Free field realizations of the Date-Jimbo-Kashiwara-Miwa algebra

We use the description of the universal central extension of the DJKM algebra $\mathfrak{sl}(2, R)$ where $R=\mathbb C[t,t^{-1},u\,|\,u^2=t^4-2ct^2+1 ]$ given in earlier work to construct realizations of the DJKM algebra in terms of sums of partial differential operators.Comment: arXiv admin note: substantial text overlap with arXiv:1303.697

Gaudin models with irregular singularities

We introduce a class of quantum integrable systems generalizing the Gaudin model. The corresponding algebras of quantum Hamiltonians are obtained as quotients of the center of the enveloping algebra of an affine Kac-Moody algebra at the critical level, extending the construction of higher Gaudin Hamiltonians from hep-th/9402022 to the case of non-highest weight representations of affine algebras. We show that these algebras are isomorphic to algebras of functions on the spaces of opers on P^1 with regular as well as irregular singularities at finitely many points. We construct eigenvectors of these Hamiltonians, using Wakimoto modules of critical level, and show that their spectra on finite-dimensional representations are given by opers with trivial monodromy. We also comment on the connection between the generalized Gaudin models and the geometric Langlands correspondence with ramification.Comment: Latex, 72 pages. Final version to appear in Advances in Mathematic

Constructing quantum vertex algebras

This is a sequel to \cite{li-qva}. In this paper, we focus on the construction of quantum vertex algebras over \C, whose notion was formulated in \cite{li-qva} with Etingof and Kazhdan's notion of quantum vertex operator algebra (over \C[[h]]) as one of the main motivations. As one of the main steps in constructing quantum vertex algebras, we prove that every countable-dimensional nonlocal (namely noncommutative) vertex algebra over \C, which either is irreducible or has a basis of PBW type, is nondegenerate in the sense of Etingof and Kazhdan. Using this result, we establish the nondegeneracy of better known vertex operator algebras and some nonlocal vertex algebras. We then construct a family of quantum vertex algebras closely related to Zamolodchikov-Faddeev algebras.Comment: 37 page

Boundary Friction on Molecular Lubricants: Rolling Mode?

A theoretical model is proposed for low temperature friction between two smooth rigid solid surfaces separated by lubricant molecules, admitting their deformations and rotations. Appearance of different modes of energy dissipation (by ''rocking'' or ''rolling'' of lubricants) at slow relative displacement of the surfaces is shown to be accompanied by the stick-and-slip features and reveals a non-monotonic (mean) friction force {\it vs} external loadComment: revtex4, 4 pages, 5 figure

Extended T-systems

We use the theory of q-characters to establish a number of short exact sequences in the category of finite-dimensional representations of the quantum affine groups of types A and B. That allows us to introduce a set of 3-term recurrence relations which contains the celebrated T-system as a special case.Comment: 36 pages, latex; v2: version to appear in Selecta Mathematic

Devil's staircase of incompressible electron states in a nanotube

It is shown that a periodic potential applied to a nanotube can lock electrons into incompressible states. Depending on whether electrons are weakly or tightly bound to the potential, excitation gaps open up either due to the Bragg diffraction enhanced by the Tomonaga - Luttinger correlations, or via pinning of the Wigner crystal. Incompressible states can be detected in a Thouless pump setup, in which a slowly moving periodic potential induces quantized current, with a possibility to pump on average a fraction of an electron per cycle as a result of interactions.Comment: 4 pages, 1 figure, published versio

The Integrals of Motion for the Deformed W-Algebra Wqt(slN)W_{qt}(sl_N^) II: Proof of the commutation relations

We explicitly construct two classes of infinitly many commutative operators in terms of the deformed W-algebra $W_{qt}(sl_N^)$, and give proofs of the commutation relations of these operators. We call one of them local integrals of motion and the other nonlocal one, since they can be regarded as elliptic deformation of local and nonlocal integrals of motion for the $W_N$ algebra.Comment: Dedicated to Professor Tetsuji Miwa on the occasion on the 60th birthda

Quasi-binary amorphous phase in a 3D system of particles with repulsive-shoulder interactions

We report a computer-simulation study of the equilibrium phase diagram of a three-dimensional system of particles with a repulsive step potential. Using free-energy calculations, we have determined the equilibrium phase diagram of this system. At low temperatures, we observe a number of distinct crystal phases. However, under certain conditions the system undergoes a glass transition in a regime where the liquid appears thermodynamically stable. We argue that the appearance of this amorphous low-temperature phase can be understood by viewing this one-component system as a pseudo-binary mixture.Comment: 4 pages, 4 figure