Related papers: Integrable Generalized Thirring Model
We present the exact solution of the Richardson-Gaudin models associated with the SU(3) Lie algebra. The derivation is based on a Gaudin algebra valid for any simple Lie algebra in the rational, trigonometric and hyperbolic cases. For the…
Standard Gaussian graphical models (GGMs) implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected form heterogeneous…
We establish, for smooth enough initial data, the global well-posedness (existence, uniqueness and continuous dependence on initial data) of solutions, for an inviscid three-dimensional {\it slow limiting ocean dynamics} model. This model…
A rigorous proof is presented of the boundedness of the entanglement entropy of a block of spins for the ground state of the one-dimensional quantum Ising model with sufficiently strong transverse field. This is proved by a refinement of…
The quantum regression formula for an open quantum system consists in an infinite hierarchy of conditions for its multi-time correlation functions, thus requiring full access to the total "system+environment" evolution, and providing a…
This paper addresses the problem of giving conditions for transcriptional systems to be globally entrained to external periodic inputs. By using contraction theory, a powerful tool from dynamical systems theory, it is shown that certain…
Defects which are predominant in a realistic model, usually spoil its integrability or solvability. We on the other hand show the exact integrability of a known sine-Gordon field model with a defect (DSG), at the classical as well as at the…
We extend a recent work by Mussardo and Penati on integrable quantum field theories with a single stable particle and an infinite number of unstable resonance states, including the presence of a boundary. The corresponding scattering and…
Exploiting the quantum integrability condition we construct an ancestor model associated with a new underlying quadratic algebra. This ancestor model represents an exactly integrable quantum lattice inhomogeneous anisotropic model and at…
Classical integrability is investigated for affine Toda field theories in the presence of a constant background tensor field. This leads to a further set of discrete possibilities for integrable boundary conditions depending upon the…
We propose the notion of integrable boundary in the context of discrete integrable systems on quad-graphs. The equation characterizing the boundary must satisfy a compatibility equation with the one characterizing the bulk that we called…
We prove an algebraic ``no-go theorem'' to the effect that a nontrivial Poisson algebra cannot be realized as an associative algebra with the commutator bracket. Using this, we show that there is an obstruction to quantizing the Poisson…
We study a forager-exploiter model with generalized logistic sources in a smooth bounded domain with homogeneous Neumann boundary conditions. A new boundedness criterion is developed to prove the global existence and boundedness of the…
We define `third derivative' General Relativity, by promoting the integration measure in Einstein-Hilbert action to be an arbitrary $4$-form field strength. We project out its local fluctuations by coupling it to another $4$-form field…
We prove two statements about the long time dynamics of integrable Hamiltonian systems. In classical mechanics, we prove the microcanonical version of the Generalized Gibbs Ensemble (GGE) by mapping it to a known theorem and then extend it…
The entanglement entropy in one dimensional critical systems with boundaries has been associated with the noninteger ground state degeneracy. This quantity, being a characteristic of boundary fixed points, decreases under renormalization…
I present here a simple proof that, under general regularity conditions, the standard parametrization of generalized linear mixed model is identifiable. The proof is based on the assumptions of generalized linear mixed models on the first…
The paper introduces a Poisson-type problem on a mixed-dimensional structure combining a Euclidean domain and a lower-dimensional self-similar component touching a compact surface (interface). The lower-dimensional piece is a so-called…
The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the domain. We establish well-posedness with inflow, outflow of…
Extension of the braid relations to the multiple braided tensor product of algebras that can be used for quantization of nonultralocal models is presented. The Yang--Baxter--type consistency conditions as well as conditions for the…