Related papers: Quantum Caustics for Systems with Quadratic Lagran…
The problem of the initial conditions for the oscillator model of quantum dissipative systems is studied. It is argued that, even in the classical case, the hypothesis that the environment is in thermal equilibrium implies a statistical…
Loop quantum cosmology predicts that quantum gravity effects resolve the big-bang singularity and replace it by a cosmic bounce. Furthermore, loop quantum cosmology can also modify the form of primordial cosmological perturbations, for…
The linear canonical transforms of position and momentum are used to construct the tomographic probability representation of quantum states where the fair probability distribution determines the quantum state instead of the wave function or…
The rotating frame is considered in quantum mechanics on the basis of the position dependent boost relating this frame to the non rotating inertial frame. We derive the Sagnac phase shift and the spin coupling with the rotation in the non…
The issue of non-locality in quantum mechanics can potentially be resolved by considering relativistically covariant diffusion in four-dimensional spacetime. Stochastic particles described by the Klein-Gordon equation are shown to undergo a…
Transitions from classical to quantum behaviour in a spin system with two degenerate ground states separated by twin energy barriers which are asymmetric due to an applied magnetic field are investigated. It is shown that these transitions…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
We recast Dirac's Lagrangian in quantum mechanics in the language of vector bundles and show that the action is an operator-valued connection one-form. Phases associated with change of frames of reference are seen to be total differentials…
This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential…
This paper discusses two distinct, but related issues in quantum fluctuation effects. The first is the frequency spectrum which can be assigned to one loop quantum processes. The formal spectrum is a flat one, but the finite quantum effects…
The reinterpretation of quantum mechanical formalism in terms of a classical model with a continuous material "$\Psi$-field" acting upon a point-like particle which is subjected to large friction and random forces is proposed. This model…
Existing approaches to analogue quantum simulations of time-dependent quantum systems rely on perturbative corrections to quantum simulations of time-independent quantum systems. We overcome this restriction to perturbative treatments with…
A new formulation of relativistic quantum mechanics is proposed in the framework of the rest-frame instant form of dynamics with its instantaneous Wigner 3-spaces and with its description of the particle world-lines by means of derived…
Quadratic Lagrangians are introduced adding surface terms to a free particle Lagrangian. Geodesic equations are used in the context of the Hamilton-Jacobi formulation of constrained sysytem. Manifold structure induced by the quadratic…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
The model of the position-dependent noncommutativety in quantum mechanics is proposed. We start with a given commutation relations between the operators of coordinates [x^{i},x^{j}]=\omega^{ij}(x), and construct the complete algebra of…
We discuss the choice of the Lagrangian in the Poincar\'e gauge theory of gravity. Drawing analogies to earlier de Sitter gauge models, we point out the possibility of deriving the Einstein-Cartan Lagrangian {\it without} cosmological term…
This paper is concerned with quadratic-exponential moments (QEMs) for dynamic variables of quantum stochastic systems with position-momentum type canonical commutation relations. The QEMs play an important role for statistical…
A quantum mechanical theory is developed for the statistics of momentum transferred to the lattice by conduction electrons. Results for the electromechanical noise power in the semiclassical diffusive transport regime agree with a recent…
From the "vibrating string" and "Kepler's equation" theories to relativistic quantum fields, perturbation theory, (divergent) series resummations, KAM theory.