Related papers: Instantaneous Bethe-Salpeter equation: utmost anal…
We apply the algebraic Bethe ansatz developed in our previous paper \cite{CM} to three different families of U(1) integrable vertex models with arbitrary $N$ bond states. These statistical mechanics systems are based on the higher spin…
An exact form is presented for the axial-vector Bethe-Salpeter equation, which is valid when the quark-gluon vertex is fully dressed. A Ward-Takahashi identity for the Bethe-Salpeter kernel is derived therefrom and solved for a class of…
We present a novel algebraic framework for computing hadron properties directly within the contact interaction model. Utilizing Fierz transformations, the method recasts the Bethe-Salpeter dynamics into equations for a minimal set of…
We consider quantum integrable models solvable by the algebraic Bethe ansatz and possessing $\mathfrak{gl}(2)$-invariant $R$-matrix. We study the models of both periodic boundary conditions and boundary conditions based on reflection…
The challenge to obtain from the Euclidean Bethe--Salpeter amplitude the amplitude in Minkowski is solved by resorting to un-Wick rotating the Euclidean homogeneous integral equation. The results obtained with this new practical method for…
We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…
We derive the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. For totally asymmetric diffusion we calculate the…
We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Generalizing earlier work \cite{Stin95a,Stin95b} we present an alternative…
Observing renewed interest in long-standing (semi-) relativistic descriptions of bound states, we would like to make a few comments on the eigenvalue problem posed by the spinless Salpeter equation and, illustrated by the examples of the…
The Poisson-Boltzmann equation offers an efficient way to study electrostatics in molecular settings. Its numerical solution with the boundary element method is widely used, as the complicated molecular surface is accurately represented by…
We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever…
Convex optimization problems arise naturally in quantum information theory, often in terms of minimizing a convex function over a convex subset of the space of hermitian matrices. In most cases, finding exact solutions to these problems is…
A system of interacting atoms is represented as an union of two subsystems, one of which is the system of atoms, and the other is an auxiliary scalar covariant field, which is equivalent to a given static interatomic potential of general…
The off-diagonal Bethe ansatz method is generalized to the integrable model associated with the $sp(4)$ (or $C_2$) Lie algebra. By using the fusion technique, we obtain the complete operator product identities among the fused transfer…
In a configuration space whose boundary can be identified with a subset of its interior, a boundary condition can relate the behaviour of a function on the boundary and in the interior. Additionally, boundary values can appear as additive…
The self-field approach to quantum electrodynamics (QED) is used to study the bound state problem in light-front two-dimensional QED with massive matter fields. A composite matter field describing bound states is introduced and the…
It is shown that the spectral points (bound states and resonances) generated by a central potential of a single-channel problem, can be found using rational parametrization of the S-matrix. To achieve this, one only needs values of the…
A quantum integrable spin chain model associated with the $G_2$ exceptional Lie algebra is studied. By using the fusion technique, the closed recursive relations among the fused transfer matrices are obtained. These identities allow us to…
Generalized eigenvalue problems (GEPs) play an important role in the variety of fields including engineering, machine learning and quantum chemistry. Especially, many problems in these fields can be reduced to finding the minimum or maximum…
We introduce a novel eigenvalue algorithm for near-diagonal matrices inspired by Rayleigh-Schr\"odinger perturbation theory and termed Iterative Perturbative Theory (IPT). Contrary to standard eigenvalue algorithms, which are either…