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The Hamiltonian constraint formalism is used to obtain the first explicit complete analysis of non-trivial viable dynamic modes for the Poincar\'e gauge theory of gravity. Two modes with propagating spin-zero torsion are analyzed. The…
We illustrate how classical chaotic dynamics influences the quantum properties at mesoscopic scales. As a model case we study semiclassically coherent transport through ballistic mesoscopic systems within the Landauer formalism beyond the…
We study transport properties of discrete quantum dynamical systems on the lattice, in particular Coined Quantum Walks and the Chalker--Coddington model. We prove existence of a non trivial charge transport and that the absolutely…
A method to construct Hamiltonian theories for systems of both ordinary and partial differential equations is presented. The knowledge of a Lagrangian is not at all necessary to achieve the result. The only ingredients required for the…
A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which involves two complex wave fields and…
A nonlinear quantum-classical transition wave equation is proposed for dissipative systems within the Caldirola-Kanai model. Equivalence of this transition equation to a scaled Schr\"{o}dinger equation is proved. The dissipative dynamics is…
Classical simulation of quantum systems plays an important role in the study of many-body phenomena and in the benchmarking and verification of quantum technologies. Exact simulation is often limited to small systems because the dimension…
A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation…
This paper deals with the classical trajectories for two super-integrable systems: a system known in quantum chemistry as the Hartmann system and a system of potential use in quantum chemistry and nuclear physics. Both systems correspond to…
Classical Hamiltonian mechanics, characterized by a single conserved Hamiltonian (energy) and symplectic geometry, `hides' other invariants into symmetries of the Hamiltonian or into the kernel of the Poisson tensor. Nambu mechanics aims to…
The qualitatively new concept of dynamic complexity in quantum mechanics is based on a new paradigm appearing within a nonperturbational analysis of the Schroedinger equation for a generic Hamiltonian system. The unreduced analysis…
One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…
Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
Most general third-order $3d$ linear gauge vector field theory is considered. The field equations involve, besides the mass, two dimensionless constant parameters. The theory admits two-parameter series of conserved tensors with the…
We formulate Lagrangian descriptors (LDs) in the path integral framework. Averaging the classical LD over fluctuations about extremal trajectories defines a quantum LD that incorporates quantum effects. Invariant manifolds, which sharply…
We characterize a class of superclassical non-Markovian open quantum system dynamics that are defined by their lack of measurement invasiveness when the corresponding observable commutates with the pre-measurement state. This diagonal…
We analyze how quantum mechanics reinstates confinement in Hamiltonian systems that are classically unstable and exhibit chaotic dynamics. Specifically, we consider two paradigmatic models: the Contopoulos Hamiltonian, an isotropic…
Described is n-level quantum system realized in the n-dimensional ''Hilbert'' space H with the scalar product G taken as a dynamical variable. The most general Lagrangian for the wave function and G is considered. Equations of motion and…
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…