相关论文: Reduced phase space optics for general relativity:…
On general symplectic manifolds we describe a correspondence between symplectic transformations and their phase functions. On the quantum level, this is a correspondence between unitary operators and phase functions of the…
The quantum phase diagram for a finite $3$-level system in the $\Lambda$ configuration, interacting with a two-mode electromagnetic field in a cavity, is determined by means of information measures such as fidelity, fidelity susceptibility…
We study propagation of high-frequency electromagnetic waves in a curved spacetime. We demonstrate how a modification of the standard geometric optics allows one to include the helicity dependent corrections into the equations of motion of…
We report on the observation of Bragg scattering at 1D atomic lattices. Cold atoms are confined by optical dipole forces at the antinodes of a standing wave generated by the two counter-propagating modes of a laser-driven high-finesse ring…
This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to $L_VY$, the bundle of vertically adapted linear frames over the…
Using symmetry considerations, we derive a unitary scattering matrix for a three-port optical Y-coupler or Y-branch. The result is shown to be unique up to external phase shifts. Unlike traditional passive linear-optical one-way splitters,…
Gauging of space translations for nonrelativistic point particles in one dimension leads to general coordinate transformations with fixed Newtonian time. The minimal gauge invariant extension of the particle velocity requires the…
Let $G$ be a Lie group, with an invariant non-degenerate symmetric bilinear form on its Lie algebra, let $\pi$ be the fundamental group of an orientable (real) surface $M$ with a finite number of punctures, and let $\bold C$ be a family of…
We develop a scattering theory to investigate the multi-photon transmission in a one-dimensional waveguide in the presence of quantum emitters. It is based on a path integral formalism, uses displacement transformations, and does not…
In this paper, we extend and investigate the properties of the semi-smooth Newton method when applied to a general projection equation in finite dimensional spaces. We first present results concerning Clarke's generalized Jacobian of the…
The transfer matrix of a possibly complex and energy-dependent scattering potential can be identified with the $S$-matrix of a two-level time-dependent non-Hermitian Hamiltonian H(t). We show that the application of the adiabatic…
A generalisation of Takens' delay-coordinate embedding theorem to stochastic systems, the Stochastic Embedding Sufficiency Theorem, is an inverse methodology enabling non-parametric recovery of both drift and diffusion fields from scalar…
Wave propagation in ray-chaotic scenarios, characterized by exponential sensitivity to ray-launching conditions, is a topic of significant interest, with deep phenomenological implications and important applications, ranging from optical…
We study the symplectic reduction of the phase space describing $k$ particles in $\mathbb{R}^n$ with total angular momentum zero. This corresponds to the singular symplectic quotient associated to the diagonal action of $\operatorname{O}_n$…
Analogous coherent states are deduced from classical optical fields on curved surface in this paper. The Gaussian laser beam, as a fundamental mode, cannot be adequately simulated by coherent states due to their inherent diffraction in flat…
We propose a geometric framework where dispersion relations are viewed as parametric surfaces in energy-momentum space. Within this picture, the presence and type of critical points of the surface emerge as clear geometric signatures of…
Symmetries are important guiding principle for phase transitions. We systematically construct field theory models with local quantum fields that exhibit the following phase transitions: (1) different symmetry protected topological (SPT)…
Using the method of Laplace transform the field amplitude in the paraxial approximation is found in the two-dimensional free space using initial values of the amplitude specified on an arbitrary shaped monotonic curve. The obtained…
A semiclassical model is presented for characterizing the linear response of elementary quantum optical systems involving cavities, optical fibers, and atoms. Formulating the transmission and reflection spectra using a scattering-wave…
This paper presents a generalisation of Sylvester's law of inertia to real non-degenerate quadratic forms on a fixed real vector bundle over a connected locally connected paracompact Hausdorff space. By interpreting the classical inertia as…