Related papers: Free Variables and the Two Matrix Model
Nonequilibrium Green's functions provide a powerful tool for computing the dynamical response and particle exchange statistics of coupled quantum systems. We formulate the theory in terms of the density matrix in Liouville space and…
Boundary value problems (BVPs) play a central role in the mathematical analysis of constrained physical systems subjected to external forces. Consequently, BVPs frequently emerge in nearly every engineering discipline and span problem…
We consider the variational problem of maximizing the weighted equilibrium Green's energy of a distribution of charges free to move in a subset of the upper half-plane, under a particular external field. We show that this problem admits a…
We discuss some aspects of a new noncombinatorial fermionic approach to the two-dimensional dimer problem in statistical mechanics based on the integration over anticommuting Grassmann variables and factorization ideas for dimer density…
We construct the Green function for the mixed boundary value problem for the linear Stokes system in a two-dimensional Lipschitz domain.
We show how to calculate correlation functions of two matrix models. Our method consists in making full use of the integrable hierarchies and their reductions, which were shown in previous papers to naturally appear in multi--matrix models.…
We study two-particle systems in a model quantum field theory, in which scalar particles and spinor particles interact via a mediating scalar field. The Lagrangian of the model is reformulated by using covariant Green's functions to solve…
The operator expansion of free Green function of Helmholtz equation for arbitrary N- dimension space leads to asymptotic extension of 3- dimension Grimus-Stockinger formula closely related to multipole expansion. Analytical examples…
This paper concerns analytic free maps. These maps are free analogs of classical analytic functions in several complex variables, and are defined in terms of non-commuting variables amongst which there are no relations - they are free…
We study the addditon problem for strongly matricially free random variables which generalize free random variables. Using operators of Toeplitz type, we derive a linearization formula for the `matricial R-transform' related to the…
We investigate the relation between on-shell and zero-momentum non-perturbative quantities entering the parametrization of the two-point Green's function of two-dimensional non-linear O(N) sigma models. We present accurate estimates of…
Green's functions characterize the fundamental solutions of partial differential equations; they are essential for tasks ranging from shape analysis to physical simulation, yet they remain computationally prohibitive to evaluate on…
Multiple scattering methods are widely used to reduce the computational complexity of acoustic or electromagnetic scattering problems when waves propagate through media containing many identical inclusions. Historically, this numerical…
We present a rather unknown version of the change of variables formula for non-autonomous functions. We will show that this formula is equivalent to Green's Theorem for regions of the plane bounded by the graphs of two continuously…
The $\beta\gamma$ system is generalized by complex(rational) powers of the fields, which leads to a corresponding extension on the Fock space. Two different approaches to compute the Green functions of the physical operators are proposed.…
Green's functions with continuum spectra are a way of avoiding the strong bounds on new physics from the absence of new narrow resonances in experimental data. We model such a situation with a five-dimensional model with two branes along…
A model of two--dimensional gravity with an action depending only on a linear connection is considered. This model is a topological one, in the sense that the classical action does not contain a metric or zweibein at all. A metric and an…
We construct an expression for the Green function of a differential operator satisfying nonlocal, homogeneous boundary conditions starting from the fundamental solution of the differential operator. This also provides the solution to the…
We construct an explicit solution of the Cauchy initial value problem for the one-dimensional Schroedinger equation with a time-dependent Hamiltonian operator for the forced harmonic oscillator. The corresponding Green function (propagator)…
In this work, we present a mesh-independent, data-driven library, chebgreen, to mathematically model one-dimensional systems, possessing an associated control parameter, and whose governing partial differential equation is unknown. The…