Related papers: Fractal position spectrum for a class of oscillato…
In this paper presents the results obtained in the field of spectral theory operators of fractional differentiation. Proven a number of propositions which represents independent interest in the theory of fractional calculus. Introduced…
We study several fractal properties of the Weierstrass-type function \[ W(x)=\sum_{n=0} ^\infty \lambda (x) \lambda(\tau x) \cdots \lambda (\tau ^{n-1}x)\, g(\tau ^n x), \] where $\tau :[0,1)\to[0,1)$ is a cookie cutter map with possibly…
We propose a q-deformation of the su(2)-invariant Schrodinger equation of a spinless particle in a central potential, which allows us not only to determine a deformed spectrum and the corresponding eigenstates, as in other approaches, but…
Previously, spectra of certain weighted composition operators on the Hardy Space were discovered under one of two hypotheses: either the compositional symbol converges under iteration to the Denjoy-Wolff point on all of the open disk rather…
The dissipative quantum mechanics of a charged particle in a uniform magnetic field and periodic potential has delocalization critical points which correspond to backgrounds for the open string. We study the phase diagram of this system (in…
We derive, from conformal invariance and quantum gravity, the multifractal spectrum f(alpha,c) of the harmonic measure (or electrostatic potential, or diffusion field) near any conformally invariant fractal in two dimensions, corresponding…
We propose a q-deformation of the su(2)-invariant Schrodinger equation of a spinless particle in a central potential, which allows us not only to determine a deformed spectrum and the corresponding eigenstates, as in other approaches, but…
The Hamiltonian of a polariton model for an inhomogeneous linear absorptive dielectric is diagonalized by means of Fano's diagonalization method. The creation and annihilation operators for the independent normal modes are explicitly found…
We present a derivation of the energy spectrum of the harmonic oscillator by using the alternative approach of topological quantization. The spectrum is derived from the topological invariants of a particular principal fiber bundle which…
The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms of a flat…
The space of entire functions which are integrable with respect to the Gaussian weight, known also as the Fock space, is one of the preferred functional Hilbert spaces for modelling and experimenting harmonic analysis, quantum mechanics or…
We propose to build a combinatorial invariant, called the spectral monodromy, from the spectrum of a single non-selfadjoint h-pseudodifferential operator with two degrees of freedom in the semi-classical limit. Our inspiration comes from…
Non-commutative Quantum Mechanics in 3D is investigated in the framework of the abelian Drinfeld twist which deforms a given Hopf algebra while preserving its Hopf algebra structure. Composite operators (of coordinates and momenta) entering…
We study the entanglement Hamiltonian for free-fermion chains with a particular form of inhomogeneity. The hopping amplitudes and chemical potentials are chosen such that the single-particle eigenstates are related to discrete orthogonal…
Celebrating its golden jubilee, the Hofstadter butterfly fractal emerges as a remarkable fusion of art and science. This iconic X shaped fractal captivates physicists, mathematicians, and enthusiasts alike by elegantly illustrating the…
We consider a class of (possibly nondiagonalizable) pseudo-Hermitian operators with discrete spectrum, showing that in no case (unless they are diagonalizable and have a real spectrum) they are Hermitian with respect to a semidefinite inner…
This work addresses a ${\theta}(\hat{x},\hat{p})-$deformation of the harmonic oscillator in a $2D-$phase space. Specifically, it concerns a quantum mechanics of the harmonic oscillator based on a noncanonical commutation relation depending…
We give a spectral description of the semi-classical Schrodinger operator with a piecewise linear, complex valued potential. Moreover, using these results, we show how an arbitrarily small bounded perturbation of a non-self-adjoint operator…
We give a perspective on the Hofstadter butterfly (fractal energy spectrum in magnetic fields), which we have shown to arise specifically in three-dimensional(3D) systems in our previous work. (i) We first obtain the `phase diagram' on a…
Classical spectral theory provides powerful tools for analyzing linear operators, but does not extend naturally to nonlinear or compositional settings. In particular, there is no general way to transport spectral invariants in a functorial…