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In this work, we establish a general relationship between the enumeration of weighted directed paths and skew Schur functions, extending work by Bousquet-M\'elou, who expressed generating functions of discrete excursions in terms of…
We define a number of related combinatorial objects, each of which possesses a surprising symmetry. We include several applications such as a combinatorial explanation for certain fixed points of the involution $\omega$ on the ring of…
We develop a simple technique for calculation of next to nearest neighbor spin-spin and chiral-spin correlation functions in inhomogeneous XXX model. Exact expression of the chiral-spin order parameter as a function of the model parameter,…
We introduce a ``non-orientable'' variation of Serre's definition of a graph, which we call an abstract isogeny graph. These objects capture the combinatorics of the graphs $G(p,\ell,H)$, the $\ell$-isogeny graphs of supersingular elliptic…
We present the construction of the full set of eigenvectors of the open ASEP and XXZ models with special constraints on the boundaries. The method combines both recent constructions of coordinate Bethe Ansatz and the old method of matrix…
The asymptotic dynamical correlation functions in one-dimensional spin chains are described by power-laws. The corresponding exponents characterize different bulk and boundary critical behavior. We present novel results for the logarithmic…
Using renormalization group methods, we study the Heisenberg-Ising XYZ chain in an external magnetic field directed as the z axis, in the case of small coupling J_3 in the z direction. We study the asymptotic behaviour of the spin…
The integrable XXZ alternating spin chain with generic non-diagonal boundary terms specified by the most general non-diagonal K-matrices is studied via the off-diagonal Bethe Ansatz method. Based on the intrinsic properties of the fused…
We study antiferromagnetic spin--1/2 Heisenberg ladders, comprised of $n_c$ chains ($2 \leq n_c \leq 6$) with ratio $J_{\bot}/J_{\|}$ of inter-- to intra--chain couplings. From measurements of the correlation function we deduce the…
We study the nonequilibrium time evolution of the spin-1/2 anisotropic Heisenberg (XXZ) spin chain, with a choice of dimer product and Neel states as initial states. We investigate numerically various short-ranged spin correlators in the…
We study correlation functions of spectrally-flowed vertex operators in bosonic string theory on $\text{AdS}_3\times X$ in the path integral formalism. By restricting the path integral to only include worldsheets which live near the…
Here we study problems related to the proportions of zeros, especially simple and distinct zeros on the critical line, of Dedekind zeta functions. We obtain new bounds on a counting function that measures the discrepancy of the zeta…
Antiferromagnetic spin chains play an important role in condensed matter physics and statistical mechanics. Recently XXX spin chain was discussed in relation to the information theory. We consider here localizable entanglement, introduced…
Non-self-adjoint Schrodinger operators A which correspond to non-symmetric zero-range potentials are investigated. For a given A, the description of non-real eigenvalues, spectral singularities and exceptional points are obtained; the…
Recurrently coupled oscillators that are sufficiently heterogeneous and/or randomly coupled can show an asynchronous activity in which there are no significant correlations among the units of the network. The asynchronous state can…
Motivated by the harmonic analysis of self-affine measures, we introduce a class of representations of the Cuntz algebra associated to random walks on graphs. The representations are constructed using the dilation theory of row…
We solve in random-phase approximation the anisotropic Heisenberg model, including nearest and next-nearest neighbour interactions by calculating all Green's functions and pair correlation functions in a cumulant decoupling scheme. The…
A square-lattice model for the formation of secondary structures in proteins, the hydrogen-bonding model, extended to include the effects of solvent quality, is examined in the framework of the Bethe approximation.
We study a one-parameter generalization of the symmetric simple exclusion process on a one dimensional lattice. In addition to the usual dynamics (where particles can hop with equal rates to the left or to the right with an exclusion…
Two discrete path integral formulations for the ground state of a spin-pinned quantum anisotropic XXZ Heisenberg chain are introduced. Their properties are discussed and two recursion relations are proved.