Related papers: Grassmann-Gaussian integrals and generalized star …
We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems through systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…
We prove the quantitative propagation of chaos for stochastic particle systems with interaction in both the drift and the diffusion coefficients, provided the drift kernel is bounded and free of Lipschitz or smoothness assumptions. Our…
We put forward a finite theory of quantum scattering of fundamental particles without using auxiliary particles. It suggests that to avoid ultraviolet divergencies and model faster-than-light effects it suffices to appropriately change only…
The study of long-range effects arising from the higher order exchange of massless particles via summation of Feynman diagrams is well known, but recently it has been shown that the use of on-shell methods can provide a streamlined route to…
We consider the scattering matrix approach to quantum electron transport in meso- and nano-conductors. This approach is an alternative to the more conventional kinetic equation and Green's function approaches, and often is more efficient…
Proposals for nonlinear extenstions of quantum mechanics are discussed. Two different concepts of "mixed state" for any nonlinear version of quantum theory are introduced: (i) >genuine mixture< corresponds to operational "mixing" of…
After an introduction to the problem of cosmological structure formation, we develop gauge invariant cosmological perturbation theory. We derive the first order perturbation equations of Einstein's equations and energy momentum…
We introduce constellation ensembles, in which charged particles on a line (or circle) are linked with charged particles on parallel lines (or concentric circles). We present formulas for the partition functions of these ensembles in terms…
This paper aims to address two issues of integral equations for the scattering of time-harmonic electromagnetic waves by a perfect electric conductor with Lipschitz continuous boundary: ill-conditioned {boundary element Galerkin matrices}…
We demonstrate that the use of on-shell methods, involving calculation of the discontinuity across the t-channel cut associated with the exchange of a pair of massless particles, can be used to evaluate loop contributions to both the…
We investigate the interplay between coherent effects characteristic of the propagation of linear waves, the non-linear effects due to interactions, and the quantum manifestations of classical chaos due to geometrical confinement, as they…
A generalization of the quantum inverse scattering method is proposed replacing the quantum group $RLL$ commutation relations of Lax operators by reflection equation type $RLRL$ commutation relations. Under some natural assumptions the most…
The perturbative framework of the space-time non-commutative real scalar field theory is formulated, based on the unitary S-matrix. Unitarity of the S-matrix is explicitly checked order by order using the Heisenberg picture of Lagrangian…
We introduce a non-exponential radiative framework that takes into account the local spatial correlation of scattering particles in a medium. Most previous works in graphics have ignored this, assuming uncorrelated media with a uniform,…
An ambiguity inherent in the partial integration procedure leading to the Bern-Kosower rules is fixed in a way which preserves the complete permutation symmetry in the scattering states. This leads to a canonical version of the Bern-Kosower…
We analyse the Gaussian wave packet transform. Based on the Fourier inversion formula and a partition of unity, which is formed by a collection of Gaussian basis functions, a new representation of square-integrable functions is presented.…
The globalised cascaded scattering matrix technique is a well proven, practical method that can be used to simulate large accelerating RF structures in which realistic fabrication errors to be incorporated in an efficient manner without the…
A general density-matrix formulation of quantum-transport phenomena in semiconductor nanostructures is presented. More specifically, contrary to the conventional single-particle correlation expansion, we shall investigate separately the…
We derive a density matrix (DM) theory for quantum cascade lasers (QCLs) that describes the influence of scattering on coherences through a generalized scattering superoperator. The theory enables quantitative modeling of QCLs, including…
A new approach to bosonization in relativistic field theories and many-body systems, based on the use of fermionic composites as integration variables in the Berezin integral defining the partition function of the system, is tested. The…