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In this work we present an introduction to Supersymmetry in the context of 1-dimensional Quantum Mechanics. For that purpose we develop the concept of hamiltonians factorization using the simple harmonic oscillator as an example, we…
We consider special elliptic operators in functional spaces on manifolds with a boundary which has some singular points. Such an operator can be represented by a sum of operators, and for a Fredholm property of an initial operator one needs…
Quasiperiodic Jacobi operators arise as mathematical models of quasicrystals and in more general studies of structures exhibiting aperiodic order. The spectra of these self-adjoint operators can be quite exotic, such as Cantor sets, and…
We demonstrate application of the method of higher-order operators to nonlinear standard optomechanics. It is shown that a symmetry breaking in frequency shifts exists, corresponding to inequivalency of red and blue side-bands. This arises…
In this work we will advance farther along a line previously developed concerning our proposal of a time interval operator, on finite dimensional spaces. The time interval operator is Hermitian, and its eigenvalues are time values with a…
Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of…
In previous work, we have considered Hamiltonians associated with 3 dimensional conformally flat spaces, possessing 2, 3 and 4 dimensional isometry algebras. Previously our Hamiltonians have represented free motion, but here we consider the…
This PhD thesis explores the potential of quantum computing to address computational challenges in high-energy physics (HEP). As the Standard Model (SM) leaves key questions unanswered and no signs of new physics have emerged since the…
We show that quadratic Hamiltonians in involution coming from a St\"ackel system are quantizable, in the sense that one can construct commutative self-adjoint operators whose symbols are the quadratic Hamiltonians. Moreover, they allow…
Muraleetharan and Thirulogasanthan in (J. Math. phys. 59, No. 10, 103506, 27p. (2018)) introduced the concept of Calkin Sspectrum of a bounded quaternionic linear operators. The study of this spectrum is establisched using the Fredholm…
Based on operators borrowed from scattering theory, several concrete realizations of index theorems are proposed. The corresponding operators belong to some C*-algebras of pseudo-differential operators with coefficients which either have…
The action of the quantum mechanical volume operator, introduced in connection with a symmetric representation of the three-body problem and recently recognized to play a fundamental role in discretized quantum gravity models, can be given…
The Newtonian potential operator for the Helmholtz equation, which is represented by the volume integral with fundamental solution as kernel function, is of great importance for direct and inverse scattering of acoustic waves. In this…
Gamow solutions are used to transform self-adjoint energy operators by means of factorization (supersymmetric) techniques. The transformed non-hermitian operators admit a discrete real spectrum which is occasionally extended by a single…
A quantum flywheel is studied with the purpose of storing useful work in quantum levels, while additional power is extracted continuously from the device. The flywheel gains its energy form a quantum heat engine. Generally, when a work…
Recent developments have made possible the computation of equilibrium dynamical correlators in quantum impurity problems. In many situations however, one is rather interested in correlators subject to a non equilibrium initial preparation;…
We consider a two-parameter non hermitean quantum-mechanical hamiltonian that is invariant under the combined effects of parity and time reversal transformation. Numerical investigation shows that for some values of the potential parameters…
Numerous experimental indications suggest that the Hume-Rothery mechanism plays an important role in stabilizing quasicrystalline and amorphous phases. However, the exponential damping of the conventional Friedel oscillations at the…
A study is presented of two-dimensional superintegrable systems separating in Cartesian coordinates and allowing an integral of motion that is a fourth order polynomial in the momenta. All quantum mechanical potentials that do not satisfy…
The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…