_ϕ$ becomes small compared to the mean dwell time $τ_{D}$. Aleiner and Larkin have predicted that the power law crosses over to an exponential suppression $\propto\exp(-τ_{E}/τ_ϕ)$ when $τ_ϕ$ drops below the Ehrenfest time $τ_{E}$. We report the first observation of this crossover in a computer simulation of universal conductance fluctuations. Their theory also predicts an exponential suppression $\propto\exp(-τ_{E}/τ_{D})$ in the absence of dephasing -- which is not observed. We show that the effective random-matrix theory proposed previously for quantum dots without dephasing explains both observations.

cond-mat.mes-hall↗

arXiv2004

Antibunched photons emitted by a quantum point contact out of equilibrium

Motivated by the experimental search for "GHz nonclassical light", we identify the conditions under which current fluctuations in a narrow constriction generate sub-Poissonian radiation. Antibunched electrons generically produce bunched photons, because the same photon mode can be populated by electrons decaying independently from a range of initial energies. Photon antibunching becomes possible at frequencies close to the applied voltage V, when the initial energy range of a decaying electron is restricted. The condition for photon antibunching in a narrow frequency interval below V is derived in terms of the eigenvalues T_n of the transmission matrix. This condition is satisfied in a quantum point contact, where only a single T_n differs from 0 or 1. The photon statistics is then a superposition of binomial distributions.

cond-mat.mes-hall↗

arXiv2003

Electron-electron dynamics in laser-induced nonsequential double ionization

For the description of nonsequential double ionization (NSDI) of rare-gas atoms by a strong linearly polarized laser field, the quantum-mechanical $S$-matrix diagram that incorporates rescattering impact ionization is evaluated in the strong-field approximation. We employ a uniform approximation, which is a generalization of the standard saddle-point approximation. We systematically analyze the manifestations of the electron-electron interaction in the momentum distributions of the ejected electrons: for the interaction, by which the returning electron frees the bound electron, we adopt either a (three-body) contact interaction or a Coulomb interaction, and we do or do not incorporate the mutual Coulomb repulsion of the two electrons in their final state. In particular, we investigate the correlation of the momentum components parallel to the laser-field polarization, with the transverse momentum components either restricted to certain finite ranges or entirely summed over. In the latter case, agreement with experimental data is best for the contact interaction and without final-state repulsion. In the former, if the transverse momenta are restricted to small values, comparison of theory with the data shows evidence of Coulomb effects. We propose that experimental data selecting events with small transverse momenta of \textit{both} electrons are particularly promising in the elucidation of the dynamics of NSDI. Also, a classical approximation of the quantum-mechanical $S$ matrix is formulated and shown to work very well inside the classically allowed region.

physics.atom-ph↗

arXiv2003

Coulomb repulsion and quantum-classical correspondence in laser-induced nonsequential double ionization

The influence of electron-electron Coulomb repulsion on nonsequential double ionization of rare-gas atoms is investigated. Several variants of the quantum-mechanical transition amplitude are evaluated that differ by the form of the inelastic electron-ion rescattering and whether or not Coulomb repulsion between the two electrons in the final state is included. For high laser intensity, an entirely classical model is formulated that simulates the rescattering scenario.

physics.atom-ph↗

arXiv2003

Short-distance wavefunction statistics in one-dimensional Anderson localization

We investigate the short-distance statistics of the local density of states nu in long one-dimensional disordered systems, which display Anderson localization. It is shown that the probability distribution function P(nu) can be recovered from the long-distance wavefunction statistics, if one also uses parameters that are irrelevant from the perspective of two-parameter scaling theory.

cond-mat.dis-nn↗

arXiv2003

Dynamical model for the quantum-to-classical crossover of shot noise

We use the open kicked rotator to model the chaotic scattering in a ballistic quantum dot coupled by two point contacts to electron reservoirs. By calculating the system-size-over-wave-length dependence of the shot noise power we study the crossover from wave to particle dynamics. Both a fully quantum mechanical and a semiclassical calculation are presented. We find numerically in both approaches that the noise power is reduced exponentially with the ratio of Ehrenfest time and dwell time, in agreement with analytical predictions.

cond-mat.mes-hall↗

arXiv2003

Quantum Andreev map: A paradigm of quantum chaos in superconductivity

We introduce quantum maps with particle-hole conversion (Andreev reflection) and particle-hole symmetry, which exhibit the same excitation gap as quantum dots in the proximity to a superconductor. Computationally, the Andreev maps are much more efficient than billiard models of quantum dots. This makes it possible to test analytical predictions of random-matrix theory and semiclassical chaos that were previously out of reach of computer simulations. We have observed the universal distribution of the excitation gap for large Lyapunov exponent and the logarithmic reduction of the gap when the Ehrenfest time becomes comparable to the quasiparticle dwell time.

cond-mat.mes-hall↗

arXiv2003

Anomalies and non-log-normal tails in one-dimensional localization with power-law disorder

Within a general framework, we discuss the wave function statistics in the Lloyd model of Anderson localization on a one-dimensional lattice with a Cauchy distribution for the random on-site potential. We demonstrate that already in leading order in the disorder strength, there exists a hierarchy of anomalies in the probability distributions of the wave function, the conductance, and the local density of states, for every energy which corresponds to a rational ratio of wave length to the lattice constant. We also show that these distribution functions do have power-law rather then log-normal tails and do not display universal single-parameter scaling. These peculiarities persist in any model with power-law tails of the disorder distribution function.

cond-mat.dis-nn↗

arXiv2002

Random matrix theory of proximity effect in disordered wires

We study analytically the local density of states in a disordered normal-metal wire at ballistic distance to a superconductor. Our calculation is based on a scattering-matrix approach, which concerns for wave-function localisation in the normal metal, and extends beyond the conventional semiclassical theory based on Usadel and Eilenberger equations. We also analyse how a finite transparency of the NS interface modifies the spectral proximity effect and demonstrate that our results agree in the dirty diffusive limit with those obtained from the Usadel equation.

cond-mat.dis-nn↗

arXiv2002

Shot noise and transport in small quantum cavities with large openings

We present a dynamical analysis of the transport through small quantum cavities with large openings. The systematic suppression of shot noise is used to distinguish direct, deterministic from indirect, indeterministic transport processes. The analysis is based on quantum mechanical calculations of $S$ matrices and their poles for quantum billiards with convex boundaries of different shape and two open channels in each of the two attached leads. Direct processes are supported when special states couple strongly to the leads, and can result in deterministic transport as signified by a striking system-specific suppression of shot noise.

cond-mat.mes-hall↗

arXiv2002

Band-center anomaly of the conductance distribution in one-dimensional Anderson localization

We analyze the conductance distribution function in the one-dimensional Anderson model of localization, for arbitrary energy. For energy at the band center the distribution function deviates from the universal form assumed in single-parameter scaling theory. A direct link to the break-down of the random-phase approximation is established. Our findings are confirmed by a parameter-free comparison to the results of numerical simulations.

cond-mat.dis-nn↗

arXiv2002

Shot noise in generic quantum dots: crossover from ballistic to diffusive transport

We study shot noise for generic quantum dots coupled to two leads and allow for an arbitrary strength of diffractive impurity scattering inside the dots. The ballistic quantum dots possess a mixed classical phase space, where regular and chaotic regions coexist. In absence of disorder, the noise is systematically suppressed below the universal value of fully chaotic systems, by an amount which varies with the positions of the leads. This suppression is due to the deterministic nature of transport through regular regions and along short chaotic trajectories, and disappears by increasing the scattering rate, which is incorporated by using the Poisson kernel of random matrix theory.

cond-mat.mes-hall↗

arXiv2002

Shot Noise in Ballistic Quantum Dots with a Mixed Classical Phase Space

We investigate shot noise for quantum dots whose classical phase space consists of both regular and chaotic regions. The noise is systematically suppressed below the universal value of fully chaotic systems, by an amount which varies with the positions of the leads. We analyze the dynamical origin of this effect by a novel way to incorporate diffractive impurity scattering. The dependence of the shot noise on the scattering rate shows that the suppression arises due to the deterministic nature of transport through regular regions and along short chaotic trajectories. Shot noise can be used to probe phase-space structures of quantum dots with generic classical dynamics.

cond-mat.mes-hall↗

arXiv2002

High-order above-threshold ionization: the uniform approximation and the effect of the binding potential

A versatile semiclassical approximation for intense laser-atom processes is presented. This uniform approximation is no more complicated than the frequently-used multi-dimensional saddle-point approximation and far superior, since it applies for all energies, both close to as well as away from classical cutoffs. In the latter case, it reduces to the standard saddle-point approximation. The uniform approximation agrees accurately with numerical evaluations for potentials, for which these are feasible, and constitutes a practicable method of calculation in general. The method is applied to the calculation of high-order above-threshold ionization spectra with various binding potentials: Coulomb, Yukawa, and shell potentials which may model C$_{60}$ molecules or clusters. The shell potentials generate high-order ATI spectra that are more structured and may feature an apparently higher cutoff.

physics.atom-ph↗