Related papers: Fractal Weyl law for open quantum chaotic maps
Wave scattering in chaotic systems can be characterized by its spectrum of resonances, $z_n=E_n-i\frac{\Gamma_n}{2}$, where $E_n$ is related to the energy and $\Gamma_n$ is the decay rate or width of the resonance. If the corresponding ray…
We numerically analyse quantum survival probability fluctuations in an open, classically chaotic system. In a quasi-classical regime, and in the presence of classical mixed phase space, such fluctuations are believed to exhibit a fractal…
We analyze the structure of the surface states and Fermi arcs of Weyl semimetals as a function of the boundary conditions parameterizing the Hamiltonian self-adjoint extensions of a minimal model with two Weyl points. These boundary…
We prove two results on Fractal Uncertainty Principle (FUP) for discrete Cantor sets with large alphabets. First, we give an example of an alphabet with dimension $\delta \in (\frac12,1)$ where the FUP exponent is exponentially small as the…
The basic ingredients in a semiclassical theory are the classical invariant objects serving as a support for the quantization. Recent studies, mainly obtained on quantum maps, have led to the commonly accepted belief that it is the…
We prove a quantum version of the Sabine law from acoustics describing the location of resonances in transmission problems. This work extends the author's previous work to a broader class of systems. Our main applications are to scattering…
The paper concerns scattering of plane waves by a bounded obstacle with complex valued impedance boundary conditions. We study the spectrum of the Neumann-to-Dirichlet operator for small wave numbers and long wave asymptotic behavior of the…
We revisit the mechanism of Poole-Frenkel non-ohmic conduction in materials of non-volatile memory. Percolation theory is shown to explain both the Poole and Frenkel dependencies corresponding to the cases of respectively small and large…
The scalar scattering of the plane wave by a strictly convex obstacle with impedance boundary conditions is considered. The uniform boundedness of the Total Cross Section for all values of frequencies is proved. The high frequency limit of…
In this paper, we study the semi-classical behavior of distorted plane waves, on manifolds that are Euclidean near infinity or hyperbolic near infinity, and of non-positive curvature. Assuming that there is a strip without resonances below…
We present how to detect type-$1$ Weyl nodes in a material by inelastic neutron scattering. Such an experiment first of all allows one to determine the dispersion of the Weyl fermions. We extend the reasoning to produce a quantitative test…
The problem of plane-wave diffraction on semi-infinite orthorhombic electromagnetic (photonic) crystals of general kind is considered. Boundary conditions are obtained in the form of infinite system of equations relating amplitudes of…
A rigorous reduction of the many-body wave scattering problem to solving a linear algebraic system is given bypassing solving the usual system of integral equation. The limiting case of infinitely many small particles embedded into a medium…
In this paper, we consider near cloaking for the full Maxwell equations. We extend the recent results, where the quasi-static limit case and the Helmholtz equation are considered, to electromagnetic scattering problems. We construct very…
We derive quantitative estimates proving the conditional propagation of chaos for large stochastic systems of interacting particles subject to both idiosyncratic and common noise. We obtain explicit bounds on the relative entropy between…
Resonances, or scattering poles, are complex numbers which mathematically describe meta-stable states: the real part of a resonance gives the rest energy, and its imaginary part, the rate of decay of a meta-stable state. This description…
A Weyl semimetal is a three dimensional topological gapless phase. In the presence of strong enough disorder it undergoes a quantum transition towards a diffusive metal phase whose universality class depends on the range of disorder…
We find that generic boundary conditions of Weyl semimetal is dictated by only a single real parameter, in the continuum limit. We determine how the energy dispersions (the Fermi arcs) and the wave functions of edge states depend on this…
The concern of this article is a semiclassical Weyl calculus on an infinite dimensional Hilbert space $H$. If $(i, H, B)$ is a Wiener triplet associated to $H$, the quantum state space will be the space of $L^2$ functions on $B$ with…
A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schr\"odinger equation, quantum Riesz fractional derivative, path integral approach to fractional quantum…