Related papers: Understanding chemical reactions within a generali…
We report the quantum computing of reacting flows by simulating the Hamiltonian dynamics. The scalar transport equation for reacting flows is transformed into a Hamiltonian system, mapping the dissipative and non-Hermitian problem in…
We consider the quantum nonequilibrium dynamics of systems where fermionic particles coherently hop on a one-dimensional lattice and are subject to dissipative processes analogous to those of classical reaction-diffusion models. Particles…
By employing special solutions of the Hamilton-Jacobi equation and tools from lattice theories, we suggest an approach to convert classical theories to quantum theories for mechanics and field theories. Some nontrivial results are obtained…
We study the back-reaction of quantum systems onto classical ones. Taking the starting point that semi-classical physics should be described at all times by a point in classical phase space and a quantum state in Hilbert space, we consider…
Through semiclassical methods the subject of quantum chaos motivates and depends on Hamiltonian chaos research. Presented here is a selection of Hamiltonian chaos topics that in this way get directly related to any of a variety of quantum…
Trajectory-based approaches to quantum mechanics include the de Broglie-Bohm interpretation and Nelson's stochastic interpretation. It is shown that the usual route to establishing the validity of such interpretations, via a decomposition…
The paper deals with Hawking radiation related to non-static spherically symmetric black hole. Quantum corrections are incorporated using Hamilton-Jacobi method beyond semi-classical approximation. It is found that different order…
This paper presents a new approach to phase space trajectories in quantum mechanics. A Moyal description of quantum theory is used, where observables and states are treated as classical functions on a classical phase space. A quantum…
A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains.…
Currently, dynamics of a massive macroparticle is given by classical analytical mechanics (CM), while that of a massive micro one is given by quantum mechanics (QM). We propose a mechanics effective for both: We transform, under coordinate…
Inspired by Wannier's threshold law, we recognize that collision complex decay meets the requirements of quantum-classical correspondence in sufficiently exothermic ultracold reactions. We make use of this correspondence to elucidate the…
Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…
We discuss time-optimal control problems for two setups involving globally driven Rydberg atoms in the blockade limit by deriving the associated Hamilton-Jacobi-Bellman equations. From these equations, we extract the globally optimal…
This paper is devoted to the analysis of massive particle in general and Newton-Cartan Background in de Broglie-Bohm Theory. We find classical and quantum version of Hamilton-Jacobi equations and find their relations to wave equations. We…
We study the motion of a particle in a particular magnetic field configuration both classically and quantum mechanically. For flux-free radially symmetric magnetic fields defined on circular regions, we establish that particle escape speeds…
Adaptation of the Hamilton--Jacobi formalism to quantum mechanics leads to a cocycle condition, which is invariant under $D$--dimensional M\"obius transformations with Euclidean or Minkowski metrics. In this paper we aim to provide a…
In this paper, we construct Hamilton-Jacobi equations for a great variety of mechanical systems (nonholonomic systems subjected to linear or affine constraints, dissipative systems subjected to external forces, time-dependent mechanical…
We used for the first time the method of periodic orbit dividing surfaces in a non-integrable Hamiltonian system with three degrees of freedom. We have studied the structure of these four dimensional objects in the five dimensional phase…
We propose a concise stochastic mechanics framework for chemical reaction systems that allows to formulate evolution equations for three general types of data: the probability generating functions, the exponential moment generating…
The numerical version of the Hamilton-Jacobi quantization method, recently proposed, is applied to the one dimensional quartic oscillator. A suitable quantization condition is formulated and various energy levels and wave functions are…