Related papers: Weyl asymptotics: From closed to open systems
The $^{181}$Ta quadrupole resonance (NQR) technique has been utilized to investigate the microscopic magnetic properties of the Weyl semi-metal TaP. We found three zero-field NQR signals associated with the transition between the quadrupole…
We present a theoretical model to study the nonlinear optical response of materials with a low-energy spectrum characterised by strongly tilted, type-II, Weyl cones in two dimensions, which we call 2D Weyl materials. Our findings reveal…
We generalize Weyl's law to inhomogeneous bodies in $d$ dimensions. Using a perturbation scheme recently obtained by us in Ref. \cite{Amore09}, we have derived an explicit formula, which describes the asymptotic behavior of the eigenvalues…
The so-called Weyl transform is a linear map from a commutative algebra of functions to a noncommutative algebra of linear operators, characterized by an action on Cartesian coordinate functions of the form $(x, y) \mapsto (X, Y)$ such that…
We experimentally study the susceptibility to symmetry breaking of a closed turbulent von K\'{a}rm\'{a}n swirling flow from $Re = 150$ to $Re \simeq 10^{6}$. We report a divergence of this susceptibility at an intermediate Reynolds number…
We demonstrate the existence and significance of diffractive orbits in an open microwave billiard, both experimentally and theoretically. Orbits that diffract off of a sharp edge strongly influence the conduction spectrum of this resonator,…
In optical detection setups to measure the deflection of micro-cantilevers, part of the sensing light is absorbed, heating the mechanical probe. We present experimental evidences of a frequency shift of the resonant modes of a cantilever…
A system of linear differential equations with oscillatory decreasing coefficients is considered. The coefficients has the form $t^{-\alpha}a(t)$,~$\alpha>0$, where $a(t)$ is trigonometric polynomial with an arbitrary set of frequencies.…
Recent advances in the periodic orbit theory of stochastically perturbed systems have permitted a calculation of the escape rate of a noisy chaotic map to order 64 in the noise strength. Comparison with the usual asymptotic expansions…
A deformed dielectric microcavity is used as an experimental platform for the analysis of the statistics of chaotic resonances, in the perspective of testing fractal Weyl laws at optical frequencies. In order to surmount the difficulties…
Using reciprocity, we investigate the breaking of time-reversal (T) symmetry due to a ferrite embedded in a flat microwave billiard. Transmission spectra of isolated single resonances are not sensitive to T-violation whereas those of pairs…
We consider the cases of the self-adjoint and skew-self-adjoint discrete Dirac systems, obtain explicit expressions for reflection coefficients and show that rational reflection coefficients and Weyl functions coincide.
We show that the electrical transport across a minimal model for a time-reversal symmetry(TRS) breaking Weyl semi-metal (WSM) involving two Weyl nodes can be interpreted as an interferometer in momentum space. The interference phase depends…
For a scalar elliptic self-adjoint operator on a compact manifold without boundary we have two-term asymptotics for the number of eigenvalues between zero and lambda when lambda tends to infinity, under an additional dynamical condition.…
Disordered non-interacting systems in sufficiently high dimensions have been predicted to display a non-Anderson disorder-driven transition that manifests itself in the critical behaviour of the density of states and other physical…
We study shape resonances of two-dimensional magnetic Stark Hamiltonians in the semiclassical limit. The magnetic field is assumed to be constant and the scalar potential is a perturbation of a linear potential. Under the assumption that…
We study the cyclotron resonance in the electron-hole joint Fermi surface of a type-II Weyl semimetal. In magnetic field, the electron and hole pockets touching at the Weyl node are hybridized to form quantized Landau levels corresponding…
By means of a simple model system, the total volume fluctuations of a tapped granular material in the steady state are studied. In the limit of a system with a large number of particles, they are found to be Gaussian distributed, and…
We consider an elliptic billiard whose shape slowly changes. During slow evolution of the billiard certain resonance conditions can be fulfilled. We study the phenomena of capture into a resonance and scattering on resonances which lead to…
We show that the autocorrelation of quantum spectra of an open chaotic system is well described by the classical Ruelle-Pollicott resonances of the associated chaotic strange repeller. This correspondence is demonstrated utilizing microwave…