Related papers: Classical and quantum stability of higher-derivati…
Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrodinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical…
We study the quantum transport through entropic barriers induced by hardwall constrictions of hyperboloidal shape in two and three spatial dimensions. Using the separability of the Schrodinger equation and the classical equations of motion…
We develop the theory of discrete time Lagrangian mechanics on Lie groups, originated in the work of Veselov and Moser, and the theory of Lagrangian reduction in the discrete time setting. The results thus obtained are applied to the…
We study the macroscopic dynamical properties of fermion and quantum-spin systems with long-range, or mean-field, interactions. The results obtained are far beyond previous ones and require the development of a mathematical framework to…
A new model is studied which describes the quantum behavior of transitions through an isotropic quantum cosmological bounce in loop quantum cosmology sourced by a free and massless scalar field. As an exactly solvable model even at the…
We investigate deviations from the plane wave model in the interaction of charged particles with strong electromagnetic fields. A general result is that integrability of the dynamics is lost when going from lightlike to timelike or…
Development of robust quantum control has been challenging and there are numerous obstacles to applying classical robust control to quantum system including bilinearity, marginal stability, state preparation errors, nonlinear figures of…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic…
The canonical structure of theories whose Lagrangian contains higher powers of time derivatives is often obscured by the nonlinear relationship between the velocities and momenta. We use the Dirac formalism and define a generalized Legendre…
We analyze the problem of one dimensional quantum particle falling in a constant gravitational field, also known as the {\it bouncing ball}, employing a semiclassical approach known as momentous effective quantum mechanics. In this…
We study the classical limit of quantum mechanics on graphs by introducing a Wigner function for graphs. The classical dynamics is compared to the quantum dynamics obtained from the propagator. In particular we consider extended open graphs…
It is shown, under mild assumptions, that classical degrees of freedom dynamically coupled to quantum ones do not inherit their quantum fluctuations. It is further shown that, if the assumptions are strengthen by imposing the existence of a…
Classical physics is approached from quantum mechanics in the macroscopic limit. The technical device to achieve this goal is the quantum version of the central limit theorem, derived for an observable at a given time and for the…
We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case.…
We further develop a recently introduced variational principle of stationary action for problems in nonconservative classical mechanics and extend it to classical field theories. The variational calculus used is consistent with an initial…
It is shown that the vacuum state of weakly interacting quantum field theories can be described, in the Heisenberg picture, as a linear combination of randomly distributed incoherent paths that obey classical equations of motion with…
We show how the tracer motion of tagged, distinguishable particles can effectively describe transport in various homogeneous quantum many-body systems with constraints. We consider systems of spinful particles on a one-dimensional lattice…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
The mathematical possibility of coupling two quantum dynamic systems having two different Planck constants, respectively, is investigated. It turns out that such canonical dynamics are always irreversible. Semiclassical dynamics is obtained…