Related papers: Markov loops, complex free field and Eulerian circ…
We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the…
We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the…
State-of-the-art algorithms for simulating fermions coupled to gauge fields often rely on integrating fermion degrees of freedom. While successful in simulating QCD at zero chemical potential, at finite density these approaches are hindered…
In the present work a general frame for the scattering theory of local, relativistic dipole quantum fields is presented and some models of interacting dipole fields are considered, i.e. local, relativistic quantum fields with indefinite…
Recurrent representations for an electron transmission and reflection amplitudes for a one-dimensional chain are obtained. The linear differential equations for scattering amplitudes of an arbitrary potential are found.
We develop a coarse-graining procedure for two-dimensional models of fluctuating loops by mapping them to interface models. The result is an effective field theory for the scaling limit of loop models, which is found to be a Liouville…
This review paper provides an introduction of Markov chains and their convergence rates which is an important and interesting mathematical topic which also has important applications for very widely used Markov chain Monte Carlo (MCMC)…
We study the asymptotic behavior of the free cumulants (in the sense of free probability theory of Voiculescu) of Jucys--Murphy elements--or equivalently--of the transition measure associated with a Young diagram. We express these cumulants…
A simple example is used to show that renormalization group limit cycles of effective quantum theories can be studied in a new way. The method is based on the similarity renormalization group procedure for Hamiltonians. The example contains…
We develop a method based on Markov chains to model fluorescence, absorption, and scattering in nanophotonic systems. We show that the method reproduces Beer-Lambert's Law and Kirchhoff's Law, but also can be used to analyze deviations from…
The master field is the large $N$ limit of the Yang-Mills measure on the Euclidean plane. It can be viewed as a non-commutative process indexed by paths on the plane. We construct and study generalized master fields, called free planar…
This is the first of two papers devoted to the proof of conformal invariance of the critical double random current model on the square lattice. More precisely, we show the convergence of loop ensembles obtained by taking the cluster…
In the present article we intend to accomplish a rigorous analysis which allows to elaborate useful symbolic and numerical codes leading to an accurate evaluation of the thermal radiation. We will consider the case of the electromagnetic…
Consider an irreducible Markov chain which satisfies a ratio limit theorem, and let $\rho$ be the spectral radius of the chain. We investigate the relation of the the $\rho\,$-Martin boundary with the boundary induced by the…
The effects of a magnetic field on the energy and on the spin of free electrons are computed in the framework of quantum field theory. In the case of a constant moderate field and with relatively slow electrons, the derived formulae are…
We revisit the quantum-mechanical two-dimensional harmonic oscillator with an electric field confined to a circular box of impenetrable walls. In order to obtain the energy spectrum we resort to the Rayleigh-Ritz method with polynomial and…
We describe $\kappa$-Minkowski space and its relation to group theory. The group theoretical picture makes it possible to analyze the symmetries of this space. As an application of this analysis we analyze in detail free field theory on…
In this study, we explore a form of quantum circuit complexity that extends to open systems. To illustrate our methodology, we focus on a basic model where the projective Hilbert space of states is depicted by the set of orientations in the…
We study circuit complexity for a free vector field of a $U(1)$ gauge theory in Coulomb gauge, and Gaussian states. We introduce a quantum circuit model with Gaussian states, including reference and target states. Using the Nielsen's…
Entanglement in finite and semi-infinite free Fermionic chains is studied. A parallel is drawn with the analysis of time and band limiting in signal processing. It is shown that a tridiagonal matrix commuting with the entanglement…