Related papers: Quasi-Exactly Solvable Models with Spin-Orbital In…
We suggest a generalization of the Lie algebraic approach for constructing quasi-exactly solvable one-dimensional Schroedinger equations which is due to Shifman and Turbiner in order to include into consideration matrix models. This…
We investigate a quantum non-relativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. Assuming that the Hamiltonian is rotationally invariant and parity conserving we identify all such systems…
We consider the Ricatti equation in the context of population dynamics, quantum scattering and a more general context. We examine some exactly solvable cases of real life interest.
Exactly solvable two-dimensional polygon models, counted by perimeter and area, are described by $q$-algebraic functional equations. We provide techniques to extract the scaling behaviour of these models up to arbitrary order and apply them…
Affine transformations in Euclidean space generates a correspondence between integrable systems on cotangent bundles to the sphere, ellipsoid and hyperboloid embedded in $R^n$. Using this correspondence and the suitable coupling constant…
We study an observable-based notion of equilibration and its application to realistic systems like spin qubits in quantum dots. On the basis of the so-called distinguishability, we analytically derive general equilibration bounds, which we…
The concept of superintegrability in quantum mechanics is extended to the case of a particle with spin s=1/2 interacting with one of spin s=0. Non-trivial superintegrable systems with 8- and 9-dimensional Lie algebras of first-order…
We study spin-1/2 fermions in spin dependent potentials under the \emph{spin model approximation}, in which interatomic collisions that change the total occupation of single-particle modes are ignored. The spin model approximation maps the…
We investigate classes of interacting quantum spin systems in a single-mode cavity with a Dicke coupling, as a paradigmatic example of strongly correlated light-matter systems. Coming from the limit of weak light-matter couplings and large…
Some exact solutions to the classical matrix model equations that arise in the context of M(embrane) theory are given, and their topological nature is identified.
We show that almost commuting real orthogonal matrices are uniformly close to exactly commuting real orthogonal matrices. We prove the same for symplectic unitary matrices. This is in contrast to the general complex case, where not all…
We clarify the algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them into the framework of the quantum inverse scattering method. The quasi-exactly solvable hamiltonians in one dimension…
We study a two-dimensional model of topological superconductor with equal spin pairing and repulsive Hubbard interaction. When the pairing gap equals to the hopping constant, half of the spectrum of this model are flat bands, which makes…
A type of electron pairing model with spin-orbit interactions or Zeeman coupling is solved exactly in the framework of Richardson ansatz. Based on the exact solutions for the case with spin-orbit interactions, it is shown rigorously that…
An emergent Fermi surface in a Mott insulator, an exotic quantum spin liquid state, was suggested by Anderson in 1987. After a quick support for its existence in spin-half Heisenberg model in a square lattice in a RVB mean field theory,…
We present some open problems in the field of exactly solvable models. Two of the problems are related to the correlation functions of the XXX spin chain and the XXZ spin chain, one to the entropy of subsystems and one to the six vertex…
Homogeneous compatible almost complex structures on symplectic manifolds are studied, focusing on those which are special, meaning that their Chern-Ricci form is a multiple of the symplectic form. Non Chern-Ricci flat ones are proven to be…
Interacting matter-radiation models close to physical systems are proposed, which without rotating wave approximation and with matter-matter interactions are Bethe ansatz solvable. This integrable system is constructed from the elliptic…
We investigate complex PT-symmetric potentials, associated with quasi-exactly solvable non-hermitian models involving polynomials and a class of rational functions. We also look for special solutions of intertwining relations of SUSY…
Several complete systems of integrability conditions on a spin chain Hamiltonian density matrix are presented. The corresponding formulas for $R$-matrices are also given. The latter is expressed via the local Hamiltonian density in the form…