Related papers: Discrete Liouville equation and Teichm\"uller theo…
The dynamics of a quantum system coupled to a classical environment and subject to constraints that drive it out of equilibrium is described. The evolution of the system is governed by the quantum-classical Liouville equation. Rather than…
In classical thermodynamics the Euler relation is an expression for the internal energy as a sum of the products of canonical pairs of extensive and intensive variables. For quantum systems the situation is more intricate, since one has to…
The classical and quantum dynamics of noncanonically coupled os- cillators is investigated in its relation to Lie superalgebras. It is shown that the quantum dynamics admits a hidden (super)hamiltonian formulation and, hence, preserves the…
Canonical coordinates for both the Schroedinger and the nonlinear Schroedinger equations are introduced, making more transparent their Hamiltonian structures. It is shown that the Schroedinger equation, considered as a classical field…
An experiment is suggested that is capable of distinguishing between the de Broglie-Bohm theory and standard quantum mechanics.
We review some recent developments in the theory of nonlinear von Neumann equations. We distinguish between the von Neumann equation (which can be nonlinear) and the Liouville equation (which should be linear). Explicit examples illustrate…
The link between Tauberian theorems and large deviations is surveyed, with particular reference to regular variation.
The quantum dynamics of a single particle in a discrete two-dimensional tilted lattice is analyzed from the perspective of the classical-quantum correspondence. Utilizing the fact that tilting the lattice results in oscillatory dynamics, we…
We study singular solutions to the fractional Laplace equation and, more generally, to nonlocal linear equations with measurable kernels. We establish B\^ocher type results that characterize the behavior of singular solutions near the…
Generalisations of the virial theorm in Classical Mechanics and Quantum Mechanics are examined. It is shown that the generalised virial theorem in Quantum Mechanics leads to certain relations between matrix elements. The differences between…
A new discrete model for energy relaxation of a quantum particle is described via a projection operator, causing the wave function collapse. Power laws for the evolution of the particle coordinate and momentum dispersions are derived. A new…
In this paper the representation of the position operator and the Lie-Hamilton equation in the discrete momentum space.
The notion of Laplace invariants is transferred to the lattices and discrete equations which are difference analogs of hyperbolic PDE's with two independent variables. The sequence of Laplace invariants satisfy the discrete analog of…
The operator realizing a Dehn twist in quantum Teichmuller theory is diagonalized and continuous spectrum is obtained. This result is in agreement with the expected spectrum of conformal weights in quantum Liouville theory at c>1. The…
In this article, it is suggested that a pedagogical point of departure in the teaching of classical mechanics is the Liouville theorem. The theorem is interpreted to define the condition that describe the conservation of information in…
We review recent efforts to construct gravitational theories on discrete space-times, usually referred to as the ``consistent discretization'' approach. The resulting theories are free of constraints at the canonical level and therefore…
An attempt is made to give a heuristic explanation of the distinguished role of measurement in the quantum theory. We question the notion of "naive" reductionism by stressing the difference between an isolated quantum and classical object.…
The derivation of the time dependent Schr\"odinger equation with transversal and longitudinal relaxation, as the quantum mechanical analog of the classical Landau-Lifshitz-Bloch equation, has been described. Starting from the classical…
A brief philosophical inquiry into the foundations of quantum mechanics is presented here. In particular, the direct relationship between granularity, discontinuity, and the presence of quantum effects will be argued. Furthermore, an…
t is well known that the difference between Quantum Mechanics and Classical Theory appears most crucially in the non Classical spin half of the former theory and the Wilson-Sommerfelt quantization rule. We argue that this is symptomatic of…