Related papers: Wave Tracing: Generalizing The Path Integral To Wa…
This paper suggests a new way to compute the path integral for simple quantum mechanical systems. The new algorithm originated from previous research in string theory. However, its essential simplicity is best illustrated in the case of a…
Transport processes underpin a multitude of phenomena, ranging from the propagation of atoms on lattices, to the mobility patterns of microorganisms and earthquakes, to name a few. The dynamics of these processes is very rich and key to…
We develop a new computational tool and framework for characterizing the scattering of photons by energy-nonconserving Hamiltonians into unidirectional (chiral) waveguides, for example, with coherent pulsed excitation. The temporal…
Compared to classical optical coherence theory based on Maxwell's electromagnetic theory and Glauber's quantum optical coherence theory based on matrix mechanics formulation of quantum mechanics, quantum optical coherence theory based on…
Surface waves on liquids act as a dynamical phase grating for incident light. In this article, we revisit the classical method of probing such waves (wavelengths of the order of mm) as well as inherent properties of liquids and liquid films…
Sampling from probability distributions of quantum circuits is a fundamentally and practically important task which can be used to demonstrate quantum supremacy using noisy intermediate-scale quantum devices. In the present work, we examine…
A path integral representation of the evolution operator for the four-dimensional Dirac equation is proposed. A quadratic form of the canonical momenta regularizes the original representation of the path integral in the electron phase…
A quantum theory of light propagation in two optical channel waveguides tunnelling-coupled to a common continuum of modes (such as those of a slab waveguide) is presented, and classical and quantum interference effects are investigated. For…
The theory of nonlinear diffraction of intensive light beams propagating through photorefractive media is developed. Diffraction occurs on a reflecting wire embedded in the nonlinear medium at relatively small angle with respect to the…
Tailored time-dependent variations of the transverse profile together with longitudinal phase shifts of laser beams are studied. It is shown theoretically that a standing wave setup and real-time beam forming techniques (e.g. by…
The linear transport theory is developed to describe the time dependence of the number density of tracer particles in porous media. The advection is taken into account. The transport equation is numerically solved by the analytical discrete…
A tutorial discussion of the propagation of waves in random media is presented. In first approximation the transport of the multiple scattered waves is given by diffusion theory, but important corrections are present. These corrections are…
Diffusion models have been successfully applied to robotics problems such as manipulation and vehicle path planning. In this work, we explore their application to end-to-end navigation -- including both perception and planning -- by…
Phase-space procedure based on coherent state representation is proposed for investigation of reflection and transmission of light beams at a curved dielectric boundary. Numerical simulations of reflection and transmission of light at…
The Easy Path Wavelet Transform is an adaptive transform for bivariate functions (in particular natural images) which has been proposed in [1]. It provides a sparse representation by finding a path in the domain of the function leveraging…
Exploring chaotic systems via Poincar\'e sections has proven essential in dynamical systems, yet measuring their characteristics poses challenges to identify the various dynamical regimes considered. In this paper, we propose a new approach…
A path integral approach has been generalized for the non-relativistic electron charge transfer processes. The charge transfer - the capture of an electron by an ion passing another atom or more generally the problem of rearrangement…
The propagation of a light ray in thin layer (film) within geometrical optics is considered. It is assumed that the ray is captured inside the layer due to reflecting walls or total internal reflection (in the case of a dielectric layer).…
Integrated optics provides an ideal test bed for the emulation of quantum systems via continuous-time quantum walks. Here we study the evolution of two-photon states in an elliptic array of waveguides. We characterise the photonic chip via…
The analysis of the Helmholtz equation is shown to lead to an exact Hamiltonian system of equations describing in terms of ray trajectories a very wide family of wave-like phenomena (including diffraction and interference) going much beyond…