Related papers: Constrained quantum dynamics
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
An effective formalism for quantum constrained systems is presented which allows manageable derivations of solutions and observables, including a treatment of physical reality conditions without requiring full knowledge of the physical…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…
We present a detailed account of the technical aspects of stochastic quantum molecular dynamics, an approach introduced recently by the authors [H. Appel and M. Di Ventra, Phys. Rev. B 80 212303 (2009)] to describe coupled electron-ion…
Quantization relates Poisson algebras to $C^*$-algebras. The analysis of local gauge symmetries in algebraic quantum field theory is approached through the quantization of classical gauge theories, regarded as constrained dynamical systems.…
A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between…
Entropic Dynamics is a framework in which dynamical laws are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to the constraints…
The basic concepts of classical mechanics are given in the operator form. The dynamical equation for a hybrid system, consisting of quantum and classical subsystems, is introduced and analyzed in the case of an ideal nonselective…
We consider quantum mechanics on constrained surfaces which have non-Euclidean metrics and variable Gaussian curvature. The old controversy about the ambiguities involving terms in the Hamiltonian of order hbar^2 multiplying the Gaussian…
As examples of models having interesting constraint structures, we derive a quantum mechanical model from the spatial freezing of a well known relativistic field theory - the chiral Schwinger model. We apply the Hamiltonian constraint…
We study classical and quantum dynamics of a kicked relativistic particle confined in a one dimensional box. It is found that in classical case for chaotic motion the average kinetic energy grows in time, while for mixed regime the growth…
By using the canonical and symplectic approaches an (nonstandard) alternative action describing linearized gravity is studied. We identify the complete set of Dirac's constraints, the counting of physical degrees of freedom is performed and…
We present a geometric formulation of quantum mechanics based on the symplectic structure of the projective Hilbert space. Building upon the standard K\"ahler framework, we introduce an extension in which the symplectic structure is allowed…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
Understanding out-of-equilibrium quantum dynamics is a critical outstanding problem, with key questions regarding characterizing adiabaticity for applications in quantum technologies. We show how the metric-space approach to quantum…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
We consider the quantum simulation of relativistic quantum mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. First, we study the…
We report recent progress on the phase space formulation of quantum mechanics with coordinate-momentum variables, focusing more on new theory of (weighted) constraint coordinate-momentum phase space for discrete-variable quantum systems.…