Related papers: Dynamics of Totally Constrained Systems I. Classic…
Using the supersymmetry approach, we study spectral statistical properties of a two-dimensional quantum particle subject to a non-uniform magnetic field. We focus mainly on the problem of regularisation of the field theory. Our analysis…
Following a minisuperspace approach to the dynamics of a spherically symmetric shell, a reduced Lagrangian for the radial degree of freedom is derived directly from the Einstein-Hilbert action. The key feature of this new Lagrangian is its…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
We give an overview of the two different methods that have been introduced in order to describe the dynamics of constrained quantum systems; the symplectic formulation and the metric formulation. The symplectic method extends the work of…
Whether gravity must be quantized remains one of the biggest open problems in fundamental physics. Classical-quantum hybrid theories have recently attracted attention as a possible framework in which gravity is treated classically yet…
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of…
The well known argument of Page and Wootters demonstrates how to "derive" the usual quantum dynamics of a subsystem in a global state which is an eigenstate of the total Hamiltonian. I show how the same argument can be made in classical…
A formulation of singular classical theories (determined by degenerate Lagrangians) without constraints is presented. A partial Hamiltonian formalism in the phase space having an initially arbitrary number of momenta (which can be smaller…
In quantum theory, equilibrium statistical mechanics is usually formulated through the canonical ensemble, whose privileged status is tied to the Euclidean continuation of time evolution. The microcanonical ensemble, by contrast, is…
We show that a noncommutative dynamical system of the type that occurs in quantum theory can often be associated with a dynamical principle; that is, an infinitesimal structure that completely determines the dynamics. The nature of these…
Mixed quantum-classical models have been proposed in several contexts to overcome the computational challenges of fully quantum approaches. However, current models typically suffer from long-standing consistency issues, and, in some cases,…
We present a classical and quantum analysis of a particle confined in a three-dimensional paraboloidal cavity formed by two confocal paraboloids. Classically, the system is integrable and presents three independent constants of motion,…
An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…
Derivation of the canonical (or Boltzmann) distribution based only on quantum dynamics is discussed. Consider a closed system which consists of mutually interacting subsystem and heat bath, and assume that the whole system is initially in a…
There exist instances of dynamical systems possessing symmetry transformations of which the conserved Noether charges generating these symmetries feature an explicit time dependence in their functional representation over phase space. The…
We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay…
We investigate the strong-field limit of a charged particle in an electromagnetic field as a toy model for general covariant systems, establishing a novel connection between constrained Hamiltonian dynamics and noncommutative geometry.…
We address the nonadiabatic quantum dynamics of macrosystems with several coupled electronic states, taking into account the possibility of multi-state conical intersections. The general situation of an arbitrary number of states and…
In this paper a formalism for studying the dynamics of quantum systems coupled to classical spin environments is reviewed. The theory is based on generalized antisymmetric brackets and naturally predicts open-path off-diagonal geometric…
One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…