Related papers: Exactly separable version of X(5) and related mode…
Let $X_1,\ldots,X_n$ be a random sample from the Gamma distribution with density $f(x)=\lambda^{\alpha}x^{\alpha-1}e^{-\lambda x}/\Gamma(\alpha)$, $x>0$, where both $\alpha>0$ (the shape parameter) and $\lambda>0$ (the reciprocal scale…
We consider two lattice models for strongly correlated electrons which are exactly-solvable in one dimension. Along with the Hubbard model and the su(2|2) spin chain, these are the only parity-invariant models that can be obtained from…
A new non-Hermitian E2-quasi-exactly solvable model is constructed containing two previously known models of this type as limits in one of its three parameters. We identify the optimal finite approximation to the double scaling limit to the…
The Separation of Variables theory for the Hamilton-Jacobi equation is 'by definition' related to the use of special kinds of coordinates, for example Jacobi coordinates on the ellipsoid or St\"ackel systems in the Euclidean space. However,…
Using the U(1)_Q invariance, the photon eigenstate and matching gauge coupling constants in SU(3)_C X SU(3)_L X U(1)_X models with beta arbitrary are given. The mass matrix of neutral gauge bosons is exactly diagonalized, and the photon…
Energies of the ground, $\beta$ and $\gamma$ bands as well as the associated B(E2) values are determined for each even-even isotope of the $^{180-196}$Pt chain by the exact solutions of some differential equations which approximate the…
We show that for a particular model, the quantum mechanical bootstrap is capable of finding exact results. We consider a solvable system with Hamiltonian $H=SZ(1-Z)S$, where $Z$ and $S$ satisfy canonical commutation relations. While this…
Many indefinite-metric (often called pseudo-Hermitian or PT-symmetric) quantum models H prove "physical" (i.e., Hermitian with respect to an innovated, ad hoc scalar product) inside a characteristic domain of parameters D. This means that…
Non-commutative QED would lead to deviations from the Standard Model depending on a new energy scale Lambda_NC and a unique direction in space defined by two angles eta and xi. Here in this analysis eta is defined as the angle between the…
The phase-space structure of two families of galactic potentials is approximated with a resonant detuned normal form. The normal form series is obtained by a Lie transform of the series expansion around the minimum of the original…
We study ideal Bose gas upon two scale-free structures with identical degree distribution. Energy spectra belonging to tight-binding Hamiltonian are exactly solved and the related spectral dimensions of $G_1$ and $ G_2$ are obtained as…
We show explicitly that the one- and two-dimensional Hubbard model does not show phase separation at any filling at T=0. Apart from a single plausible assumption, only known exact results and symmetry properties for the one-band Hubbard…
The excitation spectrum and the band structure of a Bose-Einstein condensate in a periodic potential are investigated. Analyses within full 3D systems, finite 1D systems, and ideal periodic 1D systems are compared. We find two branches of…
Analytical expressions for spectra and wave functions are derived for a Bohr Hamiltonian, describing the collective motion of deformed nuclei, in which the mass is allowed to depend on the nuclear deformation. Solutions are obtained for…
The rapid transition between spherical and $\gamma$-soft shapes in Ba and Xe nuclei in the mass region $A \geq 130$ is analyzed using excitation spectra and collective wave functions obtained by diagonalization of a five-dimensional…
We describe electromagnetic and favored \alpha-transitions to rotational bands in odd-mass nuclei built upon a single particle state with angular momentum projection $\Omega=\frac{1}{2}$ in the region $88 \le Z \le 98$. We use the particle…
The photon energy spectrum in inclusive weak radiative B -> X_s gamma decay is computed to order alpha_s^2 beta_0. This result is used to extract a value for the HQET parameter $\bar\Lambda$ from the average <1-2E_\gamma/m_B>, and a value…
We consider quasinormal modes with complex energies from the point of view of the theory of quasi-exactly solvable (QES) models. We demonstrate that it is possible to find new potentials which admit exactly solvable or QES quasinormal modes…
Several explicit examples of quasi exactly solvable `discrete' quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable Hamiltonians of one degree of freedom. These are difference analogues of the well-known…
A collective vector-boson model with broken SU(3) symmetry is applied to several deformed even-even nuclei. The model description of ground and $\gamma$ bands together with the corresponding B(E2) transition probabilities is investigated…