207 research outputs found
Bailey flows and Bose-Fermi identities for the conformal coset models
We use the recently established higher-level Bailey lemma and Bose-Fermi
polynomial identities for the minimal models to demonstrate the
existence of a Bailey flow from to the coset models
where is a
positive integer and is fractional, and to obtain Bose-Fermi identities
for these models. The fermionic side of these identities is expressed in terms
of the fractional-level Cartan matrix introduced in the study of .
Relations between Bailey and renormalization group flow are discussed.Comment: 28 pages, AMS-Latex, two references adde
Supersymmetric pairing of kinks for polynomial nonlinearities
We show how one can obtain kink solutions of ordinary differential equations
with polynomial nonlinearities by an efficient factorization procedure directly
related to the factorization of their nonlinear polynomial part. We focus on
reaction-diffusion equations in the travelling frame and
damped-anharmonic-oscillator equations. We also report an interesting pairing
of the kink solutions, a result obtained by reversing the factorization
brackets in the supersymmetric quantum mechanical style. In this way, one gets
ordinary differential equations with a different polynomial nonlinearity
possessing kink solutions of different width but propagating at the same
velocity as the kinks of the original equation. This pairing of kinks could
have many applications. We illustrate the mathematical procedure with several
important cases, among which the generalized Fisher equation, the
FitzHugh-Nagumo equation, and the polymerization fronts of microtubulesComment: 13 pages, 2 figures, revised during the 2nd week of Dec. 200
Riccati-parameter solutions of nonlinear second-order ODEs
It has been proven by Rosu and Cornejo-Perez in 2005 that for some nonlinear
second-order ODEs it is a very simple task to find one particular solution once
the nonlinear equation is factorized with the use of two first-order
differential operators. Here, it is shown that an interesting class of
parametric solutions is easy to obtain if the proposed factorization has a
particular form, which happily turns out to be the case in many problems of
physical interest. The method that we exemplify with a few explicitly solved
cases consists in using the general solution of the Riccati equation, which
contributes with one parameter to this class of parametric solutions. For these
nonlinear cases, the Riccati parameter serves as a `growth' parameter from the
trivial null solution up to the particular solution found through the
factorization procedureComment: 5 pages, 3 figures, change of title and more tex
Non-conformal asymptotic behavior of the time-dependent field-field correlators of 1D anyons
The exact large time and distance behavior of the field-field correlators has
been computed for one-dimensional impenetrable anyons at finite temperatures.
The result reproduces known asymptotics for impenetrable bosons and free
fermions in the appropriate limits of the statistics parameter. The obtained
asymptotic behavior of the correlators is dominated by the singularity in the
spectral density of the quasiparticle states at the bottom of the band, and
differs from the predictions of the conformal field theory. One can argue,
however, that the anyonic response to the low-energy probes is still determined
by the conformal terms in the asymptotic expansion.Comment: 5 pages, RevTeX
Singular responses of spin-incoherent Luttinger liquids
When a local potential changes abruptly in time, an electron gas shifts to a
new state which at long times is orthogonal to the one in the absence of the
local potential. This is known as Anderson's orthogonality catastrophe and it
is relevant for the so-called X-ray edge or Fermi edge singularity, and for
tunneling into an interacting one dimensional system of fermions. It often
happens that the finite frequency response of the photon absorption or the
tunneling density of states exhibits a singular behavior as a function of
frequency: where is a
threshold frequency and is an exponent characterizing the singular
response. In this paper singular responses of spin-incoherent Luttinger liquids
are reviewed. Such responses most often do not fall into the familiar form
above, but instead typically exhibit logarithmic corrections and display a much
higher universality in terms of the microscopic interactions in the theory.
Specific predictions are made, the current experimental situation is
summarized, and key outstanding theoretical issues related to spin-incoherent
Luttinger liquids are highlighted.Comment: 21 pages, 3 figures. Invited Topical Review Articl
Exact solutions of a Flat Full Causal Bulk viscous FRW cosmological model through factorization
We study the classical flat full causal bulk viscous FRW cosmological model
through the factorization method. The method shows that there exists a
relationship between the viscosity parameter and the parameter
entering the equations of state of the model. Also, the factorization method
allows to find some new exact parametric solutions for different values of the
viscous parameter . Special attention is given to the well known case
, for which the cosmological model admits scaling symmetries.
Furthermore, some exact parametric solutions for are obtained through
the Lie group method.Comment: 18 pas. RevTeX4. New solutions. arXiv admin note: text overlap with
arXiv:gr-qc/0107004 by other author
Exceptional structure of the dilute A model: E and E Rogers--Ramanujan identities
The dilute A lattice model in regime 2 is in the universality class of
the Ising model in a magnetic field. Here we establish directly the existence
of an E structure in the dilute A model in this regime by expressing
the 1-dimensional configuration sums in terms of fermionic sums which
explicitly involve the E root system. In the thermodynamic limit, these
polynomial identities yield a proof of the E Rogers--Ramanujan identity
recently conjectured by Kedem {\em et al}.
The polynomial identities also apply to regime 3, which is obtained by
transforming the modular parameter by . In this case we find an
A_1\times\mbox{E}_7 structure and prove a Rogers--Ramanujan identity of
A_1\times\mbox{E}_7 type. Finally, in the critical limit, we give
some intriguing expressions for the number of -step paths on the A
Dynkin diagram with tadpoles in terms of the E Cartan matrix. All our
findings confirm the E and E structure of the dilute A model found
recently by means of the thermodynamic Bethe Ansatz.Comment: 9 pages, 1 postscript figur
The Yang-Baxter equation for PT invariant nineteen vertex models
We study the solutions of the Yang-Baxter equation associated to nineteen
vertex models invariant by the parity-time symmetry from the perspective of
algebraic geometry. We determine the form of the algebraic curves constraining
the respective Boltzmann weights and found that they possess a universal
structure. This allows us to classify the integrable manifolds in four
different families reproducing three known models besides uncovering a novel
nineteen vertex model in a unified way. The introduction of the spectral
parameter on the weights is made via the parameterization of the fundamental
algebraic curve which is a conic. The diagonalization of the transfer matrix of
the new vertex model and its thermodynamic limit properties are discussed. We
point out a connection between the form of the main curve and the nature of the
excitations of the corresponding spin-1 chains.Comment: 43 pages, 6 figures and 5 table
Fermionic solution of the Andrews-Baxter-Forrester model II: proof of Melzer's polynomial identities
We compute the one-dimensional configuration sums of the ABF model using the
fermionic technique introduced in part I of this paper. Combined with the
results of Andrews, Baxter and Forrester, we find proof of polynomial
identities for finitizations of the Virasoro characters
as conjectured by Melzer. In the thermodynamic limit
these identities reproduce Rogers--Ramanujan type identities for the unitary
minimal Virasoro characters, conjectured by the Stony Brook group. We also
present a list of additional Virasoro character identities which follow from
our proof of Melzer's identities and application of Bailey's lemma.Comment: 28 pages, Latex, 7 Postscript figure
- …