Search results for "Degenerate energy levels"
showing 10 items of 221 documents
Integrable models and degenerate horizons in two-dimensional gravity
1999
We analyse an integrable model of two-dimensional gravity which can be reduced to a pair of Liouville fields in conformal gauge. Its general solution represents a pair of ``mirror'' black holes with the same temperature. The ground state is a degenerate constant dilaton configuration similar to the Nariai solution of the Schwarzschild-de Sitter case. The existence of $\phi=const.$ solutions and their relation with the solution given by the 2D Birkhoff's theorem is then investigated in a more general context. We also point out some interesting features of the semiclassical theory of our model and the similarity with the behaviour of AdS$_2$ black holes.
Host–virus evolutionary dynamics with specialist and generalist infection strategies: Bifurcations, bistability, and chaos
2019
In this work, we have investigated the evolutionary dynamics of a generalist pathogen, e.g., a virus population, that evolves toward specialization in an environment with multiple host types. We have particularly explored under which conditions generalist viral strains may rise in frequency and coexist with specialist strains or even dominate the population. By means of a nonlinear mathematical model and bifurcation analysis, we have determined the theoretical conditions for stability of nine identified equilibria and provided biological interpretation in terms of the infection rates for the viral specialist and generalist strains. By means of a stability diagram, we identified stable fixed…
A strongly degenerate quasilinear elliptic equation
2005
Abstract We prove existence and uniqueness of entropy solutions for the quasilinear elliptic equation u - div a ( u , Du ) = v , where 0 ⩽ v ∈ L 1 ( R N ) ∩ L ∞ ( R N ) , a ( z , ξ ) = ∇ ξ f ( z , ξ ) , and f is a convex function of ξ with linear growth as ∥ ξ ∥ → ∞ , satisfying other additional assumptions. In particular, this class of equations includes the elliptic problems associated to a relativistic heat equation and a flux limited diffusion equation used in the theory of radiation hydrodynamics, respectively. In a second part of this work, using Crandall–Liggett's iteration scheme, this result will permit us to prove existence and uniqueness of entropy solutions for the corresponding…
Magnetic exchange interaction in clusters of orbitally degenerate ions. I. Effective Hamiltonian
2001
Abstract A new effective Hamiltonian is reported for the kinetic exchange between two arbitrary terms 2S A +1 Λ A and 2S B +1 Λ B that can be ground or excited in octahedrally coordinated transition metal ions. This Hamiltonian is applicable to both homo- and heterometallic clusters. For the homonuclear cluster the resonance part of the effective Hamiltonian is also presented for the case when one of the ions is excited. The operator part of the exchange Hamiltonian contains symmetry adapted products of the cubic irreducible tensors acting in orbital spaces ΛA and ΛB and scalar product of site spin operators. The parameters of the Hamiltonian are defined by the relevant intercenter transfer…
Doubly nonlinear equations with unbounded operators
2004
Abstract The solvability of the evolution system v′(t)+ B (t)u(t)∋ f (t),v(t)∈ A (t)u(t) , 0 A (t) are bounded, possibly degenerate, subdifferentials and B (t) are unbounded subdifferentials.
On regularity up to the boundary of solutions to a system of degenerate nonlinear elliptic fourth-order equations
2008
Under some hypotheses on weighted functions, using the interior regularity results established in (Kovalevsky, A. and Nicolosi, F., 2005, Existence and regularity of solutions to a system of degenerate nonlinear fourth-order equations. Nonlinear Analysis, 61, 281–307) and estimating the oscillation of solutions near the boundary of Ω, we establish results on regularity up to the boundary of a solutions of the system (1.1).
Theoretical study of degenerate Boulton-Katritzky rearrangements. Semiempirical and ab initio procedures
1998
Abstract A theoretical study of degenerate Boulton–Katritzky rearrangements concerning the anions of the 3-formylamino-1,2,4-oxadiazole, 3-formylmethyl-isoxazole and 3-hydroxy-iminomethyl-1,2,5-oxadiazole has been carried out by using semiempirical MNDO and ab initio Hartree–Fock procedures. Different transition structures and reactive pathways were obtained in the two cases. Semiempirical treatment shows asymmetrical transition states and non-concerted processes via symmetrical intermediates. By contrast, ab initio procedures describe concerted and synchronous processes involving symmetrically-located transition states. Some comments and criticisms on the theoretical treatment of these typ…
Iterative pairs and multitape automata
1996
In this paper we prove that if every iterative k-tuple of a language L recognized by a k-tape automaton is very degenerate, then L is recognizable. Moreover, we prove that if L is an aperiodic langnage recognized by a deterministic k-tape automaton, then L is recognizable.
Weakly Interacting Bose-Einstein Condensates under Rotation: Mean-Field versus Exact Solutions
2000
We consider a weakly-interacting, harmonically-trapped Bose-Einstein condensed gas under rotation and investigate the connection between the energies obtained from mean-field calculations and from exact diagonalizations in a subspace of degenerate states. From the latter we derive an approximation scheme valid in the thermodynamic limit of many particles. Mean-field results are shown to emerge as the correct leading-order approximation to exact calculations in the same subspace.
Pairing in a three-component Fermi gas
2006
We consider pairing in a three-component gas of degenerate fermions. In particular, we solve the finite temperature mean-field theory of an interacting gas for a system where both interaction strengths and fermion masses can be unequal. At zero temperature we find a a possibility of a quantum phase transition between states associated with pairing between different pairs of fermions. On the other hand, finite temperature behavior of the three-component system reveals some qualitative differences from the two-component gas: for a range of parameters it is possible to have two different critical temperatures. The lower one corresponds to a transition between different pairing channels, while …