Related papers: Quantum Diffusion Process with a Complex Weight on…
Basic ideas and results which characterize quantum diffusion of defects in quantum crystals like solid helium as a new phenomenon are presented. Quantum effects in such media lead to a delocalization of point defects (vacancies, impurities…
The quantisation of the two-dimensional Liouville field theory is investigated using the path integral, on the sphere, in the large radius limit. The general form of the $N$-point functions of vertex operators is found and the three-point…
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…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
Since spin and charge are both carried by electrons (or holes) in a solid, it is natural to assume that charge and spin diffusion coefficients will be the same. Drift-diffusion models of spin transport typically assume so. Here, we show…
In this paper path integration in two- and three-dimensional spaces of constant curvature is discussed: i.e.\ the flat spaces $\bbbr^2$ and $\bbbr^3$, the two- and three-dimensional sphere and the two- and three dimensional pseudosphere.…
I study several aspects of the path(st) integral we formulated in previous papers on energetic causal sets with Cortes and others. The focus here is on quantum field theories, including the standard model of particle physics. I show that…
Low-dimensional periodic arrays of scatterers with a moving point particle are ideal models for studying deterministic diffusion. For such systems the diffusion coefficient is typically an irregular function under variation of a control…
We study quantum interference effects due to electron motion on a three-dimensional cubic lattice in a continuously-tunable magnetic field of arbitrary orientation and magnitude. These effects arise from the interference between magnetic…
The purpose of this paper is to show that: when a single particle moving under 3-proper time (three-dimensional time), the trajectories of a classical particle are equivalent to a quantum field with spin. Three-proper time models are built…
For distinguishable particles it is well known that Brownian motion and a Feynman-Kac functional can be used to calculate the path integral (for imaginary times) for a general class of scalar potentials. In order to treat identical…
The diffusion coefficient of a circular shaped inclusion in a liquid membrane is investigated by taking into account the interaction between membranes and bulk solvents of arbitrary thickness. As illustrative examples, the diffusion…
We consider percolation on the discrete torus $\mathbb{Z}_n^d$ at $p_c(\mathbb{Z}^d)$, the critical value for percolation on the corresponding infinite lattice $\mathbb{Z}^d$, and within the scaling window around it. We assume that $d$ is a…
We present a classical kinetically constrained model of interacting particles on a triangular ladder, which displays diffusion and jamming and can be treated by means of a classical-quantum mapping. Interpreted as a theory of interacting…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
Scattering transform is a well known powerful tool for quantisation of field theories in (1+1) dimensions. Conventionally only those models whose classical counterparts admit a Lax pair (origin of which is always mysterious) have been…
Quantum electrodynamics near a boundary is investigated by considering the inertial mass shift of an electron near a dielectric or conducting surface. We show that in all tractable cases the shift can be written in terms of integrals over…
This paper considers particle propagation in a cylindrical molecular communication channel, e.g. a simplified model of a blood vessel. Emitted particles are influenced by diffusion, flow, and a vertical force induced e.g. by gravity or…
We determine numerically the parallel, perpendicular, and antisymmetric diffusion coefficients for charged particles propagating in highly turbulent magnetic fields, by means of extensive Monte Carlo simulations. We propose simple…
I describe how simulations of lattice QCD using the path integral formulation provide the two basic quantum mechanical properties of QCD, its ground state in which correlation functions are calculated, and Fock state wavefunctions between…