Related papers: Positive energy quantization of linear dynamics
Resonant systems emerge as weakly nonlinear approximations to problems with highly resonant linearized perturbations. Examples include nonlinear Schroedinger equations in harmonic potentials and nonlinear dynamics in Anti-de Sitter…
A concept of kinetic energy in quantum mechanics is analyzed. Kinetic energy is a non-zero positive value in many cases of bound states, when a wave function is a real-valued one and there are no visible motion and flux. This can be…
Understanding the role of correlations in quantum systems is both a fundamental challenge as well as of high practical relevance for the control of multi-particle quantum systems. Whereas a lot of research has been devoted to study the…
The current accelerating phase of the evolution of the universe is considered by constructing most economical cosmic models that use just general relativity and some dominating quantum effects associated with the probabilistic description…
We offer a systematic account of decomposition of quantum systems into parts. Different decompositions (structures) are mutually linked via the proper linear canonical transformations. Different kinds of structures, as well as their…
The dynamics of hybrid systems -- i.e. ones in which classical and quantum degrees of freedom co-exist and interact -- feature both diffusion in the classical sector and decoherence in the quantum state. In this article, we will consider…
The quantum three-wave interaction, the lowest order nonlinear interaction in plasma physics, describes energy-momentum transfer between three resonant waves in the quantum regime. We describe how it may also act as a…
For a single degree of freedom confined mechanical system with given energy, we know that the motion is always periodic and action-angle variables are convenient choice as conjugate phase-space variables. We construct action-angle coherent…
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
A novel approach for studying phase transitions in systems with quantum degrees of freedom is discussed. Starting from the microscopic hamiltonian of a quantum model, we first derive a set of exact differential equations for the free energy…
We compare three approaches to the quantization of (2+1)-dimensional gravity with a negative cosmological constant: reduced phase space quantization with the York time slicing, quantization of the algebra of holonomies, and quantization of…
The phase space of quantum mechanics can be viewed as the complex projective space endowed with a Kaehlerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrodinger equation as…
The act of describing how a physical process changes a system is the basis for understanding observed phenomena. For quantum-mechanical processes in particular, the affect of processes on quantum states profoundly advances our knowledge of…
A path-integral quantization method is proposed for dynamical systems whose classical equations of motion do \textit{not} necessarily follow from the action principle. The key new notion behind this quantization scheme is the Lagrange…
The similarity between classical and quantum physics is large enough to make an investigation of quantization methods a worthwhile endeavour. As history has shown, Dirac's canonical quantization method works reasonably well in the case of…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions…
Theoretical approaches to one-dimensional and quasi-one-dimensional quantum rings with a few electrons are reviewed. Discrete Hubbard-type models and continuum models are shown to give similar results governed by the special features of the…
The classical phase of the matrix model of 11-dimensional M-theory is complex, infinite-dimensional Hilbert space. As a complex manifold, the latter admits a continuum of nonequivalent, complex-differentiable structures that can be placed…
We address the dynamics of a bosonic system coupled to either a bosonic or a magnetic environment, and derive a set of sufficient conditions that allow one to describe the dynamics in terms of the effective interaction with a classical…