Related papers: Exactly solvable pairing Hamiltonian for heavy nuc…
We construct exactly solvable models for four particles moving on a real line or on a circle with translation invariant two- and four-particle interactions.
We propose an interacting nonhermitian model described by a two-mode quadratic Hamiltonian along with an interaction term to locate and analyze the presence of an exceptional point in the system. Each mode is guided by a Swanson-like…
In this talk I present a simple and unified approach to both exact and quasi-exact solvabilities of the one-dimensional Schr\"odinger equation. It is based on the prepotential together with Bethe ansatz equations. This approach gives the…
Using an isomorphism between Hilbert spaces $L^2$ and $\ell^{2}$ we consider Hamiltonians which have tridiagonal matrix representations (Jacobi matrices) in a discrete basis and an eigenvalue problem is reduced to solving a three term…
The complete integrability of the hyperbolic Gaudin Hamiltonian and other related integrable systems is shown to be easily derived by taking into account their sl(2,R) coalgebra symmetry. By using the properties induced by such a coalgebra…
It is shown that the $F_4$ rational and trigonometric integrable systems are exactly-solvable for {\it arbitrary} values of the coupling constants. Their spectra are found explicitly while eigenfunctions by pure algebraic means. For both…
In this work, we present the ``EP code" (version 1.0), a user-friendly and robust computational tool. It computes the exact pairing eigenvalues and eigenvectors directly from the general nuclear pairing Hamiltonian, represented using SU(2)…
We construct Hamiltonians with only 1- and 2-body interactions that exhibit an exact non-Abelian gauge symmetry (specifically, combinatiorial gauge symmetry). Our spin Hamiltonian realizes the quantum double associated to the group of…
We present a new parton model approach for hadron-hadron interactions and, in particular, for the initial stage of nuclear collisions at very high energies (RHIC, LHC and beyond). The most important aspect of our approach is a…
We give a new reduction of a general diatomic molecular Hamiltonian, without modifying it near the collision set of nuclei. The resulting effective Hamiltonian is the sum of a smooth semiclassical pseudodifferential operator (the…
In quantum field theory, the splitting of the Hamiltonian into a strong and an electromagnetic part cannot be performed in a unique manner. We propose a convention for disentangling these two effects: one matches the parameters of two…
The non-relativistic electronic Hamiltonian, H(a)= Hkin + Hne + aHee, extended with coupling strength parameter (a), allows to switch the electron-electron repulsion energy off and on. First, the easier a=0 case is solved and the solution…
The complex eigenvalues of some non-Hermitian Hamiltonians, e.g. parity-time symmetric Hamiltonians, come in complex-conjugate pairs. We show that for non-Hermitian scattering Hamiltonians (of a structureless particle in one dimension)…
The coupling of non-Hermitian PT-symmetric Hamiltonians to standard Hermitian Hamiltonians, each of which individually has a real energy spectrum, is explored by means of a number of soluble models. It is found that in all cases the energy…
We introduce in this paper an exact solvable BCS-Hubbard model in arbitrary dimensions. The model describes a p-wave BCS superconductor with equal spin pairing moving on a bipartite (cubic, square etc.) lattice with on site Hubbard…
We present a new Gogny-type finite-range effective interaction including a third Gaussian in the central term. Based on simple arguments valid for an arbitrary radial form factor, the three ranges are fixed from physical grounds, relating…
We consider exactly solvable 1d multi-band fermionic Hamiltonians, which have affine quantum group symmetry for all values of the deformation. The simplest Hamiltonian is a multi-band t-J model with vanishing spin-spin interaction, which is…
We present an efficient algorithm for one- and two-component relativistic exact-decoupling calculations. Spin-orbit coupling is thus taken into account for the evaluation of relativistically transformed (one-electron) Hamiltonian. As the…
I present the exact energy eigenstates and eigenvalues of a quantum many-body system of bosons on non-commutative space and in a harmonic oszillator confining potential at the selfdual point. I also argue that this exactly solvable system…
The supersymmetric intertwining relations with second order supercharges allow to investigate new two-dimensional model which is not amenable to standard separation of variables. The corresponding potential being the two-dimensional…