211 research outputs found
Discrete symmetry's chains and links between integrable equations
The discrete symmetry's dressing chains of the nonlinear Schrodinger equation
(NLS) and Davey-Stewartson equations (DS) are consider. The modified NLS (mNLS)
equation and the modified DS (mDS) equations are obtained. The explicitly
reversible Backlund auto-transformations for the mNLS and mDS equations are
constructed. We demonstrate discrete symmetry's conjugate chains of the KP and
DS models. The two-dimensional generalization of the P4 equation are obtained.Comment: 20 page
The linearization method and new classes of exact solutions in cosmology
We develop a method for constructing exact cosmological solutions of the
Einstein equations based on representing them as a second-order linear
differential equation. In particular, the method allows using an arbitrary
known solution to construct a more general solution parameterized by a set of
3\textit{N} constants, where \textit{N} is an arbitrary natural number. The
large number of free parameters may prove useful for constructing a theoretical
model that agrees satisfactorily with the results of astronomical observations.
Cosmological solutions on the Randall-Sundrum brane have similar properties. We
show that three-parameter solutions in the general case already exhibit
inflationary regimes. In contrast to previously studied two-parameter
solutions, these three-parameter solutions can describe an exit from inflation
without a fine tuning of the parameters and also several consecutive
inflationary regimes.Comment: 7 page
A nonperturbative study of phase transitions in the multi-frequency sine-Gordon model
The phase spaces of the two- and three-frequency sine-Gordon models are
examined in the framework of truncated conformal space approach. The focus is
mainly on a tricritical point in the phase space of the three-frequency model.
We give substantial evidence that this point exists. We also find the critical
line in the phase space and present TCSA data showing the change of the
spectrum on the critical line as the tricritical endpoint is approached. We
find a few points of the line of first order transition as well.Comment: 26 pages, LaTeX, minor modificatio
The Big Trip and Wheeler-DeWitt equation
Of all the possible ways to describe the behavior of the universe that has
undergone a big trip the Wheeler-DeWitt equation should be the most accurate --
provided, of course, that we employ the correct formulation. In this article we
start by discussing the standard formulation introduced by Gonz\'alez-D\'iaz
and Jimenez-Madrid, and show that it allows for a simple yet efficient method
of the solution's generation, which is based on the Moutard transformation.
Next, by shedding the unnecessary restrictions, imposed on aforementioned
standard formulation we introduce a more general form of the Wheeler-DeWitt
equation. One immediate prediction of this new formula is that for the universe
the probability to emerge right after the big trip in a state with will
be maximal if and only if .Comment: accepted in Astrophysics and Space Scienc
One-point functions in integrable quantum field theory at finite temperature
We determine the form factor expansion of the one-point functions in
integrable quantum field theory at finite temperature and find that it is
simpler than previously conjectured. We show that no singularities are left in
the final expression provided that the operator is local with respect to the
particles and argue that the divergences arising in the non-local case are
related to the absence of spontaneous symmetry breaking on the cylinder. As a
specific application, we give the first terms of the low temperature expansion
of the one-point functions for the Ising model in a magnetic field.Comment: 10 pages, late
Friedman vs Abel equations: A connection unraveled
We present an interesting connection between Einstein-Friedmann equations for
the models of universe filled with scalar field and the special form of Abel
equation of the first kind. This connection works in both ways: first, we show
how, knowing the general solution of the Abel equation (corresponding to the
given scalar field potential) one can obtain the general solution of the
Friedman Equation (and use the former for studying such problems as existence
of inflation with exit for particular models). On the other hand, one can
invert the procedure and construct the B\"{a}cklund auto-transformations for
the Abel equation.Comment: Replaced raw version (with fake abstract and acknowledgments) to a
new, revised versio
Correlation functions of disorder operators in massive ghost theories
The two-dimensional ghost systems with negative integral central charge
received much attention in the last years for their role in a number of
applications and in connection with logarithmic conformal field theory. We
consider the free massive bosonic and fermionic ghost systems and concentrate
on the non-trivial sectors containing the disorder operators. A unified
analysis of the correlation functions of such operators can be performed for
ghosts and ordinary complex bosons and fermions. It turns out that these
correlators depend only on the statistics although the scaling dimensions of
the disorder operators change when going from the ordinary to the ghost case.
As known from the study of the ordinary case, the bosonic and fermionic
correlation functions are the inverse of each other and are exactly expressible
through the solution of a non-linear differential equation.Comment: 8 pages, late
Astronomical bounds on future big freeze singularity
Recently it was found that dark energy in the form of phantom generalized
Chaplygin gas may lead to a new form of the cosmic doomsday, the big freeze
singularity. Like the big rip singularity, the big freeze singularity would
also take place at a finite future cosmic time, but unlike the big rip
singularity it happens for a finite scale factor.Our goal is to test if a
universe filled with phantom generalized Chaplygin gas can conform to the data
of astronomical observations. We shall see that if the universe is only filled
with generalized phantom Chaplygin gas with equation of state
with , then such a model cannot be matched
to the data of astronomical observations. To construct matched models one
actually need to add dark matter. This procedure results in cosmological
scenarios which do not contradict the data of astronomical observations and
allows one to estimate how long we are now from the future big freeze doomsday.Comment: 8 page
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