Related papers: Reconciling Semiclassical and Bohmian Mechanics: I…
We investigate classical and semiclassical aspects of codimension--two bifurcations of periodic orbits in Hamiltonian systems. A classification of these bifurcations in autonomous systems with two degrees of freedom or time-periodic systems…
The new method of multivariate data analysis based on the complements of classical probability distribution to quantum state and Schmidt decomposition is presented. We considered Schmidt formalism application to problems of statistical…
When two-dimensional pattern-forming problems are posed on a periodic domain, classical techniques (Lyapunov-Schmidt, equivariant bifurcation theory) give considerable information about what periodic patterns are formed in the transition…
Understanding, predicting, and controlling physical processes often relies on the analysis of the dynamics of partial differential equations (PDEs). In this context, the present study offers an in-depth investigation into the nonlinear…
Most discussions of chaotic scattering systems are devoted to two-dimensional systems. It is of considerable interest to extend these studies to the, in general, more realistic case of three dimensions. In this context, it is conceptually…
The global in-time semiclassical and relaxation limits of the bipolar quantum hydrodynamic model for semiconductors are investigated in $R^3$. We prove that the unique strong solution converges globally in time to the strong solution of…
We introduce the one-dimensional PT-symmetric Schrodinger equation, with complex potentials in the form of the canonical superoscillatory and suboscillatory functions known in quantum mechanics and optics. While the suboscillatory-like…
We study the multichannel scattering in the classical three-body system and show that the problem can be formulated as a motion of the point mass on a curved hyper-surface of the energy of the body-system. It is proved that the local…
Quantum polarization is investigated by means of a trajectory picture based on the Bohmian formulation of quantum mechanics. Relevant examples of classical-like two-mode field states are thus examined, namely Glauber and SU(2) coherent…
We present a new numerical method for accurate computations of solutions to (linear) one dimensional Schr\"odinger equations with periodic potentials. This is a prominent model in solid state physics where we also allow for perturbations by…
A tight binding representation of the kicked Harper model is used to obtain an integrable semiclassical Hamiltonian consisting of degenerate "quantized" orbits. New orbits appear when renormalized Harper parameters cross integer multiples…
We predict a generic manifestation of quantum interference in many-body bosonic systems resulting in a coherent enhancement of the average return probability in Fock space. This enhancement is both robust with respect to variations of…
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described…
We study semiclassical states of the nonlinear Dirac equation \[ -i\hbar\partial_t\psi = ic\hbar\sum_{k=1}^3\alpha_k\partial_k\psi - mc^2\beta \psi - M(x)\psi + f(|\psi|)\psi,\quad t\in\mathbb{R},\ x\in\mathbb{R}^3, \] where $V$ is a…
We generalise the Kosower-Maybee-O'Connell (KMOC) formalism relating classical observables and scattering amplitudes to curved backgrounds. We show how to compute the final semiclassical state for a particle moving in a curved background in…
The results of the mean field studies on the effects of the backward scattering with large momentum transfer in a two-dimensional electron system are extended to the case with various types of the Fermi surface and coupling constants. It is…
We introduce a nonperturbative approximation scheme for performing scattering calculations in two dimensions that involves neglecting the contribution of the evanescent waves to the scattering amplitude. This corresponds to replacing the…
These lectures treat scattering theory from a non-perturbative point of view. The course begins with a review of formal aspects in scattering theory, discussing the in/out states and the $S$ matrix that connects them. Unitarity relations,…
In a previous work, we have reanalyzed the I=0 S-wave \pi\pi-scattering phase-shift through a new method of Interfering Breit-Wigner amplitudes, and have shown the existence of a light scalar, \sigma particle, accompanied by a negative…
In this paper, we develop a comprehensive mathematical toolbox for the construction and spectral stability analysis of stationary multiple front and pulse solutions to general semilinear evolution problems on the real line with spatially…