32 research outputs found
BLP dissipative structures in plane
We study the Darboux and Laplace transformations for the
Boiti-Leon-Pempinelli equations (BLP). These equations are the (1+2)
generalization of the sinh-Gordon equation. In addition, the BLP equations
reduced to the Burgers (and anti-Burgers) equation in a one-dimensional limit.
Localized nonsingular solutions in both spatial dimensions and (anti) "blow-up"
solutions are constructed. The Burgers equation's "dressing" procedure is
suggested. This procedure allows us to construct such solutions of the BLP
equations which are reduced to the solutions of the dissipative Burgers
equations when . These solutions we call the BLP dissipative
structures.Comment: 7 pages, AMS-Te
Darboux Transformation for Dirac Equations with (1+1) potentials
We study the Darboux transformation (DT) for Dirac equations with (1+1)
potentials. Exact solutions for the adiabatic external field are constructed.
The connection between the exactly soluble Dirac (1+1) potentials and the
soliton solutions of the Davey--Stewartson equations is discussed.Comment: AMS-Te
Generalized Fubini instantons
We show that nonlinear Klein-Gordon equation with negative coupling
admits an exact solution which appears to be the linear superposition of the
plane wave and the nonsingular rational soliton. We show that the same approach
allows to construct the solution of similar properties for the Euclidean
model with broken symmetry. Interestingly, this regular solution will
be of instanton type only in the Euclidean space.Comment: 10 page
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
An Infrared Divergence Problem in the cosmological measure theory and the anthropic reasoning
An anthropic principle has made it possible to answer the difficult question
of why the observable value of cosmological constant (
GeV) is so disconcertingly tiny compared to predicted value of vacuum
energy density GeV. Unfortunately, there is a
darker side to this argument, as it consequently leads to another absurd
prediction: that the probability to observe the value for randomly
selected observer exactly equals to 1. We'll call this controversy an infrared
divergence problem. It is shown that the IRD prediction can be avoided with the
help of a Linde-Vanchurin {\em singular runaway measure} coupled with the
calculation of relative Bayesian probabilities by the means of the {\em
doomsday argument}. Moreover, it is shown that while the IRD problem occurs for
the {\em prediction stage} of value of , it disappears at the {\em
explanatory stage} when has already been measured by the observer.Comment: 9 pages, RevTe
Agnesi Weighting for the Measure Problem of Cosmology
The measure problem of cosmology is how to assign normalized probabilities to
observations in a universe so large that it may have many observations
occurring at many different spacetime locations. I have previously shown how
the Boltzmann brain problem (that observations arising from thermal or quantum
fluctuations may dominate over ordinary observations if the universe expands
sufficiently and/or lasts long enough) may be ameliorated by volume averaging,
but that still leaves problems if the universe lasts too long. Here a solution
is proposed for that residual problem by a simple weighting factor 1/(1+t^2) to
make the time integral convergent. The resulting Agnesi measure appears to
avoid problems other measures may have with vacua of zero or negative
cosmological constant.Comment: 26 pages, LaTeX; discussion is added of how Agnesi weighting appears
better than other recent measure
Resonant structure of space-time of early universe
A new fully quantum method describing penetration of packet from internal
well outside with its tunneling through the barrier of arbitrary shape used in
problems of quantum cosmology, is presented. The method allows to determine
amplitudes of wave function, penetrability and reflection relatively the barrier (accuracy of the method: ), coefficient of penetration (i.e. probability of
the packet to penetrate from the internal well outside with its tunneling),
coefficient of oscillations (describing oscillating behavior of the packet
inside the internal well). Using the method, evolution of universe in the
closed Friedmann--Robertson--Walker model with quantization in presence of
positive cosmological constant, radiation and component of generalize Chaplygin
gas is studied. It is established (for the first time): (1) oscillating
dependence of the penetrability on localization of start of the packet; (2)
presence of resonant values of energy of radiation , at which the
coefficient of penetration increases strongly. From analysis of these results
it follows: (1) necessity to introduce initial condition into both
non-stationary, and stationary quantum models; (2) presence of some definite
values for the scale factor , where start of expansion of universe is the
most probable; (3) during expansion of universe in the initial stage its radius
is changed not continuously, but passes consequently through definite discrete
values and tends to continuous spectrum in latter time.Comment: 18 pages, 14 figures, 4 table
Screening of cosmological constant for De Sitter Universe in non-local gravity, phantom-divide crossing and finite-time future singularities
We investigate de Sitter solutions in non-local gravity as well as in
non-local gravity with Lagrange constraint multiplier. We examine a condition
to avoid a ghost and discuss a screening scenario for a cosmological constant
in de Sitter solutions. Furthermore, we explicitly demonstrate that three types
of the finite-time future singularities can occur in non-local gravity and
explore their properties. In addition, we evaluate the effective equation of
state for the universe and show that the late-time accelerating universe may be
effectively the quintessence, cosmological constant or phantom-like phases. In
particular, it is found that there is a case in which a crossing of the phantom
divide from the non-phantom (quintessence) phase to the phantom one can be
realized when a finite-time future singularity occurs. Moreover, it is
demonstrated that the addition of an term can cure the finite-time future
singularities in non-local gravity. It is also suggested that in the framework
of non-local gravity, adding an term leads to possible unification of the
early-time inflation with the late-time cosmic acceleration.Comment: 42 pages, no figure, version accepted for publication in General
Relativity and Gravitatio
First measurement of direct photoproduction on the proton
We report on the results of the first measurement of exclusive
meson photoproduction on protons for GeV and GeV. Data were collected with the CLAS detector at the Thomas
Jefferson National Accelerator Facility. The resonance was detected via its
decay in the channel by performing a partial wave analysis of the
reaction . Clear evidence of the meson
was found in the interference between and waves at GeV. The -wave differential cross section integrated in the mass range of
the was found to be a factor of 50 smaller than the cross section
for the meson. This is the first time the meson has been
measured in a photoproduction experiment
The Born Rule Dies
The Born rule may be stated mathematically as the rule that probabilities in
quantum theory are expectation values of a complete orthogonal set of
projection operators. This rule works for single laboratory settings in which
the observer can distinguish all the different possible outcomes corresponding
to the projection operators. However, theories of inflation suggest that the
universe may be so large that any laboratory, no matter how precisely it is
defined by its internal state, may exist in a large number of very distantly
separated copies throughout the vast universe. In this case, no observer within
the universe can distinguish all possible outcomes for all copies of the
laboratory. Then normalized probabilities for the local outcomes that can be
locally distinguished cannot be given by the expectation values of any
projection operators. Thus the Born rule dies and must be replaced by another
rule for observational probabilities in cosmology. The freedom of what this new
rule is to be is the measure problem in cosmology. A particular volume-averaged
form is proposed.Comment: LaTeX, 16 pages, typos in Eqs. (4.3) and (6.2) correcte