Related papers: Algebraic construction of quantum integrable model…
Non-equilibrium properties of strongly interacting gauge theories are often intractable with classical simulation methods. Due to recent developments of quantum simulations, studies of their properties in two spatial dimensions are becoming…
We construct a canonical basis for a class of tensor product modules of a quantum covering group associated to a Kac-Moody Lie superalgebra of anisotropic type, and use these bases to construct a canonical basis for the modified form of a…
We consider some examples of quantum super-integrable systems and the associated nonlinear extensions of Lie algebras. The intimate relationship between super-integrability and exact solvability is illustrated. Eigenfunctions are…
We establish a relation between the classical non-linear Schr\"odinger equation and the KP hierarchy, and we extend this relation to the quantum case by defining a quantum KP hierarchy. We present evidence that an integrable hierarchy of…
The Gamma-class is a characteristic class for complex manifolds with transcendental coefficients. It defines an integral structure of quantum cohomology, or more precisely, an integral lattice in the space of flat sections of the quantum…
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…
We introduce a new concept of infinite quasi-exactly solvable models which are constructable through multi-parameter deformations of known exactly solvable ones. The spectral problem for these models admits exact solutions for infinitely…
We propose a general construction principle which allows to include an infinite number of resonance states into a scattering matrix of hyperbolic type. As a concrete realization of this mechanism we provide new S-matrices generalizing a…
A universal algorithm to construct N-particle (classical and quantum) completely integrable Hamiltonian systems from representations of coalgebras with Casimir element is presented. In particular, this construction shows that quantum…
Nuclear lattice effective field theory has become an important framework for quantum many-body calculations in nuclear physics, yet its classical implementation remains increasingly challenging for more general interactions and larger…
Quantum matrix models in the large-N limit arise in many physical systems like Yang-Mills theory with or without supersymmetry, quantum gravity, string-bit models, various low energy effective models of string theory, M(atrix) theory,…
Mathematical models use information from past observations to generate predictions about the future. If two models make identical predictions the one that needs less information from the past to do this is preferred. It is already known…
In this paper we introduce a new class of integrable 3D lattice models, possessing continuous families of commuting layer-to-layer transfer matrices. Algebraically, this commutativity is based on a very special construction of local…
We consider a class of simple quasi one-dimensional classically non-integrable systems which capture the essence of the periodic orbit structure of general hyperbolic nonintegrable dynamical systems. Their behavior is simple enough to allow…
In this lecture, we survey a number of recent results and developments regarding the representation theory of infinite-dimensional quantum groups (quantum affine algebras and related algebras), as well as their connections with cluster…
Hybrid classical-quantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum co-processor, while benefitting from quantum resources. Here we present experiments…
In this note we are dealing with a particular class of quadratic algebras -- the so-called quantum matrix algebras. The well-known examples are the algebras of quantized functions on classical Lie groups (the RTT algebras). We consider the…
We study the scalar modes of linear perturbations in loop quantum cosmology. This is done on a lattice where each cell is taken to be homogeneous and isotropic and can be quantized via standard homogeneous loop quantum cosmology techniques.…
The spectral curve is the key ingredient in the modern theory of classical integrable systems. We develop a construction of the ``quantum spectral curve'' and argue that it takes the analogous structural and unifying role on the quantum…
This contribution to the Proceedings of the Workshop on Integrable Theories, Solitons and Duality in Sao Paulo in July 2002 summarizes results from the papers hep-th/0112023 and math.QA/0208043. We derive the non-local conserved charges in…