Related papers: Calogero-Sutherland Model with Anti-periodic Bound…
We present an algebraic construction of the orthogonal eigenfunctions of the supersymmetric extension of the rational Calogero-Moser-Sutherland model with harmonic confinement. These eigenfunctions are the superspace extension of the…
Effective (i.e., subspace-constrained) Hamiltonians become, by construction, energy-dependent while all the energy-dependent forces prove non-linear because the energy itself is merely an eigenvalue of the Hamiltonian H. One of the most…
In this work, we study the spectral properties of matrix Hamiltonians generated by linearizing the nonlinear Schr\"odinger equation about soliton solutions. By a numerically assisted proof, we show that there are no embedded eigenvalues for…
In the model considered, the nonlocal interaction of the fermions in different sublattices of a bipartite lattice is introduced. It can also be regarded as local interaction of fermions with opposite ``hypercharge''. The corresponding term…
Relations between the free motion on the GL^+(n, R) group manifold and the dynamics of an n-particle system with spin degrees of freedom on a line interacting with the pairwise 1/sinh^2 x ``potential'' (Euler-Calogero-Sutherland model) is…
Model two-dimensional singular perturbed eigenvalue problem for Laplacian with frequently alternating type of boundary condition is considered. Complete two-parametrical asymptotics for the eigenelements are constructed.
We consider quantum Hamiltonians of the form H(t)=H+V(t) where the spectrum of H is semibounded and discrete, and the eigenvalues behave as E_n~n^\alpha, with 0<\alpha<1. In particular, the gaps between successive eigenvalues decay as…
The hyperspherical harmonic basis is used to describe bound states in an $A$--body system. The approach presented here is based on the representation of the potential energy in terms of hyperspherical harmonic functions. Using this…
The nonlinear supersymmetry of one-dimensional systems is investigated in the context of the quantum anomaly problem. Any classical supersymmetric system characterized by the nonlinear in the Hamiltonian superalgebra is symplectomorphic to…
Employing Forrester-Ha method of Jack polynomials, we derive an integral identity connecting certain N-fold coordinate average of the Calogero-Sutherland model with the n-fold replica integral. Subsequent analytical continuation to…
We consider invariant matrix models with log-normal (asymptotic) weight. It is known that their eigenvalue distribution is intermediate between Wigner-Dyson and Poissonian, which candidates these models for describing a system intermediate…
We use large scale quantum Monte Carlo simulations to study an extended version of the canonical Shastry-Sutherland model -- including additional interactions and exchange anisotropy -- over a wide range of interaction parameters and an…
The spectrum and partition function of a model consisting of SU(n) spins positioned at the equilibrium positions of a classical Calogero model and interacting through inverse-square exchange are derived. The energy levels are equidistant…
In the previous paper math-ph/0507015 we have studied the characters and Clebsch-Gordan series for the exceptional Lie algebra E7 by relating them to the quantum trigonometric Calogero-Sutherland Hamiltonian with coupling constant K=1. Now…
We introduce a {\it lattice} version of the Calogero Sutherland model adapted to describe $1/d^2$ pairwise interacting steps with discrete positions on a vicinal surface. The configurational free energy is obtained within a transfer matrix…
A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…
The quantum rotor is shown to be supersymmetric. The supercharge $Q$, whose square equals the Hamiltonian, is constructed with reflection operators. The conserved quantities that commute with $Q$ form the algebra $so(3)_{-1}$, an…
A novel realization of the classical SU(2) algebra is introduced for the Dirac relativistic hydrogen atom defining a set of operators that, besides, allow the factorization of the problem. An extra phase is needed as a new variable in order…
The quantization of many-body systems with balanced loss and gain is investigated. Two types of models characterized by either translational invariance or rotational symmetry under rotation in a pseudo-Euclidean space are considered. A…
Kinetically constrained models were originally introduced to capture slow relaxation in glassy systems, where dynamics are hindered by local constraints instead of energy barriers. Their quantum counterparts have recently drawn attention…