Related papers: Path Integrals for Photonic Crystals
Charged particle optics, the description of particle trajectories in the vicinity of some optical axis, describe the imaging properties of particle optics devices. Here, we present a complete and compact description of charged particle…
Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have influence of a universal sort and manifest themselves in scaling…
Based on quantum mechanical approach the polarization transport of photons which propagate in a medium with slow varying refractive index is studied. The photon polarizations are separated in opposite directions normal to the ray which is…
Light propagation in systems with anti-Hermitian coupling, described by a spinor-like wave equation, provides a general route for the observation of anti parity-time ($\mathcal{PT}$ ) symmetry in optics. Remarkably, under a different…
A recent proposal to connect the loop quantization with the spin foam model for cosmology via the path integral is hereby adapted to the case of mechanical systems within the framework of the so called polymer quantum mechanics. The…
The one-sided bouncer and the symmetric bouncer involve a one-dimensional particle in a piecewise linear potential. For such problems, the time-dependent quantum mechanical propagator cannot be found in closed form. The semiclassical…
While it is well-known that quantum mechanics can be reformulated in terms of a path integral representation, it will be shown that such a formulation is also possible in the case of classical mechanics. From Koopman-von Neumann theory,…
We reveal all the linear optical responses, reflection, transmission, and, diffraction, of typical one-dimensional metallic photonic crystal slabs (MPhCS) with the periodicity of a half micrometer. Maxwell equations for the structure of…
The semiclassical propagation of spin coherent states is considered in complex phase space. For two time-independent systems we find the appropriate classical trajectories and show that their combined contributions are able to describe…
The use of variational method in functional integral approach is discussed for fermion and boson systems with Coulomb interaction. The formal general expression of thermodynamic potential is obtained by Feynman path integral technique and…
We consider photonic crystal fibres (PCFs) made from arbitrary base materials and introduce a short-wavelength approximation which allows for a mapping of the Maxwell's equations onto a dimensionless eigenvalue equations which has the form…
We show that the requirement of manifest coordinate invariance of perturbatively defined quantum-mechanical path integrals in curved space leads to an extension of the theory of distributions by specifying unique rules for integrating…
Phase space path integral is worked out in a riemannian geometry, by employing a prescription for the infinitesimal propagator that takes riemannian normal coordinates and momenta on an equal footing. The operator ordering induced by this…
Path integral formulations for the Smorodinsky-Winternitz potentials in two- and three-dimen\-sional Euclidean space are presented. We mention all coordinate systems which separate the Smorodinsky-Winternitz potentials and state the…
A general path integral analysis of the separable Hamiltonian of Liouville-type is reviewed. The basic dynamical principle used is the Jacobi's principle of least action for given energy which is reparametrization invariant, and thus the…
Manipulation of qudits in optical tables is a difficult and nonscalable task. The use of integrated optical circuits opens new possibilities for the generation, manipulation, and characterization of high dimensional states besides the ease…
Phase-space path-integrals are used in order to illustrate various aspects of a recently proposed interpretation of quantum mechanics as a gauge theory of metaplectic spinor fields.
This thesis addresses a fundamental problem in deformation quantization: the difficulty of calculating the star-exponential, the symbol of the evolution operator, due to convergence issues. Inspired by the formalism that connects the…
Path integral-based simulation methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical…
We give a mathematical definition of some path integrals, emphasizing those relevant to the quantization of symplectic manifolds (and more generally, Poisson manifolds) $\unicode{x2013}$ in particular, the coherent state path integral. We…