Related papers: Solvability of eigenvalues in jn configurations
The existence and structure of steady gaseous detonation propagating in a packed bed of solid inert particles are analyzed in the one-dimensional approximation by taking into consideration frictional and heat losses between the gas and the…
We prove local solvability for large classes of operators of the form $$ L=\sum_{j,k=1}^{2n}a_{jk}V_jV_k+i\alpha U,$$ where the $V_j$ are left-invariant vector fields on the Heisenberg group satisfying the commutation relations…
Interplay of spin-orbit coupling and vibronic coupling on heavy $d^1$ site of cubic double perovskites is investigated by ab initio calculations. The stabilization energy of spin-orbital-lattice entangled states is found comparable to or…
A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spin 0 and 1/2, is performed. We restrict to integrals of motion that are first-order (matrix) polynomials in the components…
We establish new analytic and numerical results on a general class of rational operator Nevanlinna functions that arise e.g. in modelling photonic crystals. The capability of these dielectric nano-structured materials to control the flow of…
In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product $|z\rangle \langle z|$. Because no pair of coherent states is orthogonal, one…
We examine the quantum dynamics of both a single spin-J particle and a pair of spin-J particles in the presence of static and rotating magnetic fields, which can be important for qudit-based quantum technologies. Notably, we find resonant,…
The quantum dynamics of interacting many-body systems has become a unique venue for the realization of novel states of matter. Here we unveil a new class of nonequilibrium states that are eigenstates of an emergent local Hamiltonian. The…
Correlated Basis Function theory and Fermi Hypernetted Chain technique are extended to study medium-heavy, doubly closed shell nuclei in j-j coupling scheme, with different single particle wave functions for protons and neutrons and isospin…
The nature of the $\Lambda nn$ and ${\rm ^3_\Lambda H^*} (J^\pi=3/2^+,~I=0)$ states is investigated within a pionless effective field theory at leading order, constrained by the low energy $\Lambda N$ scattering data and hypernuclear 3- and…
The construction of fully (anti-)symmetric states with many particles, when the single particle state carries multiple quantum numbers, is a problem that seems to have not been systematically addressed in the literature. A quintessential…
We consider a reformulation of QED in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. It is shown that exact few-fermion eigenstates of the resulting Hamiltonian can be…
This paper deals with the partial solution of the energy-eigenvalue problem for one-dimensional Schr\"odinger operators of the form $H_N=X_0^2+V_N$, where $V_N=X_N^2+\alpha X_{N-1}$ is a polynomial potential of degree $(2N-2)$ and $X_i$ are…
In this paper we present an elementary theory about the existence of eigenvalues for fully nonlinear radially symmetric 1-homogeneous operators. A general theory for first eigenvalues and eigenfunctions of 1-homogeneous fully nonlinear…
The purpose of the present paper is to show that the components of the unit normal of any minimal surface with free boundary in the unit ball, are eigenfunctions associated with the eigenvalue $-2$, for some (new) natural eigenvalue problem…
We prove the existence of extensive many-body Hamiltonians with few-body interactions and a many-body mobility edge: all eigenstates below a nonzero energy density are localized in an exponentially small fraction of "energetically allowed…
This paper adds two observations to the work solv-int/9701016 where some eigenstates for a model based on tetrahedron equation have been constructed. The first observation is that there exists a more "algebraic" construction of one-particle…
We present a model where the lepton masses are the eigenvalues of relativistic nonlinear field equations. The eigenfunctions correspond in the model to lepton states with inner structure. In this picture the self-interaction leads to the…
An analytical solution of the collective Bohr equation with a Coulomb-like and a Kratzer-like $\gamma-$unstable potential in quadrupole deformation space is presented. Eigenvalues and eigenfunctions are given in closed form and transition…
Existence of degenerate stationary bound states with square integrable radial wave functions was proved when second-order equations are used with the effective potential of the Reissner-Nordstr\"{o}m (RN) field with two event horizons for…