15,834 research outputs found
Ultraviolet cascade in the thermalization of the classical phi^4 theory in 3+1 dimensions
We investigate the dynamics of thermalization and the approach to equilibrium
in the classical phi^4 theory in 3+1 spacetime dimensions. The non-equilibrium
dynamics is studied by numerically solving the equations of motion in a light-
cone-like discretization of the model for a broad range of initial conditions
and energy densities.A smooth cascade of energy towards the ultraviolet is
found to be the basic mechanism of thermalization.After an initial transient
stage,at a time scale of several hundreds inverse masses,the squared of the
field gradient becomes larger than the nonlinear term and a stage of universal
cascade emerges. As the cascade progresses, the modes with higher wavenumbers
exhibit weaker and weaker nonlinearities well described by the Hartree
approximation while the infrared modes retain strong selfinteractions. Two
timescales for equilibration appears.For k^2>(t) we observe an effective
thermalization with a time scale in the thousands of inverse masses and the
Hartree approximation holds. By effective thermalization we mean that the
observable acquires the equilibrium functional form with an effective time
dependent temperature Teff, which slowly decreases with time. Infrared modes
with k^2 (t) equilibrate only by time scales in the millions of
inverse masses. Infrared modes with k^2 (t) equilibrate only by time
scales in the millions.Virialization and the equation of state start to set
much earlier than effective thermalization.The applicability of these results
in quantum field theory for large occupation numbers and small coupling is
analyzed.Comment: 47 pages, 31 figures. Presentation improved, 4 new figure
Yang--Baxter symmetry in integrable models: new light from the Bethe Ansatz solution
We show how any integrable 2D QFT enjoys the existence of infinitely many
non--abelian {\it conserved} charges satisfying a Yang--Baxter symmetry
algebra. These charges are generated by quantum monodromy operators and provide
a representation of deformed affine Lie algebras. We review and generalize
the work of de Vega, Eichenherr and Maillet on the bootstrap construction of
the quantum monodromy operators to the sine--Gordon (or massive Thirring)
model, where such operators do not possess a classical analogue. Within the
light--cone approach to the mT model, we explicitly compute the eigenvalues of
the six--vertex alternating transfer matrix \tau(\l) on a generic physical
state, through algebraic Bethe ansatz. In the thermodynamic limit \tau(\l)
turns out to be a two--valued periodic function. One determination generates
the local abelian charges, including energy and momentum, while the other
yields the abelian subalgebra of the (non--local) YB algebra. In particular,
the bootstrap results coincide with the ratio between the two determinations of
the lattice transfer matrix.Comment: 30 page
String dynamics in cosmological and black hole backgrounds: The null string expansion
We study the classical dynamics of a bosonic string in the --dimensional
flat Friedmann--Robertson--Walker and Schwarzschild backgrounds. We make a
perturbative development in the string coordinates around a {\it null} string
configuration; the background geometry is taken into account exactly. In the
cosmological case we uncouple and solve the first order fluctuations; the
string time evolution with the conformal gauge world-sheet --coordinate
is given by , where
are given by Eqs.\ (3.15), and is the exponent of the conformal factor
in the Friedmann--Robertson--Walker metric, i.e. . The string
proper size, at first order in the fluctuations, grows like the conformal
factor and the string energy--momentum tensor corresponds to that of
a null fluid. For a string in the black hole background, we study the planar
case, but keep the dimensionality of the spacetime generic. In the null
string expansion, the radial, azimuthal, and time coordinates are
and The first terms of the series represent a
{\it generic} approach to the Schwarzschild singularity at . First and
higher order string perturbations contribute with higher powers of . The
integrated string energy-momentum tensor corresponds to that of a null fluid in
dimensions. As the string approaches the singularity its proper
size grows indefinitely like . We end the paper
giving three particular exact string solutions inside the black hole.Comment: 17 pages, REVTEX, no figure
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