Related papers: Inversion identities for inhomogeneous face models
Functional relation for commuting quantum transfer matrices of quantum integrable models is identified with classical Hirota's bilinear difference equation. This equation is equivalent to the completely discretized classical 2D Toda lattice…
Exact critical properties of the one-dimensional SU($N$) interacting fermion model with open boundaries are studied by using the Bethe ansatz method. We derive the surface critical exponents of various correlation functions using boundary…
We propose a Hermite spectral method for the spatially inhomogeneous Boltzmann equation. For the inverse-power-law model, we generalize an approximate quadratic collision operator defined in the normalized and dimensionless setting to an…
We construct a QFT for the Thirring model for any value of the mass in a functional integral approach, by proving that a set of Grassmann integrals converges, as the cutoffs are removed and for a proper choice of the bare parameters, to a…
Many vision applications require identity consistency beyond strict biometric recognition, especially under non-frontal views or when facial cues are missing. However, conventional face recognition models enforce intra-identity invariance,…
The dilute A_3 model is a solvable IRF (interaction-round-a-face) model with three local states and adjacency conditions encoded by the Dynkin diagram of the Lie algebra A_3. It can be regarded as a solvable version of a critical Ising…
The $so(5)$ (i.e., $B_2$) quantum integrable spin chains with both periodic and non-diagonal boundaries are studied via the off-diagonal Bethe Ansatz method. By using the fusion technique, sufficient operator product identities (comparing…
The affine-Virasoro Ward identities are a system of non-linear differential equations which describe the correlators of all affine-Virasoro constructions, including rational and irrational conformal field theory. We study the Ward…
Interferometers play an increasingly important role for spatially resolved observations. If employed at full potential, interferometry can probe an enormous dynamic range in spatial scale. Interpretation of the observed visibilities…
We study the Izergin-Korepin Gaudin models with both periodic and open integrable boundary conditions, which describe quantum systems exhibiting novel long-range interactions. Using the Bethe ansatz approach, we derive the eigenvalues of…
We investigate iterated function systems (IFS) that randomly alternate between two non-identical one-dimensional maps. Our primary focus is on finite invariant sets exhibiting ``toss-and-catch'' dynamics, in which trajectories alternate…
We show that the set of transfer matrices of an arbitrary fusion type for an integrable quantum model obey these bilinear functional relations, which are identified with an integrable dynamical system on a Grassmann manifold (higher Hirota…
We present a thorough analysis of the Non Intersecting String (NIS) model and its exact solution. This is an integrable $q$-states vertex model describing configurations of non-intersecting polygons on the lattice. The exact eigenvalues of…
We study integrable models solvable by the nested algebraic Bethe ansatz and possessing the GL(3)-invariant R-matrix. We consider a composite model where the total monodromy matrix of the model is presented as a product of two partial…
The intermolecular potential plays crucial roles in real-fluid interactions away from the ideal-gas equilibrium, such as supercritical fluid, high-enthalpy fluid, plasma interactions, etc. We propose a Boltzmann-weighted Full-dimensional…
We study the roughening transition of the dual of the 2D XY model, of the Discrete Gaussian model, of the Absolute Value Solid-On-Solid model and of the interface in an Ising model on a 3D simple cubic lattice. The investigation relies on a…
For multivariate stationary time series many important properties, such as partial correlation, graphical models and autoregressive representations are encoded in the inverse of its spectral density matrix. This is not true for…
We study the microlocal properties of generalized Radon transforms over a family of quadric hypersurfaces whose centers lie on an orientable hypersurface $S$. The quadric surfaces we consider are level sets of the quadratic form associated…
In this work, we establish a generalized transfer matrix method that provides exact analytical and numerical solutions for lattice versions of topological models with surface termination in one direction. We construct a generalized…
We consider a one-dimensional one-phase inverse Stefan problem for the heat equation. It consists in recovering a boundary influx condition from the knowledge of the position of the moving front, and the initial state. We derived a…