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The Hamilton-Jacobi equation of relativistic quantum mechanics is revisited. The equation is shown to permit solutions in the form of breathers (oscillating/spinning solitons), displaying simultaneous particle-like and wave-like behaviour.
Quantum Hamilton-Jacobi quantization scheme uses the singularity structure of the potential of a quantum mechanical system to generate its eigenspectrum and eigenfunctions, and its efficacy has been demonstrated for several well known…
In this work, we uncover new features on the study of a two-level atom interacting with one of two cavities in a coherent superposition. The James-Cummings model is used to describe the atom-field interaction and to study the effects of…
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and…
The dynamics of few two-level atoms interacting with one cavity mode is described in master equation formalism. Two different configurations are considered: a transient one with all atoms initially in the excited state and a stationary one…
Stochastic perturbation of two-level atoms strongly driven by a coherent light field is analyzed by the quantum trajectory method. A new method is developed for calculating the resonance fluorescence spectra from numerical simulations. It…
In this work we present a formal generalization of the Hamilton-Jacobi formalism, recently developed for singular systems, to include the case of Lagrangians containing variables which are elements of Berezin algebra. We derive the…
This paper investigates wave-packet dynamics in non-Hermitian lattice systems and reveals a surprising phenomenon: The simultaneous propagation of two distinct wavefronts, one traveling at the non-Hermitian velocity and the other at the…
Quantum collision models allow for the dynamics of open quantum systems to be described by breaking the environment into small segments, typically consisting of non-interacting harmonic oscillators or two-level systems. This work introduces…
Special relativity combined with the stochastic vacuum flux impact model lead to an explicit interpretation of many of the phenomena of elementary quantum mechanics. We examine characteristics of a repetitively impacted submicroscopic…
A numerical study has been done of collisions between protons and hydrogen atoms, treated as classical particles, at low impact velocities. The presence of chaos has been looked for by investigating the processes with standard techniques of…
We study the vortex dynamics of a quantum degenerate Bose gas through the intensity fluctuations of the interference from particles extracted at two different positions. It is shown numerically with classical field simulations that an…
We apply the quantum Hamilton-Jacobi formalism, naturally defined in the complex domain, to a number of complex Hamiltonians, characterized by discrete parity and time reversal (PT) symmetries and obtain their eigenvalues and…
We connect Quantum Hamilton-Jacobi Theory with supersymmetric quantum mechanics (SUSYQM). We show that the shape invariance, which is an integrability condition of SUSYQM, translates into fractional linear relations among the quantum…
This article presents a general master equation formalism for the interaction between travelling pulses of quantum radiation and localized quantum systems. Traveling fields populate a continuum of free space radiation modes and the…
Wave turbulence formalism for long internal waves in a stratified fluid is developed, based on a natural Hamiltonian description. A kinetic equation appropriate for the description of spectral energy transfer is derived, and its…
Scattering from a compound barrier, one composed of a number of distinct non-overlapping sub-barriers, has a number of interesting and subtle mathematical features. If one is scattering classical particles, where the wave aspects of the…
The concept of quantum superposition is reconsidered and discussed from the viewpoint of Bohmian mechanics, the hydrodynamic formulation of quantum mechanics, in order to elucidate some physical consequences that go beyond the simple…
We have developed a method for complementing an arbitrary classical dynamical system to a quantum system using the Lorenz and R\"ossler systems as examples. The Schr\"odinger equation for the corresponding quantum statistical ensemble is…
The mathematical formalism of quantum theory exhibits significant effectiveness when applied to cognitive phenomena that have resisted traditional (set theoretical) modeling. Relying on a decade of research on the operational foundations of…