Related papers: Weyl's problem: A computational approach
The Weyl particle is the massless fermionic cousin of the photon. While no fundamental Weyl particles have been identified, they arise in condensed matter and meta-material systems, where their spinor nature imposes topological constraints…
In this review article we present a comprehensive review of degenerate solutions to the Dirac and Weyl equations, highlighting novel and significant findings. Specifically, we demonstrate that all Weyl particles, and under certain…
It is necessary to study the properties of Weyl semimetal nanostructures for potential applications in nanoelectronics. Here we study the Weyl semimetal quantum dot with a most simple model Hamiltonian with only two Weyl points. We focus on…
For a compact Riemannian manifold, Weyl's law describes the asymptotic behavior of the counting function of the eigenvalues of the associated Laplace operator. In this paper we discuss Weyl's law in the context of automorphic forms. The…
We compute the generic mode sum that quantifies the effect on the spectrum of a harmonic field when a spherical shell is inserted into vacuum. This encompasses a variety of problems including the Weyl spectral problem and the Casimir effect…
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…
We present a result relating the density of quantum resonances for an open chaotic system to the fractal dimension of the associated classical repeller. The result is supported by numerical computation of the resonances of the system of n…
We find Weyl upper bounds for the quantum open baker's map in the semiclassical limit. For the number of eigenvalues in an annulus, we derive the asymptotic upper bound $\mathcal O(N^\delta)$ where $\delta$ is the dimension of the trapped…
A state of a single particle can be represented by a quantum blob in the corresponding phase space, or by a cell in its 2-D subspace. Its area is frequently stated to be no less than one half of the Plank constant, implying that such a cell…
The Jaynes-Cummings model, with and without the rotating wave approximation, is expressed in the conjugate variable representation and solved numerically by wave packet propagation. Both cases are then cast into systems of two coupled…
We show that when the thermal wavelength is comparable to the spatial size of a system, thermodynamic observables like Pressure and Volume have quantum fluctuations that cannot be ignored. They are now represented by operators; conventional…
A phase space formulation of the filtering process upon an incident quantum state is developed. This formulation can explain the results of both quantum interference and delayed-choice experiments without making use of the controversial…
We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The…
Weyl semimetals have been intensely studied as a three dimensional realization of a Dirac-like excitation spectrum where the conduction bands and valence bands touch at isolated Weyl points in momentum space. Like in graphene, this property…
It is demonstrated that the probability density function, given by the square of a quantum mechanical wavefunction that is a real-valued eigenvector of a time-independent, one-body Schroedinger equation, satisfies a compressible-flow…
The thesis is devoted to the phase space representation of relativistic quantum mechanics. For a class of observables with matrix-valued Weyl symbols proportional to the identity matrix, the Weyl-Wigner-Moyal formalism is proposed. The…
We discuss the r\^ole of quantum deformation of Weyl-Heisenberg algebra in dissipative systems and finite temperature systems. We express the time evolution generator of the damped harmonic oscillator and the generator of thermal Bogolubov…
In this paper we study the quantum cosmology of homogeneous and isotropic cosmology, via the Weyl-Wigner-Groenewold-Moyal formalism of phase space quantization, with perfect fluid as a matter source. The corresponding quantum cosmology is…
A generalization of Brillouin-Wigner perturbation theory is applied numerically to the Wigner Band Random Matrix model. The perturbation theory tells that a perturbed energy eigenstate can be divided into a perturbative part and a…
Quantum wires and electromagnetic waveguides possess common features since their physics is described by the same wave equation. We exploit this analogy to investigate experimentally with microwave waveguides and theoretically with the help…