Related papers: Crum's Theorem for `Discrete' Quantum Mechanics
We derive the category-theoretic backbone of quantum theory from a process ontology. More specifically, we treat quantum theory as a theory of systems, processes and their interactions. In this first part of a three-part overview, we first…
The two-body problem with a central interaction on simply connected constant curvature spaces of an arbitrary dimension is considered. The explicit expression for the quantum two-body Hamiltonian via a radial differential operator and…
A formalism is developed to study certain five-term recursion relations by discrete phase integral (or Wentzel-Kramers-Brillouin) methods. Such recursion relations arise naturally in the study of the Schrodinger equation for certain spin…
The variational Hamiltonian approach to Quantum Chromodynamics in Coulomb gauge is investigated within the framework of the canonical recursive Dyson--Schwinger equations. The dressing of the quark propagator arising from the variationally…
In the frames of classical mechanics the generalized Langevin equation is derived for an arbitrary mechanical subsystem coupled to the harmonic bath of a solid. A time-acting temperature operator is introduced for the quantum Klein-Kramers…
We develop a microscopic theory for biasing the quantum trajectories of an open quantum system, which renders rare trajectories typical. To this end we consider a discrete-time quantum dynamics, where the open system collides sequentially…
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…
We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional nonrelativistic quantum dual theories (with oscillator and Coulomb-like potentials) and compare their spectra and the sets of eigenfunctions. We…
Quantum mechanics of a general one dimensional dissipative system investigated by it's coupling to a Klein-Gordon field as the environment using a minimal coupling method. Heisenberg equation for such a dissipative system containing a…
Some recent experiments claim to show that any model in which a quantum state represents mere information about an underlying physical reality of the system must make predictions which contradict those of quantum theory. The present work…
In this paper, we develop spectral analysis of a discrete non-Hermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple conditions for discreteness of the spectrum…
In the paper, Sturm--Liouville differential operators on time scales consisting of a finite number of isolated points and segments are considered. Such operators unify differential and difference operators. We obtain properties of their…
The method of separation of variables is shown to apply to both the classical and quantum Neumann model. In the classical case this nicely yields the linearization of the flow on the Jacobian of the spectral curve. In the quantum case the…
A general quantum theory encompassing Mechanics, Thermodynamics and irreversible dynamics is presented in two parts. The first part is concerned exclusively with the description of the states of any individual physical system. It is based…
The development of a self-consistent thermodynamic theory of quantum systems is of fundamental importance for modern physics. Still, despite its essential role in quantum science and technology, there is no unifying formalism for…
We discuss direct and inverse spectral theory of self-adjoint Sturm-Liouville relations with separated boundary conditions in the left-definite setting. In particular, we develop singular Weyl-Titchmarsh theory for these relations.…
We present a two-dimensional classical stochastic differential equation for a displacement field of a point particle in two dimensions and show that its components define real and imaginary parts of a complex field satisfying the…
By assuming that a particle of energy hbar.omega is actually a dissipative system maintained in a nonequilibrium steady state by a constant throughput of energy (heat flow), the exact Schroedinger equation is derived, both for conservative…
Quantum thermodynamics addresses the emergence of thermodynamical laws from quantum mechanics. The link is based on the intimate connection of quantum thermodynamics with the theory of open quantum systems. Quantum mechanics inserts…
The spectral collocation method (SCM) exhibits a clear superiority in solving ordinary and partial differential equations compared to conventional techniques, such as finite difference and finite element methods. This makes SCM a powerful…