arXiv subjects

Jan Wiersig

Publications and source records attributed to Jan Wiersig.

53 records · Page 3Linked to original sources

arXiv2006

Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities

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.

physics.optics↗

arXiv2006

Spontaneously Symmetry-Broken Current in Coupled Nanomechanical Shuttles

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 $ω$. 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 $ω=Ω_{0}/(2j-1)$, ($j=1,2,...$), where $Ω_{0}$ is the dressed resonance frequency of the relative motion of the two shuttles.

cond-mat.mes-hall↗

arXiv2006

Unidirectional light emission from high-Q modes in optical microcavities

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.

cond-mat.other↗

arXiv2004

Opto-mechanical probes of resonances in amplifying microresonators

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.

physics.optics↗

arXiv2003

Evanescent wave approach to diffractive phenomena in convex billiards with corners

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.

nlin.CD↗

arXiv2003

Low rank perturbations and the spectral statistics of pseudointegrable billiards

We present an efficient method to solve Schrödinger'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 $π/5$). 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.

nlin.CD↗

arXiv2003

Spectral Correlation in Incommensurate Multi-Walled Carbon Nanotubes

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.

cond-mat.mes-hall↗

arXiv2002

Boundary element method for resonances in dielectric microcavities

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.

physics.optics↗

arXiv2002

Hexagonal dielectric resonators and microcrystal lasers

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.

physics.optics↗

arXiv2002

Spectral properties of quantized barrier billiards

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.

nlin.CD↗

arXiv2002

A pseudointegrable Andreev billiard

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.

nlin.CD↗

arXiv2001

The Quantum-Classical Correspondence in Polygonal Billiards

We show that wave functions in planar rational polygonal billiards (all angles rationally related to Pi) can be expanded in a basis of quasi-stationary and spatially regular states. Unlike the energy eigenstates, these states are directly related to the classical invariant surfaces in the semiclassical limit. This is illustrated for the barrier billiard. We expect that these states are also present in integrable billiards with point scatterers or magnetic flux lines.

nlin.CD↗

arXiv2001

Devil's Staircase in Magnetoresistance of a Periodic Array of Scatterers

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.

cond-mat.mes-hall↗

arXiv2001

Resonance zones in action space

The classical and quantum mechanics of isolated, nonlinear resonances in integrable systems with N>=2 degrees of freedom is discussed in terms of geometry in the space of action variables. Energy surfaces and frequencies are calculated and graphically presented for invariant tori inside and outside the resonance zone. The quantum mechanical eigenvalues, computed in the semiclassical WKB approximation, show a regular pattern when transformed into the action space of the associated symmetry reduced system: eigenvalues inside the resonance zone are arranged on N-dimensional cubic lattices, whereas those outside are, in general, non-periodically distributed. However, N-dimensional triclinic (skewed) lattices exist locally. Both kinds of lattices are joined smoothly across the classical separatrix surface. The statements are illustrated with the help of two and three coupled rotors.

nlin.CD↗

arXiv2000

Multistability and nonsmooth bifurcations in the quasiperiodically forced circle map

It is well-known that the dynamics of the Arnold circle map is phase-locked in regions of the parameter space called Arnold tongues. If the map is invertible, the only possible dynamics is either quasiperiodic motion, or phase-locked behavior with a unique attracting periodic orbit. Under the influence of quasiperiodic forcing the dynamics of the map changes dramatically. Inside the Arnold tongues open regions of multistability exist, and the parameter dependency of the dynamics becomes rather complex. This paper discusses the bifurcation structure inside the Arnold tongue with zero rotation number and includes a study of nonsmooth bifurcations that happen for large nonlinearity in the region with strange nonchaotic attractors.

nlin.CD↗

arXiv2000

Singular continuous spectra in a pseudo-integrable billiard

The pseudo-integrable barrier billiard invented by Hannay and McCraw [J. Phys. A 23, 887 (1990)] -- rectangular billiard with line-segment barrier placed on a symmetry axis -- is generalized. It is proven that the flow on invariant surfaces of genus two exhibits a singular continuous spectral component.

nlin.CD↗

arXiv1998

Triaxial Ellipsoidal Quantum Billiards

The classical mechanics, exact quantum mechanics and semiclassical quantum mechanics of the billiard in the triaxial ellipsoid is investigated. The system is separable in ellipsoidal coordinates. A smooth description of the motion is given in terms of a geodesic flow on a solid torus, which is a fourfold cover of the interior of the ellipsoid. Two crossing separatrices lead to four generic types of motion. The action variables of the system are integrals of a single Abelian differential of second kind on a hyperelliptic curve of genus 2. The classical separability carries over to quantum mechanics giving two versions of generalized Lam{é} equations according to the two sets of classical coordinates. The quantum eigenvalues define a lattice when transformed to classical action space. Away from the separatrix surfaces the lattice is given by EBK quantization rules for the four types of classical motion. The transition between the four lattices is described by a uniform semiclassical quantization scheme based on a WKB ansatz. The tunneling between tori is given by penetration integrals which again are integrals of the same Abelian differential that gives the classical action variables. It turns out that the quantum mechanics of ellipsoidal billiards is semiclassically most elegantly explained by the investigation of its hyperelliptic curve and the real and purely imaginary periods of a single Abelian differential.

chao-dyn↗