相关论文: Borel Quantization: Kinematics and Dynamics
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
An universal exact description of kinetics of open quantum systems in terms of random wave functions and stochastic Schr\"{o}dinger equation is suggested. It is shown that evolution of random quantum states of an open system is unitary on…
An introduction to some basic ideas of the author's "quantum cybernetics" is given, which depicts waves and "particles" as mutually dependent system components, thus defining "organizationally closed systems" characterized by a fundamental…
We unify Brownian motion and quantum mechanics in a single mathematical framework. In particular, we show that non-relativistic quantum mechanics of a single spinless particle on a flat space can be described by a Wiener process that is…
Coupling any interacting quantum mechanical system to gravity in one (time) dimension requires the cosmological constant to belong to the matter energy spectrum and thus to be quantised, even though the gravity sector is free of any quantum…
It is shown that quantum mechanics on noncommutative (NC) spaces can be obtained by canonical quantization of some underlying constrained systems. Noncommutative geometry arises after taking into account the second class constraints…
In this work, we theoretically study the quantum correlations present in an optomechanical system by invoking an additional cross-Kerr coupling between the optical and mechanical mode. Under experimentally achievable conditions, we first…
We study a quantum spin system with local bilinear interactions and without quenched disorder which seems to display characteristic signatures of a many-body localisation (MBL) transition. From direct diagonalisation of small systems, we…
We investigate a quantum dynamical entropy of one-dimesional quantum spin systems. We show that the dynamical entropy is bounded from above by a quantity which is related with group velocity determined by the interaction and mean entropy of…
Nonadiabatic dressed states of a quantum system interacting with an external electromagnetic field and the environment are presented. The relevant matrix elements within the specified states are found. A closed form expression of the…
In the current quest for efficient and experimentally feasible platforms for implementation of multimode squeezing and entanglement in the continuous variable regime, we underpin and complement our results on the generation of versatile…
A kinematic approach to the geometric phase for mixed quantal states in nonunitary evolution is proposed. This phase is manifestly gauge invariant and can be experimentally tested in interferometry. It leads to well-known results when the…
We propose a nonlinear Schr\"odinger equation in a Hilbert space enlarged with an ancilla such that the partial trace of its solution obeys to the Lindblad equation of an open quantum system. The dynamics involved by this nonlinear…
A relation between the eigenvalues of an effective Hamilton operator and the poles of the $S$ matrix is derived which holds for isolated as well as for overlapping resonance states. The system may be a many-particle quantum system with…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
We introduce a quantum generalization of classical kinetic Ising models, described by a certain class of quantum many body master equations. Similarly to kinetic Ising models with detailed balance that are equivalent to certain Hamiltonian…
The fundamental principle of quantum mechanics is that the probabilities of physical outcomes are obtained from the intermediate states and processes of the interacting particles, considered as happening concurrently. When the interaction…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The…
We describe a $q$-deformed dynamical system corresponding to the quantum free particle moving along the circle. The algebra of observables is constructed and discussed. We construct and classify irreducible representations of the system.