Related papers: Quantization of classical integrable systems. Part…
We apply the factorization technique developed by Kuru and Negro [Ann. Phys. 323 (2008) 413] to study complex classical systems. As an illustration we apply the technique to study the classical analogue of the exactly solvable PT symmetric…
A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…
We propose a new method of quantization of a wide class of dynamical systems that originates directly from the equations of motion. The method is based on the correspondence between the classical and the quantum Poisson brackets, postulated…
Recently, a geometric embedding of the classical space and classical phase space of an n-particle system into the space of states of the system was constructed and shown to be physically meaningful. Namely, the Newtonian dynamics of the…
We present a two-dimensional classical stochastic differential equation for a displacement field of a point particle in two dimensions and show that its components define real and imaginary parts of a complex field satisfying the…
We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to…
The McMillan map is a well-known example of a rational integrable system for one particle in a two-dimensional phase space. An elegant recent paper presented a generalization of the McMillan map to an $N$-body system, for particles moving…
Methods for measuring an integral of a classical field via local interaction of classical bits or local interaction of qubits passing through the field one at a time are analyzed. A quantum method, which has an exponentially better…
A consistent description of interactions between classical and quantum systems is relevant to quantum measurement theory, and to calculations in quantum chemistry and quantum gravity. A solution is offered here to this longstanding problem,…
In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over…
Quantum mechanics exhibits a wide range of nonclassical features, of which entanglement in multipartite systems takes a central place. In several specific settings, it is well known that nonclassicality (e.g., squeezing, spin squeezing,…
The extraction of classical degrees of freedom in quantum mechanics is studied in the stochastic variational method. By using this classicalization, a hybrid model constructed from quantum and classical variables (quantum-classical hybrids)…
We review some essential aspects of classically integrable systems. The detailed outline of the lectures consists of: 1. Introduction and motivation, with historical remarks; 2. Liouville theorem and action-angle variables, with examples…
In a previous paper, we have developed a general theory of thermodynamic limits. We apply it here to three different Coulomb quantum systems, for which we prove the convergence of the free energy per unit volume. The first system is the…
A careful reexamination of the quantization of systems with first- and second-class constraints from the point of view of coherent-state phase-space path integration reveals several significant distinctions from more conventional…
We relate a large class of classical spin models, including the inhomogeneous Ising, Potts, and clock models of q-state spins on arbitrary graphs, to problems in quantum physics. More precisely, we show how to express partition functions as…
We study a system of two pointlike particles coupled to three dimensional Einstein gravity. The reduced phase space can be considered as a deformed version of the phase space of two special-relativistic point particles in the centre of mass…
An infinite family of classical superintegrable Hamiltonians defined on the N-dimensional spherical, Euclidean and hyperbolic spaces are shown to have a common set of (2N-3) functionally independent constants of the motion. Among them, two…
Enormous activity in the Quantum Computing area has resulted in considering them to solve different difficult problems, including those of applied nature, together with classical computers. An attempt is made in this work to nail down a…
The quantization rules recently proposed by M. Navarro (and independently I.V. Kanatchikov) for a finite-dimensional formulation of quantum field theory are applied to the Klein-Gordon and the Dirac fields to obtain the quantum equations of…