相关论文: Factorizations of one dimensional classical system…

A Hamiltonian approach is presented to study the two dimensional motion of damped electric charges in time dependent electromagnetic fields. The classical and the corresponding quantum mechanical problems are solved for particular cases…

Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the…

We show how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories ("emergent dualities"), can be unveiled, and systematically established. Our method relies on the use of morphisms of…

We present all second order classical integrable systems of the cylindrical type in a three dimensional Euclidean space $\mathbb{E}_3$ with a nontrivial magnetic field. The Hamiltonian and integrals of motion have the form $H…

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…

The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part…

If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below.…

The definition of "classical anomaly" is introduced. It describes the situation in which a purely classical dynamical system which presents both a lagrangian and a hamiltonian formulation admits symmetries of the action for which the…

It is well known that the action functional can be used to define classical, quantum, closed, and open dynamics in a generalization of the variational principle and in the path integral formalism in classical and quantum dynamics,…

We construct Poisson structures for Ermakov systems, using the Ermakov invariant as the Hamiltonian. Two classes of Poisson structures are obtained, one of them degenerate, in which case we derive the Casimir functions. In some situations,…

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…

Canonical quantization has served wonderfully for the quantization of a vast number of classical systems. That includes single classical variables, such as $p$ and $q$, and numerous classical Hamiltonians $H(p,q)$, as well as field…

We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…

Bosonic quantum conversion systems can be modeled by many-particle single-mode Hamiltonians describing a conversion of $n$ molecules of type A into $m$ molecules of type B and vice versa. These Hamiltonians are analyzed in terms of…

We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of…

We discuss classical and quantum computations in terms of corresponding Hamiltonian dynamics. This allows us to introduce quantum computations which involve parallel processing of both: the data and programme instructions. Using mixed…

The analogy between monodromy in dynamical (Hamiltonian) systems and defects in crystal lattices is used in order to formulate some general conjectures about possible types of qualitative features of quantum systems which can be interpreted…

We study a certain class of classical one dimensional piecewise linear maps. For these systems we introduce an infinite family of Markov partitions into equal cells. The symbolic dynamics generated by these systems is described by…

Factorization algebras are local-to-global objects living on manifolds, and they arise naturally in mathematics and physics. Their local structure encompasses examples like associative algebras and vertex algebras; in these examples, their…

Some positive answers to the problem of endowing a dynamical system with a Hamiltonian formulation are presented within the class of Poisson structures in a geometric framework. We address this problem on orientable manifolds and by using…