Integrable Extensions of N=2 Supersymmetric KdV Hierarchy Associated with the Nonuniqueness of the Roots of the Lax operator

We preesent a new supersymmetric integrable extensions of the a=4,N=2 KdV hierarchy. The root of the supersymmetric Lax operator of the KdV equation is generalized, by including additional fields. This generalized root generate new hierarchy of integrable equations, for which we investigate the hamiltonian structure. In special case our system describes the interaction of the KdV equation with the two MKdV equations.Comment: 9 pages Latex,e-mail [email protected]

The Even and Odd Supersymmetric Hunter - Saxton and Liouville Equations

It is shown that two different supersymmetric extensions of the Harry Dym equation lead to two different negative hierarchies of the supersymmetric integrable equations. While the first one yields the known even supersymmetric Hunter - Saxton equation, the second one is a new odd supersymmetric Hunter - Saxton equation. It is further proved that these two supersymmetric extensions of the Hunter - Saxton equation are reciprocally transformed to two different supersymmetric extensions of the Liouville equation.Comment: typos corrected and references added. To appear in Phys.Lett

Dispersionless Fermionic KdV

We analyze the dispersionless limits of the Kupershmidt equation, the SUSY KdV-B equation and the SUSY KdV equation. We present the Lax description for each of these models and bring out various properties associated with them as well as discuss open questions that need to be addressed in connection with these models.Comment: 15 page

The sTB-B Hierarchy

We construct a new supersymmetric two boson (sTB-B) hierarchy and study its properties. We derive the conserved quantities and the Hamiltonian structures (proving the Jacobi identity) for the system. We show how this system gives the sKdV-B equation and its Hamiltonian structures upon appropriate reduction. We also describe the zero curvature formulation of this hierarchy both in the superspace as well as in components.Comment: 15 pages, Te

Bethe ansatz for the SU(4) extension of the Hubbard Model

We apply the nested algebraic Bethe ansatz method to solve the eigenvalue problem for the SU(4) extension of the Hubbard model. The Hamiltonian is equivalent to the SU(4) graded permutation operator. The graded Yang-Baxter equation and the graded Quantum Inverse Scattering Method are used to obtain the eigenvalue of the SU(4) extension of the Hubbard model.Comment: Latex file, 12 page

Fermionization and Hubbard Models

We introduce a transformation which allows the fermionization of operators of any one-dimensional spin-chain. This fermionization procedure is independent of any eventual integrable structure and is compatible with it. We illustrate this method on various integrable and non-integrable chains, and deduce some general results. In particular, we fermionize XXC spin-chains and study their symmetries. Fermionic realizations of certain Lie algebras and superalgebras appear naturally as symmetries of some models. We also fermionize recently obtained Hubbard models, and obtain for the first time multispecies analogues of the Hubbard model, in their fermionic form. We comment on the conflict between symmetry enhancement and integrability of these models. Finally, the fermionic versions of the non integrable spin-1 and spin-3/2 Heisenberg chains are obtained.Comment: 24 pages, Latex. Minor typos corrected, one equation adde

New Integrable Models from Fusion

Integrable multistate or multiflavor/color models were recently introduced. They are generalizations of models corresponding to the defining representations of the U_q(sl(m)) quantum algebras. Here I show that a similar generalization is possible for all higher dimensional representations. The R-matrices and the Hamiltonians of these models are constructed by fusion. The sl(2) case is treated in some detail and the spin-0 and spin-1 matrices are obtained in explicit forms. This provides in particular a generalization of the Fateev-Zamolodchikov Hamiltonian.Comment: 11 pages, Latex. v2: statement concerning symmetries qualified, 3 minor misprints corrected. J. Phys. A (1999) in pres

Fermionisation of the Spin-S Uimin-Lai-Sutherland Model: Generalisation of Supersymmetric t-J Model to Spin-S

The spin-1 Uimin-Lai-Sutherland (ULS) isotropic chain model is expressed in terms of fermions and the equivalence of the fermionic representation to the supersymmetric t-J model is established directly at the level of Hamiltonians.The spin-S ULS model is fermionized and the Hamiltonian of the corresponding generalisation of the t-J model is written down.Comment: 16 page

DOES POPULATION DENSITY AFFECT THE SINGING BEHAVIOR OF FEMALE CANYON WRENS (CATHERPES MEXICANUS)?

Bird song has historically been considered from the perspective of temperate males despite females in many bird species being prolific singers. In this study, I investigated one species with female song, the canyon wren (Catherpes mexicanus). Canyon wrens do not duet like many other species with female song or other wrens. Instead, males and females sing sex-specific songs. The resource defense function of male canyon wren song is well-described, and males sing often during the breeding season. Females have only been observed to sing sporadically during the breeding season but sing reliably and often when exposed to playback of other females. Therefore, I hypothesized that females in higher breeding density areas would sing more and be more aggressive than those in lower breeding density areas, and females with closer distances between neighbors would sing more and be more aggressive than those with farther neighbors. I conducted this study over the course of two field seasons in two regions: southeastern Arizona (high density) and northcentral Colorado (low density). I spot-mapped breeding pairs in both areas, observed unprompted levels of song from females, and conducted playback experiments on females. I measured several behavioral parameters and song spectral parameters. I found that individuals in Arizona had significantly lower 95% frequencies in their songs, but did not find any other significant relationships between behavioral or spectral parameters and nearest neighbor distance, suggesting that other variables such as age, body size, breeding status, time of year, or genetic drift may better explain the variation in female songs between populations in Arizona vs. Colorado