10 research outputs found
Integrability of the and Ruijsenaars-Schneider models
We study the and Ruijsenaars-Schneider(RS) models with
interaction potential of trigonometric and rational types. The Lax pairs for
these models are constructed and the involutive Hamiltonians are also given.
Taking nonrelativistic limit, we also obtain the Lax pairs for the
corresponding Calogero-Moser systems.Comment: 20 pages, LaTeX2e, no figure
The Lax pairs for elliptic C_n and BC_n Ruijsenaars-Schneider models and their spectral curves
We study the elliptic C_n and BC_n Ruijsenaars-Schneider models which is
elliptic generalization of system given in hep-th/0006004. The Lax pairs for
these models are constructed by Hamiltonian reduction technology. We show that
the spectral curves can be parameterized by the involutive integrals of motion
for these models. Taking nonrelativistic limit and scaling limit, we verify
that they lead to the systems corresponding to Calogero-Moser and Toda types.Comment: LaTeX2e, 25 pages, 1 table, some references added and rearranged
together with misprints correcte
A class of Calogero type reductions of free motion on a simple Lie group
The reductions of the free geodesic motion on a non-compact simple Lie group
G based on the symmetry given by left- and right
multiplications for a maximal compact subgroup are
investigated. At generic values of the momentum map this leads to (new) spin
Calogero type models. At some special values the `spin' degrees of freedom are
absent and we obtain the standard Sutherland model with three
independent coupling constants from SU(n+1,n) and from SU(n,n). This
generalization of the Olshanetsky-Perelomov derivation of the model with
two independent coupling constants from the geodesics on with
G=SU(n+1,n) relies on fixing the right-handed momentum to a non-zero character
of . The reductions considered permit further generalizations and work at
the quantized level, too, for non-compact as well as for compact G.Comment: shortened to 13 pages in v2 on request of Lett. Math. Phys. and
corrected some spelling error
Neutralino-Nucleon Cross Section and Charge and Colour Breaking Constraints
We compute the neutralino-nucleon cross section in several supersymmetric
scenarios, taking into account all kind of constraints. In particular, the
constraints that the absence of dangerous charge and colour breaking minima
imposes on the parameter space are studied in detail. In addition, the most
recent experimental constraints, such as the lower bound on the Higgs mass, the
branching ratio, and the muon are considered. The
astrophysical bounds on the dark matter density are also imposed on the
theoretical computation of the relic neutralino density, assuming thermal
production. This computation is relevant for the theoretical analysis of the
direct detection of dark matter in current experiments. We consider first the
supergravity scenario with universal soft terms and GUT scale. In this scenario
the charge and colour breaking constraints turn out to be quite important, and
\tan\beta\lsim 20 is forbidden. Larger values of can also be
forbidden, depending on the value of the trilinear parameter . Finally, we
study supergravity scenarios with an intermediate scale, and also with
non-universal scalar and gaugino masses where the cross section can be very
large.Comment: Final version to appear in JHE
A Unified Algebraic Approach to Few and Many-Body Correlated Systems
The present article is an extended version of the paper {\it Phys. Rev.} {\bf
B 59}, R2490 (1999), where, we have established the equivalence of the
Calogero-Sutherland model to decoupled oscillators. Here, we first employ the
same approach for finding the eigenstates of a large class of Hamiltonians,
dealing with correlated systems. A number of few and many-body interacting
models are studied and the relationship between their respective Hilbert
spaces, with that of oscillators, is found. This connection is then used to
obtain the spectrum generating algebras for these systems and make an algebraic
statement about correlated systems. The procedure to generate new solvable
interacting models is outlined. We then point out the inadequacies of the
present technique and make use of a novel method for solving linear
differential equations to diagonalize the Sutherland model and establish a
precise connection between this correlated system's wave functions, with those
of the free particles on a circle. In the process, we obtain a new expression
for the Jack polynomials. In two dimensions, we analyze the Hamiltonian having
Laughlin wave function as the ground-state and point out the natural emergence
of the underlying linear symmetry in this approach.Comment: 18 pages, Revtex format, To appear in Physical Review
Knowledge-based energy functions for computational studies of proteins
This chapter discusses theoretical framework and methods for developing
knowledge-based potential functions essential for protein structure prediction,
protein-protein interaction, and protein sequence design. We discuss in some
details about the Miyazawa-Jernigan contact statistical potential,
distance-dependent statistical potentials, as well as geometric statistical
potentials. We also describe a geometric model for developing both linear and
non-linear potential functions by optimization. Applications of knowledge-based
potential functions in protein-decoy discrimination, in protein-protein
interactions, and in protein design are then described. Several issues of
knowledge-based potential functions are finally discussed.Comment: 57 pages, 6 figures. To be published in a book by Springe
Inequivalent quantization of the rational Calogero model with a Coulomb type interaction
We consider the inequivalent quantizations of a -body rational Calogero
model with a Coulomb type interaction. It is shown that for certain range of
the coupling constants, this system admits a one-parameter family of
self-adjoint extensions. We analyze both the bound and scattering state sectors
and find novel solutions of this model. We also find the ladder operators for
this system, with which the previously known solutions can be constructed.Comment: 15 pages, 3 figures, revtex4, typos corrected, to appear in EPJ
Geometric construction of elliptic integrable systems and N=1* superpotentials
We show how the elliptic Calogero-Moser integrable systems arise from a symplectic quotient construction, generalising the construction for AN â1 by Gorsky and Nekrasov to other algebras. This clarifies the role of (twisted) affine Kac-Moody algebras in elliptic Calogero-Moser systems and allows for a natural geometric con- struction of Lax operators for these systems. We elaborate on the connection of the associated Hamiltonians to superpotentials for N = 1â deformations of N = 4 supersymmetric gauge theory, and argue how non-perturbative physics generates the elliptic superpotentials. We also discuss the relevance of these systems and the asso- ciated quotient construction to open problems in string theory. In an appendix, we use the theory of orbit algebras to show the systematics behind the folding procedures for these integrable models