5,389 research outputs found
Collision of two breathers at surface of deep water
We applied canonical transformation to water wave equation not only to remove
cubic nonlinear terms but to simplify drastically fourth order terms in
Hamiltonian. This transformation explicitly uses the fact of vanishing exact
four waves interaction for water gravity waves for 2D potential fluid. After
the transformation well-known but cumbersome Zakharov equation is drastically
simplified and can be written in X-space in compact way. This new equation is
very suitable as for analytic study as for numerical simulation. Localized in
space breather-type solution was found. Numerical simulation of collision of
two such breathers strongly supports hypothesis of integrability of 2-D free
surface hydrodynamics
Non-Perturbative Formulation of Time-Dependent String Solutions
We formulate here a new world-sheet renormalization-group technique for the
bosonic string, which is non-perturbative in the Regge slope alpha' and based
on a functional method for controlling the quantum fluctuations, whose
magnitudes are scaled by the value of alpha'. Using this technique we exhibit,
in addition to the well-known linear-dilaton cosmology, a new, non-perturbative
time-dependent background solution. Using the reparametrization invariance of
the string S-matrix, we demonstrate that this solution is conformally invariant
to alpha', and we give a heuristic inductive argument that conformal invariance
can be maintained to all orders in alpha'. This new time-dependent string
solution may be applicable to primordial cosmology or to the exit from
linear-dilaton cosmology at large times
Nonequilibrium Evolution of Correlation Functions: A Canonical Approach
We study nonequilibrium evolution in a self-interacting quantum field theory
invariant under space translation only by using a canonical approach based on
the recently developed Liouville-von Neumann formalism. The method is first
used to obtain the correlation functions both in and beyond the Hartree
approximation, for the quantum mechanical analog of the model. The
technique involves representing the Hamiltonian in a Fock basis of annihilation
and creation operators. By separating it into a solvable Gaussian part
involving quadratic terms and a perturbation of quartic terms, it is possible
to find the improved vacuum state to any desired order. The correlation
functions for the field theory are then investigated in the Hartree
approximation and those beyond the Hartree approximation are obtained by
finding the improved vacuum state corrected up to . These
correlation functions take into account next-to-leading and
next-to-next-to-leading order effects in the coupling constant. We also use the
Heisenberg formalism to obtain the time evolution equations for the equal-time,
connected correlation functions beyond the leading order. These equations are
derived by including the connected 4-point functions in the hierarchy. The
resulting coupled set of equations form a part of infinite hierarchy of coupled
equations relating the various connected n-point functions. The connection with
other approaches based on the path integral formalism is established and the
physical implications of the set of equations are discussed with particular
emphasis on thermalization.Comment: Revtex, 32 pages; substantial new material dealing with
non-equilibrium evolution beyond Hartree approx. based on the LvN formalism,
has been adde
Brane Gravity at Low Energy
Four dimensional gravity in the low energy limit of a higher dimensional
theory has been expected to be a (generalized) Brans-Dicke theory. A subtle
point in brane world scenarios is that the system of four dimensional effective
gravitational equations is not closed due to bulk gravitational waves and bulk
scalars. Nonetheless, weak gravity on the brane can be analyzed completely. We
revisit the theory of weak brane gravity using gauge-invariant gravitational
and scalar perturbations around a background warped geometry with a bulk scalar
between two flat branes. We obtain a simple condition for the radion
stabilization in terms of the scalar field potentials. We show that for general
potentials of the scalar field which provides radion stabilization and a
general conformal transformation to a frame in which matter on the branes are
minimally coupled to the metric, 4-dimensional Einstein gravity, not BD
gravity, is restored at low energies on either brane. In contrast, in RS brane
world scenario without a bulk scalar, low energy gravity is BD one. We
conjecture that in general brane world scenarios with more than one scalar
field, one will again encounter the situation that low energy gravity is not
described by the Einstein theory. Equipped with the weak gravity results, we
discuss the properties of 4d brane gravitational equations, in particular, the
value and sign of 4d Newton's gravitational coupling.Comment: Latex, 22 pages, 1 figure; version accepted for publication in
Phys.Rev.
The Growth of Correlations in the Matter Power Spectrum
We find statistically significant correlations in the cosmological matter
power spectrum over the full range of observable scales. While the correlations
between individual modes are weak, the band-averaged power spectrum shows
strong non-trivial correlations. The correlations are significant when the
modes in either one or both bands are in the non-linear regime, and approach
100% for pairs of bands in which all the modes are non-linear. The correlations
are weaker, but not absent, when computed in redshift space. Since estimates of
the power spectrum from galaxy surveys require band-averaging, the correlations
must be taken into account when comparing a measured power spectrum with
theoretical models.Comment: 7 pages, 6 Figures, accepted for publication to MNRAS. Revise
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