相关论文: Exact Solvability via the KP Hierarchy for $\beta=…

Let $\{P_t\}_{t>0}$ be the Dunkl-Poisson semigroup associated with a root system $R\subset \mathbb R^N$ and a multiplicity function $k\geq 0$. Analogously to the classical theory, we say that a bounded measurable function $f$ defined on…

Using recently developed methods, we perform high-accuracy calculations of the susceptibility near beta_c for the D=3 version of Dyson's hierarchical model. Using linear fits, we estimate the leading gamma and subleading Delta exponents.…

Matroids, particularly linear ones, have been a powerful tool in parameterized complexity for algorithms and kernelization. They have sped up or replaced dynamic programming. Delta-matroids generalize matroids by encapsulating structures…

The two-neutrino double-$\beta$ Gamow-Teller and Fermi transitions are studied within an exactly solvable model, which allows a violation of both spin-isospin SU(4) and isospin SU(2) symmetries, and is expressed with generators of the SO(8)…

We present recent developments on geometric theory of the Hirota system and of the non-commutative discrete Kadomtsev-Petviashvili (KP) hierarchy adding also some new results which make the picture more complete. We pay special attention to…

We consider divergence form elliptic operators of the form $L=-\dv A(x)\nabla$, defined in $R^{n+1} = \{(x,t)\in R^n \times R \}$, $n \geq 2$, where the $L^{\infty}$ coefficient matrix $A$ is $(n+1)\times(n+1)$, uniformly elliptic, complex…

We claim that some non-trivial theta-function identities at higher genus can stand behind the Poisson commutativity of the Hamiltonians of elliptic integrable systems, which are made from the theta-functions on Jacobians of the…

An exact invariant is derived for three-dimensional Hamiltonian systems of $N$ particles confined within a general velocity-independent potential. The invariant is found to contain a time-dependent function $f_{2}(t)$, embodying a solution…

The Hamiltonian conservative system of two interacting particles has been considered both in classical and quantum description. The quantum model has been realized using a symmetrized two-particle basis reordered in the unperturbed energy.…

We present an exact computation of effective Hamiltonians for an elementary model obtained from the Yukawa theory by going to the limit of bare fermions being infinitely heavy and bare bosons being at rest with respect to the fermions that…

We present a fast algorithm for linear least squares problems governed by hierarchically block separable (HBS) matrices. Such matrices are generally dense but data-sparse and can describe many important operators including those derived…

To each partition function of cohomological field theory one can associate an Hamiltonian integrable hierarchy of topological type. The Givental group acts on such partition functions and consequently on the associated integrable…

We review the notion of differential Fay identities and demonstrate, through case studies, its new role in integrable hierarchies of the KP type. These identities are known to be a convenient tool for deriving dispersionless Hirota…

We study the Hamiltonian truncation for the two-dimensional $\lambda\phi^4$ theory within the framework of Hamiltonian truncation effective theory, where truncation artifacts are mitigated through a systematic inclusion of corrective terms…

Quantum nonrelativistic systems with $2\times2$ matrix potentials are investigated. Physically, they simulate charged or neutral fermions with non-trivial dipole momenta, interacting with an external electric field. Assuming rotationally…

We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Using the Bethe ansatz and similarity transformations this yields new exact…

The calculation of ground-state energies of physical systems can be formalised as the k-local Hamiltonian problem, which is the natural quantum analogue of classical constraint satisfaction problems. One way of making the problem more…

We study line operators in the two-dimensional sigma-model on PSl(n|n) using the current-current OPEs. We regularize and renormalize these line operators, and compute their fusion up to second order in perturbation theory. In particular we…

We summarize the recent results about complete solvability of Hermitian and rectangular complex matrix models. Partition functions have very simple character expansions with coefficients made from dimensions of representation of the linear…

This study examines the identifiability of interaction kernels in mean-field equations of interacting particles or agents, an area of growing interest across various scientific and engineering fields. The main focus is identifying…