Related papers: Borel Quantization: Kinematics and Dynamics

We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one and is in harmony with the modern trends in theoretical physics and potentially admits new…

The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured…

We introduce a geometrical framework to construct a large class of time-dependent quantum systems, in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over…

The phenomenon of quantum entanglement is thoroughly investigated, focussing especially on geometrical aspects and on bipartite systems. After introducing the formalism and discussing general aspects, some of the most important separability…

The quantum dynamic equation (QDE) of machine learning is obtained based on Schr\"odinger equation and potential energy equivalence relationship. Through Wick rotation, the relationship between quantum dynamics and thermodynamics is also…

I describe a possible perspective on the current state of loop quantum gravity, at the light of the developments of the last years. I point out that a theory is now available, having a well-defined background-independent kinematics and a…

A generalized formalism of the so-called non-adiabatic quantum molecular dynamics is presented, which applies for atomic many-body systems in external laser fields. The theory treats the nuclear dynamics and electronic transitions…

We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism,…

A formalism for studying the dynamics of quantum systems embedded in classical spin baths is introduced. The theory is based on generalized antisymmetric brackets and predicts the presence of open-path off-diagonal geometric phases in the…

It is shown that quantization of the dynamical systems with second class constraints actually can be reduced to quantization of the systems with first class constraints. The motion of the non-relativistic particle along the plane curve and…

We study theoretically transitions between the localized and chaotic many-body regimes in one-dimensional quantum lattice systems with long-range couplings between particles and linear external potential. In terms of established criteria…

Some of the important non-classical aspects of quantum mechanics can be described in more intuitive terms if they are reformulated in a geometrical picture based on an extension of the classical phase space. This contribution presents…

We analyze the quantization of dynamical systems that do not involve any background notion of space and time. We give a set of conditions for the introduction of an intrinsic time in quantum mechanics. We show that these conditions are a…

The relation between the dynamical properties of a coupled quasiparticle-oscillator system in the mixed quantum-classical and fully quantized descriptions is investigated. The system is considered to serve as a model system for applying a…

We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…

We show that when a quantum system is coupled to an environment in a mean field way, then its effective dynamics is governed by a unitary group with a time-dependent Hamiltonian. The time-dependent modification of the bare system…

Quantum observables can be identified with vector fields on the sphere of normalized states. The resulting vector representation is used in the paper to undertake a simultaneous treatment of macroscopic and microscopic bodies in quantum…

In this paper we explore the mathematical structure of hierarchical organization in smooth dynamical systems. We start by making precise what we mean by a level in a hierarchy, and how the higher le vels need to respect the dynamics on the…

The paper contains a brief review of an approach to quantum entanglement based on analysis of dynamic symmetry of systems and quantum uncertainties, accompanying the measurement of mean value of certain basic observables. The latter are…

We investigate the differential geometry of bipartite quantum states. In particular the manifold structures of pure bipartite states are studied in detail. The manifolds with respect to all normalized pure states of arbitrarily given…