相关论文: q-Boson in Quantum Integrable Systems
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
Various forms of the $q$-boson are explained and their hidden symmetry revealed by transformations using the exponential phase operator. Both the one-component and the multicomponent $q$-bosons are discussed. As a byproduct, we obtain a new…
We discuss connections between certain classes of supersymmetric quiver gauge theories and integrable lattice models from the point of view of topological quantum field theories (TQFTs). The relevant classes include 4d $\mathcal{N} = 1$…
We present a novel approach to the Bose polaron based on the notion of quantum groups, also known as $q$-deformed Lie algebras. In this approach, a mobile impurity can be depicted as a deformation of the Lie algebra of the bosonic creation…
We present an approach to interacting quantum many-body systems based on the notion of quantum groups, also known as $q$-deformed Lie algebras. In particular, we show that if the symmetry of a free quantum particle corresponds to a Lie…
Various applications of quantum algebraic techniques in nuclear structure physics, such as the su$_q$(2) rotator model and its extensions, the use of deformed bosons in the description of pairing correlations, and the construction of…
We introduce higher order polynomial deformations of $A_1$ Lie algebra. We construct their unitary representations and the corresponding single-variable differential operator realizations. We then use the results to obtain exact (Bethe…
A family of maximally superintegrable systems containing the Coulomb atom as a special case is constructed in N-dimensional Euclidean space. Two different sets of N commuting second order operators are found, overlapping in the Hamiltonian…
A quantum $n$-particle model consisting of an open $q$-difference Toda chain with two-sided boundary interactions is placed on a finite integer lattice. The spectrum and eigenbasis are computed by establishing the equivalence with a…
The quasi-Gaudin algebra was introduced to construct integrable systems which are only quasi-exactly solvable. Using a suitable representation of the quasi-Gaudin algebra, we obtain a class of bosonic models which exhibit this curious…
Plane partitions naturally appear in many problems of statistical physics and quantum field theory, for instance, in the theory of faceted crystals and of topological strings on Calabi-Yau threefolds. In this paper a connection is made…
We consider the deformed Bose gas model with the deformation structure function that is the combination of a q-deformation and a quadratically polynomial deformation. Such a choice of the unifying deformation structure function enables us…
Considering anyonic oscillators in a two-dimensional lattice, we realize the quantum semi-group $sl_{(q,s)}(2)$ by means of a generalized Schwinger construction. We find that the parameter $q$ of the algebra is connected to the statistical…
Quantum groups were invented largely to provide solutions of the Yang-Baxter equation and hence solvable models in 2-dimensional statistical mechanics and one-dimensional quantum mechanics. They have been hugely successful. But not all…
In this paper we show that (a) all the known exact solutions of the problem of N-anyons in oscillator potential precisely arise from the collective degrees of freedom, (b) the system is pseudo-integrable ala Richens and Berry. We conclude…
A unified integrable system, generating a new series of interacting matter-radiation models with interatomic coupling and different atomic frequencies, is constructed and exactly solved through algebraic Bethe ansatz. Novel features in Rabi…
We present two lists of multi-component systems of integrable difference equations defined on the edges of a $\mathbb{Z}^2$ graph. The integrability of these systems is manifested by their Lax formulation which is a consequence of the…
In this thesis, the connection between recently introduced algebraic structures (tridiagonal algebra, $q$-Onsager algebra, generalized $q-$Onsager algebras), related representation theory (tridiagonal pair, Leonard pair, orthogonal…
We construct a family of quasi-solvable quantum many-body systems by an algebraic method. The models contain up to two-body interactions and have permutation symmetry. We classify these models under the consideration of invariance property.…
In one spatial dimension, anyons in the original description of Leinaas and Myrheim are formally equivalent to locally interacting bosons described by the Lieb-Liniger model. This admits an interesting reinterpretation of interacting bosons…