Related papers: Geometric potentials in quantum optics: A semi-cla…
A particle that is constrained to freely move on a hyperspherical surface in an $N\left( \geq 2\right) $ dimensional flat space experiences a curvature-induced gauge potential, whose form was given long ago (J. Math. Phys.…
Vast literature on the experiments and mathematical formulations on the geometric phases signifies the importance of this subject. Physical mechanism for the origin of the geometric phases in optics was suggested in 1992 by the author in…
Raman-type laser excitation of a trapped atom allows one to realize the quantum mechanical counterpart of phenomena of nonlinear optics, such as Kerr-type nonlinearities, parametric amplification, and multi-mode mixing. Additionally, huge…
I discuss some theoretical ideas concerning the representation of quantum gravity as a Lorentz-symmetry-violating `medium' with non-trivial optical properties, which include a refractive index in `vacuo' and stochastic effects associated…
The nonlinear optical behavior of quantum systems plays a crucial role in various photonic applications. This study introduces a novel framework for understanding these nonlinear effects by incorporating gauge-covariant formulations based…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
We introduce and analyze several low-dimensional scattering systems that exhibit geometric phase phenomena. The systems are fully solvable and we compare exact solutions of them with those obtained in a Born-Oppenheimer projection…
The behaviour of a relativistic scalar particle in a possible scenario that arises from the violation of the Lorentz symmetry is investigated. The background of the Lorentz symmetry violation is defined by a tensor field that governs the…
Semi-classical gravity is an approximation to quantum gravity where gravity is treated classically and matter quantum mechanically. Matter is described by quantum field theory on curved space-time, whereas gravity is described by a…
We theoretically study the Casimir-Polder force on an atom in a arbitrary initial state in a rather general electromagnetic environment wherein the materials may have a nonreciprocal bianisotropic dispersive response. It is shown that under…
We investigate theoretically the Casimir-Polder potential of an atom which is driven by a laser field close to a surface. This problem is addressed in the framework of macroscopic quantum electrodynamics using the Green's tensor formalism…
We review in this paper the use of the theory of scale relativity and fractal space-time as a tool particularly well adapted to the possible development of a future genuine theoretical systems biology. We emphasize in particular the concept…
The properties of the quantum universe on extremely small spacetime scales are studied in the semi-classical approach to the well-defined quantum model. It is shown that near the initial cosmological singularity point quantum gravity…
We propose a geometric interpretation for the Stokes phenomenon in de Sitter spacetime that particles are produced in even dimensions but not in odd dimensions. The scattering amplitude for a quantum field between the in-vacuum and the…
Within the wave-packet semiclassical approach, the Bloch electron energy is derived to second order in the magnetic field and classified into gauge-invariant terms with clear physical meaning, yielding a fresh understanding of the complex…
The semiclassical evolution of spinning particles has recently been re-examined in condensed matter physics, high energy physics, and optics, resulting in the prediction of the intrinsic spin Hall effect associated with the Berry phase. A…
Modern undergraduate textbooks in electricity and magnetism typically focus on a force representation of electrodynamics with an emphasis on Maxwell's Equations and the Lorentz Force Law. The vector potential $\mathbf{A}$ and scalar…
We show how to formulate physical theory taking as a starting point the set of states (geometric approach). We discuss the relation of this formulation to the conventional approach to classical and quantum mechanics and the theory of…
A problem of self-energy and self-force for a charged point-like particle in a higher dimensional homogeneous gravitational field is considered. We study two cases, when a particle has usual electric charge and a case when it has a scalar…
If the presence of a gravitational field breaks the Lorentz symmetry valid for special relativity, an "absolute motion" might be detectable. We summarize a scalar theory of gravity with a such "ether", which starts from a tentative…