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Exceptional points are spectral degeneracies of non-Hermitian systems where both eigenfrequencies and eigenmodes coalesce. The eigenfrequency sensitivities near an exceptional point are significantly enhanced, whereby they diverge directly at the exceptional point. Capturing this enhanced sensitivity is crucial for the investigation and optimization of exceptional-point-based applications, such as optical sensors. We present a numerical framework, based on contour integration and algorithmic differentiation, to accurately and efficiently compute eigenfrequency sensitivities near exceptional points. We demonstrate the framework to an optical microdisk cavity and derive a semi-analytical solution to validate the numerical results. The computed eigenfrequency sensitivities are used to track the exceptional point along an exceptional surface in the parameter space. The presented framework can be applied to any kind of resonance problem, e.g., with arbitrary geometry or with exceptional points of arbitrary order.

Open systems with non-Hermitian degeneracies called exceptional points show a significantly enhanced response to perturbations in terms of large energy splittings induced by a small perturbation. This reaction can be quantified by the spectral response strength of the exceptional point. We extend the underlying theory to the general case where the dimension of the Hilbert space is larger than the order of the exceptional point. This generalization allows us to demonstrate an intriguing phenomenon: The spectral response strength of an exceptional point increases considerably and may even diverge to infinity under a parameter variation that eventually increases the order of the exceptional point. This dramatic behavior is in general not accompanied by a divergence of the energy eigenvalues and is shown to be related to the well-known divergence of Petermann factors near exceptional points. Finally, an accurate and robust numerical scheme for the computation of the spectral response strength based on the general theory and residue calculus is presented., Comment: 11 pages, 5 figures

The Petermann factor and the phase rigidity are convenient measures for various aspects of open quantum and wave systems, such as the sensitivity of energy eigenvalues to perturbations or the magnitude of quantum excess noise in lasers. We discuss the behavior of these two important quantities near non-Hermitian degeneracies, so-called exceptional points. For small generic perturbations, we derive analytically explicit formulas which reveal a relation to the spectral response strength of the exceptional point. These formulas shed light on the possibilities for enhanced sensing in passive systems. The predictions of the general theory are successfully compared to analytical solutions of a toy model. Moreover, it is demonstrated that the connection between the Petermann factor and the spectral response strength provides the basis for an efficient numerical scheme to calculate the latter. Our theory is also important in the presence of the unavoidable imperfections in the fabrication of exceptional points as it allows to determine of what is left of the sensitivity for such imperfect exceptional points studied in experiments., Comment: 9 pages, 4 figures

Non-Hermitian wave engineering has attracted a surge of interest in photonics in recent years. One of the prominent phenomena is coherent perfect absorption (CPA), in which the annihilation of electromagnetic scattering occurs by destructive interference of multiple incident waves. This concept has been implemented in various platforms to demonstrate real-time control of absorption, scattering and radiation by varying the relative phase of the excitation signals. However, so far these studies have been limited to simple photonic systems involving single or few modes at well-defined resonant frequencies. Realizing CPA in more complex photonic systems is challenging because it typically requires engineering the interplay of a large number of resonances featuring large spatial complexity within a narrow frequency range. Here, we extend the paradigm of coherent control of light to a complex photonic system involving more than 1,000 optical modes in a chaotic microresonator. We efficiently model the optical fields within a quasi-normal mode (QNM) expansion, and experimentally demonstrate chaotic CPA states, as well as their non-Hermitian degeneracies, which we leverage to efficiently control the cavity excitation through the input phases of multiple excitation channels. Our results shed light on the universality of non-Hermitian physics beyond simple resonant systems, paving the way for new opportunities in the science and technology of complex nanophotonic systems by chaotic wave interference., Comment: 22 pages, 5 figures

Higher-order exceptional points in the spectrum of non-Hermitian Hamiltonians describing open quantum or wave systems have a variety of potential applications in particular in optics and photonics. However, the experimental realization is notoriously difficult. Recently, Q. Zhong et al. [Phys. Rev. Lett. 125, 203602 (2020)] have introduced a robust construction where a unidirectional coupling of two subsystems having exceptional points of the same order leads generically to a single exceptional point of twice the order. Here, we investigate this scheme in a different manner by exploiting the nilpotency of the traceless part of the involved Hamiltonians. We generalize the scheme and derive a simple formula for the spectral response strength of the composite system hosting a higher-order exceptional point. Its relation to the spectral response strengths of the subsystems is discussed. Moreover, we investigate nongeneric perturbations. The results are illustrated with an example., Comment: 8 pages, 3 figures

Exceptional points are non-Hermitian degeneracies in open quantum and wave systems at which not only eigenenergies but also the corresponding eigenstates coalesce. This is in strong contrast to degeneracies known from conservative systems, so-called diabolic points, at which only eigenenergies degenerate. Here we connect these two kinds of degeneracies by introducing the concept of the distance of a given exceptional point in matrix space to the set of diabolic points. We prove that this distance determines an upper bound for the response strength of a non-Hermitian system with this exceptional point. A small distance therefore implies a weak spectral response to perturbations and a weak intensity response to excitations. This finding has profound consequences for physical realizations of exceptional points that rely on perturbing a diabolic point. Moreover, we exploit this concept to analyze the limitations of the spectral response strength in passive systems. A number of optical and photonics systems are investigated to illustrate the theory., Comment: 11 pages, 4 figures

Open quantum and wave systems exhibit exotic degeneracies at exceptional points in parameter space that have attracted considerable attention in various fields of physics, including optics and photonics. One reason is the strong response of open systems at such degeneracies to external perturbations and excitations. We introduce two characteristics of exceptional points that quantify the response in terms of energy eigenvalues and eigenstates, intensity, and dynamics. The concept is verified for several physically relevant examples. This work provides a new perspective on the physics of exceptional points., Comment: 13 pages, 5 figures

Recent experiments have demonstrated the feasibility of exploiting spectral singularities in open quantum and wave systems, so-called exceptional points, for sensors with strongly enhanced sensitivity. Here, we study theoretically the influence of classical parametric noise on the performance of such sensors. Within a Lindblad-type formalism for stochastic Hamiltonians we discuss the resolvability of frequency splittings and the dynamical stability of the sensor, and show that these properties are interrelated. Of central importance are the different features of exceptional points in the spectra of the Hamiltonian and the corresponding Liouvillian. Two realistic examples, a parity-time-symmetric dimer and a whispering-gallery microcavity with asymmetric backscattering, illustrate the findings., Comment: 10 pages, 3 figures

We analyze the scattering dynamics and spectrum of a quantum particle on a tight-binding lattice subject to a non-Hermitian (purely imaginary) local potential. The reflection, transmission and absorption coefficients are studied as a function of the strength of this absorbing potential. The system is found to have an exceptional point at a certain strength of the potential. Unusually, all (or nearly all) of the spectrum pairs up into mutually coalescing eigenstate pairs at this exceptional point. At large potential strengths, the absorption coefficient decreases and the effect of the imaginary potential is similar to that of a real potential. We quantify this similarity by utilizing properties of a localized eigenstate., Comment: v2: Updated with changes made for publication in Phys. Rev. A. 14 pages, 14 figures. v1: 12 pages, 14 figures

It is known that the overlap of two energy eigenstates in a decaying quantum system is bounded from above by a function of the energy detuning and the individual decay rates. This is usually traced back to the positive definiteness of an appropriately defined decay operator. Here, we show that the weaker and more realistic condition of positive semi-definiteness is sufficient. We prove also that the bound becomes an equality for the case of single-channel decay. However, we show that the condition of positive semi-definiteness can be spoiled by quantum backflow. Hence, the overlap of quasibound quantum states subjected to outgoing-wave conditions can be larger than expected from the bound. A modified and less stringent bound, however, can be introduced. For electromagnetic systems, it turns out that a modification of the bound is not necessary due to the linear free-space dispersion relation. Finally, a geometric interpretation of the nonorthogonality bound is given which reveals that in this context the complex energy space can seen as a surface of constant negative curvature., Comment: 9 pages, 3 figures

The excitation of semiconductor quantum dots often involves an attached wetting layer with delocalized single-particle energy eigenstates. These wetting-layer states are usually approximated by (orthogonalized) plane waves. We show that this approach is too crude. Even for a simple model based on the effective-mass approximation and containing one or a few lens-shaped quantum dots in a rectangular wetting layer, the wetting-layer states typically show a substantially irregular and complex morphology. To quantify this complexity we use concepts from the field of quantum chaos such as spectral analysis of energy levels, amplitude distributions, and localization of energy eigenstates., Comment: 12 pages, 13 figures

The perturbation theory by L. Ge et al. [Phys. Rev. A 87, 023833] for transverse-electric polarized modes in weakly deformed microdisks omits terms related to the variation of the normal derivative of the magnetic field along the boundary. Here we show that these terms are necessary to accurately describe microdisks with a strongly winding boundary. In particular, it is demonstrated that the corrected perturbation theory allows to describe the counterintuitive phenomenon of Q-factor enhancement due to weak boundary deformation. We discuss in detail the microflower cavity and the limacon cavity. Good agreement of the corrected perturbation theory with full numerical results is observed., Comment: 13 pages, 9 figures

Spontaneous symmetry breaking has revolutionized the understanding in numerous fields of modern physics. Here, we theoretically demonstrate the spontaneous time-reversal symmetry breaking in a cavity quantum electrodynamics system in which an atomic ensemble interacts coherently with a single resonant cavity mode. The interacting system can be effectively described by two coupled oscillators with positive and negative mass when the two-level atoms are prepared in their excited states. The occurrence of symmetry breaking is controlled by the atomic detuning and the coupling to the cavity mode, which naturally divides the parameter space into the symmetry broken and symmetry unbroken phases. The two phases are separated by a spectral singularity, a so-called exceptional point, where the eigenstates of the Hamiltonian coalesce. When encircling the singularity in the parameter space, the quasi-adiabatic dynamics shows chiral mode switching which enables topological manipulation of quantum states.

Numerical methods for the description of nonequilibrium many-particle quantum systems such as equation of motion techniques often cannot compute the full statistics of observables but only moments of it, such as mean, variance and higher-order moments. We employ here the maximum entropy method to numerically construct unbiased statistics based on the knowledge of moments. We verify the feasibility of the proposed method by numerical simulation of a simple birth-death model for quantum-dot-microcavity lasers, where the full photon and carrier statistics are available for comparison. We show that not only the constructed statistics but also the computed entropy and the Lagrange multipliers, which appear here as a byproduct, provide valuable insight into the physics of the considered system. For example, the entropy reveals that, in contrast to common wisdom, the photon statistics of the microcavity laser above threshold is better described by a Gaussian distribution than by a Poisson distribution. Our approach is general and can be applied to many other systems emerging in physics and related fields.

A photon-number resolving transition edge sensor (TES) is used to measure the photon-number distribution of two microcavity lasers. The investigated devices are bimodal microlasers with similar emission intensity and photon statistics with respect to the photon auto-correlation. Both high-$\beta$ microlasers show partly thermal and partly coherent emission around the lasing threshold. For higher pump powers, the strong mode of microlaser A emits Poissonian distributed photons while the emission of the weak mode is thermal. In contrast, laser B shows a bistability resulting in overlayed thermal and Poissonian distributions. While a standard Hanbury Brown and Twiss experiment cannot distinguish between simple thermal emission of laser A and the mode switching of laser B, a TES allows us to measure the photon-number distribution which provides important insight into the underlying emission processes. Indeed, our experimental data and its theoretical description by a master equation approach show that TESs are capable of revealing subtle effects like temporal mode switching of bimodal microlasers. As such our studies clearly demonstrate the huge benefit and importance of investigating nanophotonic devices via photon-number resolving sensors., Comment: 6 pages, 4 figures

Coupled-resonator optical waveguides (CROWs) are known to have interesting and useful dispersion properties. Here, we study the transport in these waveguides in the general case where each resonator is open and asymmetric, i.e., is leaky and possesses no mirror-reflection symmetry. Each individual resonator then exhibits asymmetric backscattering between clockwise and counterclockwise propagating waves, which in combination with the losses induces non-orthogonal eigenmodes. In a chain of such resonators, the coupling between the resonators induces an additional source of non-hermiticity, and a complex band structure arises. We show that in this situation the group velocity of wave packets differs from the velocity associated with the probability density flux, with the difference arising from a non-hermitian correction to the Hellmann-Feynman theorem. Exploring these features numerically in a realistic scenario, we find that the complex band structure comprises almost-real branches and complex branches, which are joined by exceptional points, i.e., nonhermitian degeneracies at which not only the frequencies and decay rates coalesce but also the eigenmodes themselves. The non-hermitian corrections to the group velocity are largest in the regions around the exceptional points., Comment: 11 pages, 9 figures

We demonstrate in open microcavities with broken chiral symmetry, quasi-degenerate pairs of co-propagating modes in a non-rotating cavity evolve to counter-propagating modes with rotation. The emission patterns change dramatically by rotation, due to distinct output directions of CW and CCW waves. By tuning the degree of spatial chirality, we maximize the sensitivity of microcavity emission to rotation. The rotation-induced change of emission is orders of magnitude larger than the Sagnac effect, pointing to a promising direction for ultrasmall optical gyroscopes., Comment: 5 pages, 5 figures

The effect of a Kerr nonlinearity on dynamical tunneling is studied, using coupled whispering gallery modes in an optical microcavity. The model system that we have chosen is the 'add-drop filter', which comprises an optical microcavity and two waveguide coupled to the cavity. Due to the evanescent field's scattering on the waveguide, the whispering gallery modes in the microcavity form doublets, which manifest themselves as splittings in the spectrum. As these doublets can be regarded as a spectral feature of dynamical tunneling between two different dynamical states with a spatial overlap, the effect of a Kerr nonlinearity on the doublets is numerically investigated in the more general context of the relationship between cubic nonlinearity and dynamical tunneling. Within the numerical realization of the model system, it is observed that the doublets shows a bistable transition in its transmission curve as the Kerr-nonlinearity in the cavity is increased. At the same time, one rotational mode gets dominant over the other one in the transmission, since the two states in the doublet have uneven linewidths. By using coupled mode theory, the underlying mode dynamics of the phenomena is theoretically modelled and clarified., Comment: 7 pages, 5 figures

We show that coupling among multiple resonances can be conveniently introduced and controlled by boundary wave scattering. We demonstrate this principle in optical microcavities of quasi-circular shape, where the couplings of multiple modes are determined by the scattering from different harmonic boundary deformations. We analyze these couplings using a perturbation theory, which gives an intuitive understanding of the first-order and higher-order scattering processes. Different scattering paths between two boundary waves can either enhance or reduce their coupling strength. The effect of controlled multimode coupling is most pronounced in the direction of output from an open cavity, which can cause a dramatic change of the external cavity field distribution., Comment: 9 pages, 10 figures

The local chiral symmetry between clockwise (CW) and counter-clockwise (CCW) propagating light in a deformed microcavity can be broken by wave optics effects, which become significant as the cavity size approaches the wavelength. We show that the spatial separation of the CW and CCW ray orbits underlying the high quality factor resonant modes results in unidirectional emission in free space. In the presence of a waveguide, evanescent coupling also becomes directional, and the output direction can be varied by selecting the coupling position along the cavity boundary. Our results demonstrate that the local chirality can be utilized to control the output directionality and enhance the collection efficiency of emission from ultrasmall resonators., Comment: 11 pages, 4 figures

Recently, it has been shown that spiral-shaped microdisk cavities support highly nonorthogonal pairs of copropagating modes with a preferred sense of rotation (spatial chirality) [Wiersig et al., Phys. Rev. A 78, 053809 (2008)]. Here, we provide numerical evidence which indicates that such pairs are a common feature of deformed microdisk cavities which lack mirror symmetries. In particular, we demonstrate that discontinuities of the cavity boundary such as the notch in the spiral cavity are not needed. We find a quantitative relation between the nonorthogonality and the chirality of the modes which agrees well with the predictions from an effective non-Hermitian Hamiltonian. A comparison to ray-tracing simulations is given.

We present measurements of the Goos-H\"anchen shift in a two-dimensional dielectric microwave cavity. Microwave beams are generated by a suitable superposition of the spherical waves generated by an array of antennas; the resulting beams are then reflected at a planar interface. By measuring the electric field including its phase, Poynting vectors of the incoming and reflected beams can be extracted, which in turn are used to find the incoming angle and the positions where the beam hits the interface and where it is reflected. These positions directly yield the Goos-H\"anchen shift. The results are compared to the classical Artmann result and a numerical calculation using Gaussian beams., Comment: 10 pages, 5 figures

We discuss electromagnetic modes in cavities formed by metamaterials with negative refraction and demonstrate that the straightforward approach to substitute negative values of the electric permittivity and the magnetic permeability leads to quasi-bound states with a negative quality factor. To ensure positive quality factors and a consistent physical interpretation of the quasi-bound states it is essential to include the frequency dispersion of the permittivity and the permeability, as required by positive field energy and causality. The basic mode equation and the boundary conditions including linear frequency dispersion are derived. As an example we consider a disk-like cavity with deformed cross sectional shape. The transition from the unphysical nondispersive case with negative quality factors to the dispersive case with positive quality factors is demonstrated numerically and in an analytical perturbative treatment., Comment: 7 pages, 4 figures

The limacon-shaped semiconductor microcavity is a ray-chaotic cavity sustaining low-loss modes with mostly unidirectional emission patterns. Investigating these modes systematically, we show that the modes correspond to ray description collectively, rather than individually. In addition, we present experimental data on multimode lasing emission patterns that show high unidirectionality and closely agree with the ray description. The origin of this agreement is well explained by the collective correspondence mechanism., Comment: 4 pages, 4 figures, to appear in PRA

Optical mushroom shaped billiards offer a unique opportunity to isolate and study non-dispersive, marginally unstable periodic orbits. Here we show that the openness of the cavity to external fields presents unanticipated consequences for the far-field distribution, including directional emission. This is mediated by interactions of marginally unstable periodic orbits with chaotic modes and is potentially relevant for the design of microcavity lasers. We also show that such orbits are robust against perturbations to the shape of the cavity, despite the non-generic character of the classical counterpart and the lack of structural stability of the corresponding classical orbits., Comment: 10 pages, 6 figures

The key characteristic of an optical mode in a microcavity is its quality factor describing the optical losses. The numerical computation of this quantity can be very demanding for present-day devices. Here we show for a certain class of whispering-gallery cavities that the quality factor is related to dynamical tunneling, a phenomenon studied in the field of quantum chaos. We extend a recently developed approach for determining dynamical tunneling rates to open cavities. This allows us to derive an analytical formula for the quality factor which is in very good agreement with full solutions of Maxwell's equations., Comment: 7 pages, 5 figures

We discuss the statistical properties of lifetimes of electromagnetic eigenmodes in dielectric microresonators with fully chaotic ray dynamics. Using the example of a resonator of stadium geometry, we find that a recently proposed random-matrix model very well describes the lifetime statistics of long-lived resonances, provided that two effective parameters are appropriately renormalized. This renormalization is linked to the formation of anomalously short-lived resonances, a mechanism also known from the fractal Weyl law and the resonance trapping phenomenon., Comment: 7 pages, 5 figures

Quasi-bound states in an open system do in general not form an orthogonal and complete basis. It is, however, expected that the non-orthogonality is weak in the case of well-confined states except close to a so-called exceptional point in parameter space. We present numerical evidence showing that for passive optical microspiral cavities the parameter regime where the non-orthogonality is significant is rather broad. Here we observe almost-degenerate pairs of well-confined modes which are highly non-orthogonal. Using a non-Hermitian model Hamiltonian we demonstrate that this interesting phenomenon is related to the asymmetric scattering between clockwise and counterclockwise propagating waves in the spiral geometry. Numerical simulations of ray dynamics reveal a clear ray-wave correspondence., Comment: 8 pages, 10 figures

Recently, an interesting phenomenon of spatial localization of optical modes along periodic ray trajectories near avoided resonance crossings has been observed [J. Wiersig, Phys. Rev. Lett. 97, 253901 (2006)]. For the case of a microdisk cavity with elliptical cross section we use the Husimi function to analyse this localization in phase space. Moreover, we present a semiclassical explanation of this phenomenon in terms of the Goos-Haenchen shift which works very well even deep in the wave regime. This semiclassical correction to the ray dynamics modifies the phase space structure such that modes can localize either on stable islands or along unstable periodic ray trajectories., Comment: 9 pages, 14 figures in reduced quality

We demonstrate that the harmonic inversion technique is a powerful tool to analyze the spectral properties of optical microcavities. As an interesting example we study the statistical properties of complex frequencies of the fully chaotic microstadium. We show that the conjectured fractal Weyl law for open chaotic systems [W. T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. 91, 154101 (2003)] is valid for dielectric microcavities only if the concept of the chaotic repeller is extended to a multifractal by incorporating Fresnel's laws., Comment: 8 pages, 12 figures

A drawback of high-quality modes in optical microdisks is their isotropic light emission characteristics. Here we report a novel, robust, and general mechanism that results in highly directional light emission from those modes. This surprising finding is explained by a combination of wave phenomena (wave localization along unstable periodic ray trajectories) and chaotic ray dynamics in open systems (escape along unstable manifolds). The emission properties originating in the chaotic ray dynamics permit directional light output even from microlasers operating in the common multi-mode regime. We demonstrate our novel mechanism for the limacon billiard family and find directional emission with narrow angular divergence for a significant range of geometries and material parameters., Comment: 4 pages

We investigate the transport and the dynamical properties of tunnel-coupled double charge shuttles. The oscillation frequencies of two shuttles are mode-locked to integer multiples of the applied voltage frequency $\omega$. We show that left/right-symmetric double shuttles may generate direct net current due to bistable motions caused by parametric instability. The symmetry-broken direct current appears near $\omega =\Omega_{0}/(2j-1)$, ($j=1,2,...$), where $\Omega_{0}$ is the dressed resonance frequency of the relative motion of the two shuttles., Comment: Phys. Rev. Lett. (accepted)

We study the formation of long-lived states near avoided resonance crossings in open systems. For three different optical microcavities (rectangle, ellipse, and semi-stadium) we provide numerical evidence that these states are localized along periodic rays, resembling scarred states in closed systems. Our results shed light on the morphology of long-lived states in open mesoscopic systems., Comment: 4 pages, 5 figures (in reduced quality), to appear in Phys. Rev. Lett

We introduce a new scheme to design optical microcavities supporting high-Q modes with unidirectional light emission. This is achieved by coupling a low-Q mode with unidirectional emission to a high-Q mode. The coupling is due to enhanced dynamical tunneling near an avoided resonance crossing. Numerical results for a microdisk with a suitably positioned air hole demonstrate the feasibility and the potential of this concept., Comment: 4 pages, 6 figures (in reduced resolution)

We investigate whether the force and torque exerted by light pressure on an irregularly shaped dielectric resonator allow to detect resonant frequencies, delivering information complemental to the scattering cross section by mechanical means. The peak-to-valley ratio in the torque signal can be many times larger than in the scattering cross section, and, furthermore, depends on the structure of the resonance wave pattern. The far-field emission pattern of the associated quasi-bound states can be tested by the angular dependence of the mechanical probes at finite amplification rate. We relate the force and torque to the scattering matrix and present numerical results for an annularly shaped dielectric resonator., Comment: 4 pages, 3 figures (2 in color)

We present an efficient method to solve Schr\"odinger's equation for perturbations of low rank. In particular, the method allows to calculate the level counting function with very little numerical effort. To illustrate the power of the method, we calculate the number variance for two pseudointegrable quantum billiards: the barrier billiard and the right triangle billiard (smallest angle $\pi/5$). In this way, we obtain precise estimates for the level compressibility in the semiclassical (high energy) limit. In both cases, our results confirm recent theoretical predictions, based on periodic orbit summation., Comment: 4 pages

What we are going to call in this paper "diffractive phenomena" in billiards is far from being deeply understood. These are sorts of singularities that, for example, some kind of corners introduce in the energy eigenfunctions. In this paper we use the well-known scaling quantization procedure to study them. We show how the scaling method can be applied to convex billiards with corners, taking into account the strong diffraction at them and the techniques needed to solve their Helmholtz equation. As an example we study a classically pseudointegrable billiard, the truncated triangle. Then we focus our attention on the spectral behavior. A numerical study of the statistical properties of high-lying energy levels is carried out. It is found that all computed statistical quantities are roughly described by the so-called semi-Poisson statistics, but it is not clear whether the semi-Poisson statistics is the correct one in the semiclassical limit., Comment: 7 pages, 8 figures

We study long-lived resonances (lowest-loss modes) in hexagonally shaped dielectric resonators in order to gain insight into the physics of a class of microcrystal lasers. Numerical results on resonance positions and lifetimes, near-field intensity patterns, far-field emission patterns, and effects of rounding of corners are presented. Most features are explained by a semiclassical approximation based on pseudointegrable ray dynamics and boundary waves. The semiclassical model is also relevant for other microlasers of polygonal geometry., Comment: 12 pages, 17 figures (3 with reduced quality)

We investigate the energy spectra of clean incommensurate double-walled carbon nanotubes, and find that the overall spectral properties are described by the so-called critical statistics of Anderson metal-insulator transition. In the energy spectra, there exist three different regimes characterized by Wigner-Dyson, Poisson, and semi-Poisson distributions. This feature implies that the electron transport in incommensurate multi-walled nanotubes can be either diffusive, ballistic, or intermediate between them, depending on the position of the Fermi energy., Comment: final version to appear in Phys. Rev. Lett

A boundary element method based on a Green's function technique is introduced to compute resonances with intermediate lifetimes in quasi-two-dimensional dielectric cavities. It can be applied to single or several optical resonators of arbitrary shape, including corners, for both TM and TE polarization. For cavities with symmetries a symmetry reduction is described. The existence of spurious solutions is discussed. The efficiency of the method is demonstrated by calculating resonances in two coupled hexagonal cavities., Comment: 9 pages, 7 figures (quality reduced)

The properties of energy levels in a family of classically pseudointegrable systems, the barrier billiards, are investigated. An extensive numerical study of nearest-neighbor spacing distributions, next-to-nearest spacing distributions, number variances, spectral form factors, and the level dynamics is carried out. For a special member of the billiard family, the form factor is calculated analytically for small arguments in the diagonal approximation. All results together are consistent with the so-called semi-Poisson statistics., Comment: 8 pages, 9 figures

A circular Andreev billiard in a uniform magnetic field is studied. It is demonstrated that the classical dynamics is pseudointegrable in the same sense as for rational polygonal billiards. The relation to a specific polygon, the asymmetric barrier billiard, is discussed. Numerical evidence is presented indicating that the Poincare map is typically weak mixing on the invariant sets. This link between these different classes of dynamical systems throws some light on the proximity effect in chaotic Andreev billiards., Comment: 5 pages, 5 figures, to appear in PRE

The nonlinear response to an external electric field is studied for classical non-interacting charged particles under the influence of a uniform magnetic field, a periodic potential, and an effective friction force. We find numerical and analytical evidence that the ratio of transversal to longitudinal resistance forms a Devil's staircase. The staircase is attributed to the dynamical phenomenon of mode-locking., Comment: two-column 4 pages, 5 figures