Related papers: Continuous vs. discrete models for the quantum har…
We discuss possible definitions of discrete Dirac operators, and discuss their continuum limits. It is well-known in the lattice field theory that the straightforward discretization of the Dirac operator introduces unwanted spectral…
This paper is devoted to study the qualitative properties of hybrid measure differential equations (HMDEs, for short). We establish several results on the existence of global solutions, including the existence of regulated, continuous,…
The driven quantum harmonic oscillator is fundamental to a number of important physical systems. Here, we consider the quantum harmonic oscillator under non-Hermitian, PT-symmetric driving, showing that the resulting set of Wigner-space…
In this paper, we describe a numerical continuation method that enables harmonic analysis of nonlinear periodic oscillators. This method is formulated as a boundary value problem that can be readily implemented by resorting to a standard…
This paper presents the geometric setting of quantum variational principles and extends it to comprise the interaction between classical and quantum degrees of freedom. Euler-Poincar\'e reduction theory is applied to the Schr\"odinger,…
The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.
These lecture notes aim to provide a self-contained, pedagogical introduction to the physics of local constraints, fractionalisation and topological liquids organised around the Rokhsar-Kivelson quantum dimer model. Topics and phenomena…
In this paper we introduce discrete gradient methods to discretize irreversible port-Hamiltonian systems showing that the main qualitative properties of the continuous system are preserved using this kind discretizations methods.
We construct the integrals of motion for several models of the quantum damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic…
The investigation of the generalized coherent states for oscillator-like systems connected with given family of orthogonal polynomials is continued. In this work we consider oscillators connected with Meixner and Meixner-Pollaczek…
Using a nonlinear Schr\"{o}dinger equation for the wave function of all systems, continuous transitions between quantum and classical motions are demonstrated for (i) the double-slit set up, (ii) the 2D harmonic oscillator and (iii) the…
Klauder's recent generalization of the harmonic oscillator coherent states [J. Phys. A 29, L293 (1996)] is applicable only in non-degenerate systems, requiring some additional structure if applied to systems with degeneracies. The author…
We consider the application of the consistent lattice quantum gravity approach we introduced recently to the situation of a Friedmann cosmology and also to Bianchi cosmological models. This allows us to work out in detail the computations…
We develop an action principle for those models arising from isotropic loop quantum cosmology, and show that there is a natural conserved quantity $Q$ for the discrete difference equation arising from the Hamiltonian constraint. This…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
The classical dynamical system possessing a quantum spectrum of energy and "quantum" behavior is suggested and investigated. The proposed model can be considered as a dynamical variant of the old quantum theory for harmonic oscillator in…
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…
Causal rigid particles whose action includes an {\it arbitrary} dependence on the world-line extrinsic curvature are considered. General classes of solutions are constructed, including {\it causal tachyonic} ones. The Hamiltonian…
Some first principles that, we believe, could serve as foundation for quantum theory of extended particles are formulated. It is also shown that in the point-like particles limit the non-relativistic quantum mechanics can be restored. As an…