Related papers: Supersymmetric structures for second order differe…
We study properties of steady states (states with time-independent density operators) of systems of coupled harmonic oscillators. Formulas are derived showing how adiabatic change of the Hamiltonian transforms one steady state into another.…
Superoscillations are a phenomenon in physics, where linear combinations of low-frequency plane waves interfere almost destructively in such a way that the resulting wave has a higher frequency than any of the individual waves. The…
A new class of self-similar ordered structures with non-crystallographic point symmetries is presented. Each of these structures, named superquasicrystals, is given as a section of a higher-dimensional "crystal" with recursive superlattice…
In this investigation, the displacement operator is revisited. We established a connection between the Hermitian version of this operator with the well-known Weyl ordering. Besides, we characterized the quantum properties of a simple…
The divergence-like operator on an odd symplectic superspace which acts invariantly on a specially chosen odd vector field is considered. This operator is used to construct an odd invariant semidensity in a geometrically clear way. The…
The space of linear differential operators on a smooth manifold $M$ has a natural one-parameter family of $Diff(M)$ (and $Vect(M)$)-module structures, defined by their action on the space of tensor-densities. It is shown that, in the case…
We investigate supersymmetry in one-dimensional quantum mechanics with point interactions. We clarify a class of point interactions compatible with supersymmetry and present N=2 supersymmetric models on a circle with two point interactions…
The existence of bi-Hamiltonian structures for the rational Harmonic Oscillator (non-central harmonic oscillator with rational ratio of frequencies) is analyzed by making use of the geometric theory of symmetries. We prove that these…
We investigate a 2-dimensional N=2 supersymmetric model which consists of n chiral superfields with Kahler potential. When we define quantum observables, we are always plagued by operator ordering problem. Among various ways to fix the…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
We present a systematic method of constructing limit-quasiperiodic structures with non-crystallographic point symmetries. Such structures are different aperiodic ordered structures from quasicrystals, and we call them "superquasicrystals".…
A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n-1 functionally independent constants of the motion that are polynomial in the momenta,…
After a brief introduction recalling how, in the limit in which the mass and the electric charge of the electron and the positron tend to zero, Quantum Electrodynamics reduces to a collection of uncoupled quantum supersymmetric harmonic…
We obtain sharp uniform bounds on the low lying eigenfunctions for a class of semiclassical pseudodifferential operators with double characteristics and complex valued symbols, under the assumption that the quadratic approximations along…
We obtain a necessary and sufficient condition for the existence of equivariant real structures on complex symmetric spaces for semisimple groups and discuss how to determine the number of equivalence classes for such structures.
Supersymmetric quantum mechanics is formulated on a two dimensional noncommutative plane and applied to the supersymmetric harmonic oscillator. We find that the ordinary commutative supersymmetry is partially broken and only half of the…
We analytically identify sufficient conditions for manifesting thermal rectification in two-terminal hybrid structures within the quantum master equation formalism. We recognize two classes of rectifiers. In type A rectifiers the contacts…
In the first part of this series of papers we developed the invariant differentiation with respect to a Cartan connection, we described this procedure in the terms of the underlying principal connections, and we discussed applications of…
For a symmetric system, we want to study the problem of crossing an hypersurface in the neighborhood of a given point, when we suppose that all of the available vector fields are tangent to the hypersurface at the point. Classically one…
If $a$ is a densely defined sectorial form in a Hilbert space which is possibly not closable, then we associate in a natural way a holomorphic semigroup generator with $a$. This allows us to remove in several theorems of semigroup theory…