Related papers: Spectral theory for interacting particle systems s…
We define one-dimensional particles with generalized exchange statistics. The exact solution of a Hubbard-type Hamiltonian constructed with such particles is achieved using the Coordinate Bethe Ansatz. The chosen deformation of the…
We prove the modified algebraic Bethe Ansatz characterization of the spectral problem for the closed XXX Heisenberg spin chain with an arbitrary twist and arbitrary positive (half)-integer spin at each site of the chain. We provide two…
We give a derivation of quantum spectral curve (QSC) - a finite set of Riemann-Hilbert equations for exact spectrum of planar N=4 SYM theory proposed in our recent paper Phys.Rev.Lett. 112 (2014). We also generalize this construction to all…
We solve the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups ${\cal U}% _{q}(X_{n})$ for $X_{n}=A_{1},$ $B_{n},$ $C_{n}$ and $D_{n}$. The tool is a modified version…
We investigate a rich new class of exactly solvable particle systems generalizing the Totally Asymmetric Simple Exclusion Process (TASEP). Our particle systems can be thought of as new exactly solvable examples of tandem queues, directed…
We present a spectral-theoretic approach to time-average statistical mechanics for general, non-equilibrium initial conditions. We consider the statistics of bounded, local additive functionals of reversible as well as irreversible ergodic…
The Baker-Akhiezer (wave) functions corresponding to soliton solutions of the KP hierarchy are shown to satisfy eigenvalue equations for a commutative ring of translational operators in the spectral parameter. In the rational limit, these…
Using the Bethe ansatz analysis as was reformulated by Edwards, we calculate the spectral properties of a particle interacting with a bath of fermions in one dimension for the case of equal particle-fermion masses. These are directly…
We present a new approach to the problem of Bloch electrons in magnetic ( sometimes called Azbel-Hofstadter problem) field, by making explicit a natural relation between the group of magnetic translations and the quantum group…
We investigate the profound relation between the equations of biological evolution and quantum mechanics by writing a biologically inspired equation for the stochastic dynamics of an ensemble of particles. Interesting behavior is observed…
The construction of analytic solutions for quasi-exactly solvable systems is an interesting problem. We revisit a class of models for which the odd solutions were largely missed previously in the literature: the anharmonic oscillator, the…
We employ a discrete integral-reflection representation of the double affine Hecke algebra of type $C^\vee C$ at the critical level q=1, to endow the open finite $q$-boson system with integrable boundary interactions at the lattice ends. It…
We apply the algebraic Bethe ansatz technique to the nuclear pairing problem with orbit dependent coupling constants and degenerate single particle energy levels. We find the exact energies and eigenstates. We show that for a given shell,…
We construct models of exactly solvable two-particle quantum graphs with certain non-local two-particle interactions, establishing appropriate boundary conditions via suitable self-adjoint realisations of the two-particle Laplacian. Showing…
We present an algebraic method for solving the Bethe ansatz equations for the periodic totally asymmetric exclusion process (TASEP) with an arbitrary number of sites and particles. The Bethe ansatz equations are realized as an algebraic…
We consider the exact solution of a model of correlated particles, which is presented as a system of interacting XX and Fateev-Zamolodchikov chains. This model can also be considered as a generalization of the multiband anisotropic $t-J$…
We develop a general technique, based on a Bochner-type identity, to estimate spectral gaps of a class of Markov operator. We apply this technique to various interacting particle systems. In particular, we give a simple and short proof of…
We have constructed a one dimensional exactly solvable model, which is based on the t-J model of strongly correlated electrons, but which has additional quantum group symmetry, ensuring the degeneration of states. We use Bethe Ansatz…
Recently, Ryu et al. showed that two broadened bands connected by a set of four Einstein-coefficient spectra for stimulated and spontaneous single-photon transitions will obey detailed balance at equilibrium if the spectra satisfy…
We solve for the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups ${\cal U}_q(X_n } for $X_n = A_1,B_n,C_n$ and $D_n$. We employ a generalization of the coordinate…