Related papers: Magnetic Schroeodinger Operator: Geometry, Classic…
Using the transformations from paper I, we show that the Schr\"odinger equations for: (1)systems described by quadratic Hamiltonians, (2) systems with time-varying mass, and (3) time-dependent oscillators, all have isomorphic Lie space-time…
We provide a theory of spin and acoustic wave coupled nonlinear dynamics in continuum systems. Combining the Landau-Lifshitz-Gilbert equations with the magnetoelastic Hamiltonian, we derive classical equations of motion for the…
In this article, we consider the asymptotic behaviour of the spectral function of Schr\"odinger operators on the real line. Let $H: L^2(\mathbb{R})\to L^2(\mathbb{R})$ have the form $$ H:=-\frac{d^2}{dx^2}+V, $$ where $V$ is a formally…
We study the eigenvalues of the magnetic Schroedinger operator associated with a magnetic potential A and a scalar potential q, on a compact Riemannian manifold M, with Neumann boundary conditions if the boundary is not empty. We obtain…
We consider Schr\"odinger operators with periodic electric and magnetic potentials on periodic discrete graphs. The spectrum of such operators consists of an absolutely continuous (a.c.) part (a union of a finite number of non-degenerate…
We present a general semiclassical theory of the orbital magnetic response of noninteracting electrons confined in two-dimensional potentials. We calculate the magnetic susceptibility of singly-connected and the persistent currents of…
We study a magnetic Schr{\"o}dinger Hamiltonian, with axisymmetric potential in any dimension. The associated magnetic field is unitary and non constant. The problem reduces to a 1D family of singular Sturm-Liouville operators on the…
We study the effect of non-negative potentials on the spectral gap of one-dimensional Schr\"odinger operators in the limit of large intervals. In particular, we derive upper and lower bounds on the gap for different classes of potentials…
In this paper, we study the geometry associated with Schroedinger operator via Hamiltonian and Lagrangian formalism. Making use of a multiplier technique, we construct the heat kernel with the coefficient matrices of the operator both…
The dynamical equation of quantum mechanics are rewritten in form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated and squeezed quadrature introduced in the so called "symplectic tomography".…
We give a mathematically rigorous construction of a magnetic Schr\"odinger operator corresponding to a field with flux through finitely many holes of the Sierpinski Gasket. The operator is shown to have discrete spectrum accumulating at…
In this paper, we study spectral properties of the one dimensional periodic Schrodinger operator with an adiabatic quasi-periodic perturbation. We show that in certain energy regions the perturbation leads to resonance effects related to…
We study the phase-space concentration of the so-called generalized metaplectic operators whose main examples are Schr\"odinger equations with bounded perturbations. To reach this goal, we perform a so-called $\mathcal{A}$-Wigner analysis…
The behaviour of the interaction of the induced electric dipole moment of an atom with a uniform magnetic field and a non-uniform electric field are investigated in a rotating reference frame. An interesting aspect of this interaction is…
We prove existence results and lower bounds for the resonances of Schr\"odinger operators associated to smooth, compactly support potentials on hyperbolic space. The results are derived from a combination of heat and wave trace expansions…
Quantum mechanics is one of the basic theories of modern physics. Here, the famous Schr\"odinger equation and the differential operators representing mechanical quantities in quantum mechanics are derived, just based on the principle that…
The purpose of this paper is to prove that the spectrum of an isotropic Maxwell operator with electric permittivity and magnetic permeability that are periodic along certain directions and tending to a constant super-exponentially fast in…
In this work we uncover the mathematical structure of the Schwinger algebra and introduce an almost unitary Schwinger operators which are derived by considering translation operators on a finite lattice. We calculate mathematical relations…
Electromagnetic modes with parabolic-cylindrical symmetry and their dynamical variables are studied both in the classical and quantum realm. As a result, a new dynamical constant for the electromagnetic field is identified and linked to the…
We establish two-term spectral asymptotics for the operator of linear elasticity with mixed boundary conditions on a smooth compact Riemannian manifold of arbitrary dimension. We illustrate our results by explicit examples in dimension two…