相关论文: Borel Quantization: Kinematics and Dynamics
An approach to the description of kinetics which taking into account the large-scale hydrodynamic transport processes for quantum Bose system is proposed. The nonequilibrium statistical operator which consistently describes both the kinetic…
Quantum theory of field (extended) objects without a priori space-time geometry has been represented. Intrinsic coordinates in the tangent fibre bundle over complex projective Hilbert state space $CP(N-1)$ are used instead of space-time…
This contribution to the present Workshop Proceedings outlines a general programme for identifying geometric structures--out of which to possibly recover quantum dynamics as well--associated to the manifold in Hilbert space of the quantum…
We explain why, in a configuration space that is multiply connected, i.e., whose fundamental group is nontrivial, there are several quantum theories, corresponding to different choices of topological factors. We do this in the context of…
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…
This colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems. We particularly focus on quantum quenches: the temporal evolution following a sudden or…
We introduce an energy-resolved variant of quantum thermodynamics for open systems strongly coupled to their baths. The approach generalizes the Landauer-Buttiker inside-outside duality method [Phys. Rev. Lett. 120, 107701 (2018)] to…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
The Schrodinger equation for non-relativistic quantum systems is derived from some classical physics axioms within an ensemble hamiltonian framework. Such an approach enables one to understand the structure of the equation, in particular…
In this paper, the physical realizability property is investigated for a class of nonlinear quantum systems. This property determines whether a given set of nonlinear quantum stochastic differential equations corresponds to a physical…
The quantum mechanics of a simple mechanical system is considered. A group of gears can serve as a model for several different systems such as an artifically constructed nanomechanical device or a group of ring molecules. It is shown that…
Quantum systems subjected to a continuous weak measurement process evolve according to stochastic differential equations (SDE). Depending on the outcomes of these stochastic measurements, the quantum state may diffuse in various directions…
We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of…
We study the quantum dynamics resulting from preparing a one-dimensional quantum system in the ground state of initially two decoupled parts which are then joined together (local quench). Specifically we focus on the transverse Ising chain…
We develop the idea of employing localization systems of Boolean coverings, associated with measurement situations, in order to comprehend structures of Quantum Observables. In this manner, Boolean domain observables constitute structure…
The problem of characterizing complexity of quantum dynamics - in particular of locally interacting chains of quantum particles - will be reviewed and discussed from several different perspectives: (i) stability of motion against external…
The kicked rotor system is a textbook example of how classical and quantum dynamics can drastically differ. The energy of a classical particle confined to a ring and kicked periodically will increase linearly in time whereas in the quantum…
The planar quantum dynamics of a neutral particle with a magnetic dipole moment in the presence of electric and magnetic fields is considered. The criteria to establish the planar dynamics reveal that the resulting nonrelativistic…
We develop a general approach to setting up and studying classes of quantum dynamical systems close to and structurally similar to systems having specified properties, in particular detailed balance. This is done in terms of transport plans…
We study mirror symmetry (A-side vs B-side) in the framework of quantum differential systems. We focuse on the logarithmic and non-resonant case, which describes the geometric situation. We show that quantum differential systems provide a…