905 research outputs found
Feynman rules for string field theories with discrete target space
We derive a minimal set of Feynman rules for the loop amplitudes in unitary
models of closed strings, whose target space is a simply laced (extended)
Dynkin diagram. The string field Feynman graphs are composed of propagators,
vertices (including tadpoles) of all topologies, and leg factors for the
macroscopic loops. A vertex of given topology factorizes into a fusion
coefficient for the matter fields and an intersection number associated with
the corresponding punctured surface. As illustration we obtain explicit
expressions for the genus-one tadpole and the genus-zero four-loop amplitude.Comment: 19 pages, harvmac, 4 uuencoded figures included using epsf. A missing
term added to the expression for the genus-one tadpole and Fig.3 modified
correspondingl
Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type
New reductions for the multicomponent modified Korteveg-de Vries (MMKdV)
equations on the symmetric spaces of {\bf DIII}-type are derived using the
approach based on the reduction group introduced by A.V. Mikhailov. The
relevant inverse scattering problem is studied and reduced to a Riemann-Hilbert
problem. The minimal sets of scattering data , which
allow one to reconstruct uniquely both the scattering matrix and the potential
of the Lax operator are defined. The effect of the new reductions on the
hierarchy of Hamiltonian structures of MMKdV and on are
studied. We illustrate our results by the MMKdV equations related to the
algebra and derive several new MMKdV-type equations
using group of reductions isomorphic to , ,
.Comment: This is a contribution to the Proc. of the Seventh International
Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007,
Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
Bulk correlation functions in 2D quantum gravity
We compute bulk 3- and 4-point tachyon correlators in the 2d Liouville
gravity with non-rational matter central charge c<1, following and comparing
two approaches. The continuous CFT approach exploits the action on the tachyons
of the ground ring generators deformed by Liouville and matter ``screening
charges''. A by-product general formula for the matter 3-point OPE structure
constants is derived. We also consider a ``diagonal'' CFT of 2D quantum
gravity, in which the degenerate fields are restricted to the diagonal of the
semi-infinite Kac table. The discrete formulation of the theory is a
generalization of the ADE string theories, in which the target space is the
semi-infinite chain of points.Comment: 14 pages, 2 figure
On N-wave type systems and their gauge equivalent
The class of nonlinear evolution equations - gauge equivalent to the N-wave
equations related to the simple Lie algebra g are derived and analyzed. They
are written in terms of the functions S(x,t) satisfying r= rank g nonlinear
constraints. The corresponding Lax pairs and the time evolution of the
scattering data are found. The Zakharov-Shabat dressing method is appropriately
modified to construct their soliton solutions.Comment: 5 pages, LaTeX 2e, revised versio
Bose-Einstein condensates with F=1 and F=2. Reductions and soliton interactions of multi-component NLS models
We analyze a class of multicomponent nonlinear Schrodinger equations (MNLS)
related to the symmetric BD.I-type symmetric spaces and their reductions. We
briefly outline the direct and the inverse scattering method for the relevant
Lax operators and the soliton solutions. We use the Zakharov-Shabat dressing
method to obtain the two-soliton solution and analyze the soliton interactions
of the MNLS equations and some of their reductions.Comment: SPIE UNO-09-UN101-19, SPIE Volume: 7501, (2009
Bound state of dimers on a spherical surface
The study of particle motion on spherical surfaces is relevant to adsorption
on buckyballs and other solid particles. This paper reports results for the
binding energy of such dimers, consisting of two light particles (He atoms or
hydrogen molecules) constrained to move on a spherical surface. The binding
energy reaches a particularly large value when the radius of the sphere is
about 3/4 of the particles' diameter.Comment: 6 pages, 3 figures, submitted to JLTP, conference proceedings QFS
200
Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice
We present two new families of stationary solutions for equations of
Bose-Fermi mixtures with an elliptic function potential with modulus . We
also discuss particular cases when the quasiperiodic solutions become periodic
ones. In the limit of a sinusoidal potential () our solutions model a
quasi-one dimensional quantum degenerate Bose-Fermi mixture trapped in optical
lattice. In the limit the solutions are expressed by hyperbolic
function solutions (vector solitons). Thus we are able to obtain in an unified
way quasi-periodic and periodic waves, and solitons. The precise conditions for
existence of every class of solutions are derived. There are indications that
such waves and localized objects may be observed in experiments with cold
quantum degenerate gases.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
Theory for the nonequilibrium dynamics of flexible chain molecules: relaxation to equilibrium of pentadecane from an all-trans conformation
We extend to nonequilibrium processes our recent theory for the long time
dynamics of flexible chain molecules. While the previous theory describes the
equilibrium motions for any bond or interatomic separation in (bio)polymers by
time correlation functions, the present extension of the theory enables the
prediction of the nonequilibrium relaxation that occurs in processes, such as
T-jump experiments, where there are sudden transitions between, for example,
different equilibrium states. As a test of the theory, we consider the
``unfolding'' of pentadecane when it is transported from a constrained
all-trans conformation to a random-coil state at thermal equilibrium. The time
evolution of the mean-square end-to-end distance after release of the
constraint is computed both from the theory and from Brownian dynamics (BD)
simulations. The predictions of the theory agree very well with the BD
simulations. Furthermore, the theory produces enormous savings in computer
time. This work is a starting point for the application of the new method to
nonequilibrium processes with biological importance such as the helix-coil
transition and protein folding.Comment: 11 pages total, including 2 Postscript figures; submitted to Journal
of Chemical Physic
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