43,930 research outputs found
Exact and approximate dynamics of the quantum mechanical O(N) model
We study a quantum dynamical system of N, O(N) symmetric, nonlinear
oscillators as a toy model to investigate the systematics of a 1/N expansion.
The closed time path (CTP) formalism melded with an expansion in 1/N is used to
derive time evolution equations valid to order 1/N (next-to-leading order). The
effective potential is also obtained to this order and its properties
areelucidated. In order to compare theoretical predictions against numerical
solutions of the time-dependent Schrodinger equation, we consider two initial
conditions consistent with O(N) symmetry, one of them a quantum roll, the other
a wave packet initially to one side of the potential minimum, whose center has
all coordinates equal. For the case of the quantum roll we map out the domain
of validity of the large-N expansion. We discuss unitarity violation in the 1/N
expansion; a well-known problem faced by moment truncation techniques. The 1/N
results, both static and dynamic, are also compared to those given by the
Hartree variational ansatz at given values of N. We conclude that late-time
behavior, where nonlinear effects are significant, is not well-described by
either approximation.Comment: 16 pages, 12 figrures, revte
Non-equilibrium dynamics in quantum field theory at high density: the tsunami
The dynamics of a dense relativistic quantum fluid out of thermodynamic
equilibrium is studied in the framework of the Phi^4 scalar field theory in the
large N limit. The time evolution of a particle distribution in momentum space
(the tsunami) is computed. The effective mass felt by the particles in such a
high density medium equals the tree level mass plus the expectation value of
the squared field. The case of negative tree level squared mass is particularly
interesting. In such case dynamical symmetry restoration as well as dynamical
symmetry breaking can happen. Furthermore, the symmetry may stay broken with
vanishing asymptotic squared mass showing the presence of out of equilibrium
Goldstone bosons. We study these phenomena and identify the set of initial
conditions that lead to each case. We compute the equation of state which turns
to depend on the initial state. Although the system does not thermalize, the
equation of state for asymptotically broken symmetry is of radiation type. We
compute the correlation functions at equal times. The two point correlator for
late times is the sum of different terms. One stems from the initial particle
distribution. Another term accounts for the out of equilibrium Goldstone bosons
created by spinodal unstabilities when the symmetry is asymptotically
broken.Both terms are of the order of the inverse of the coupling for distances
where causal signals can connect the two points. The contribution of the out of
equilibrium Goldstones exhibits scaling behaviour in a generalized sense.Comment: LaTex, 49 pages, 15 .ps figure
Resumming the large-N approximation for time evolving quantum systems
In this paper we discuss two methods of resumming the leading and next to
leading order in 1/N diagrams for the quartic O(N) model. These two approaches
have the property that they preserve both boundedness and positivity for
expectation values of operators in our numerical simulations. These
approximations can be understood either in terms of a truncation to the
infinitely coupled Schwinger-Dyson hierarchy of equations, or by choosing a
particular two-particle irreducible vacuum energy graph in the effective action
of the Cornwall-Jackiw-Tomboulis formalism. We confine our discussion to the
case of quantum mechanics where the Lagrangian is . The
key to these approximations is to treat both the propagator and the
propagator on similar footing which leads to a theory whose graphs have the
same topology as QED with the propagator playing the role of the photon.
The bare vertex approximation is obtained by replacing the exact vertex
function by the bare one in the exact Schwinger-Dyson equations for the one and
two point functions. The second approximation, which we call the dynamic Debye
screening approximation, makes the further approximation of replacing the exact
propagator by its value at leading order in the 1/N expansion. These two
approximations are compared with exact numerical simulations for the quantum
roll problem. The bare vertex approximation captures the physics at large and
modest better than the dynamic Debye screening approximation.Comment: 30 pages, 12 figures. The color version of a few figures are
separately liste
Line-of-sight effects on observability of kink and sausage modes in coronal structures with imaging telescopes
Kink modes of solar coronal structures, perturbing the loop in the direction along the line-of-sight (LOS), can be observed as emission intensity disturbances propagating along the loop provided the angle between the LOS and the structure is not ninety degrees. The effect is based upon the change of the column depth of the loop (along the LOS) by the wave. The observed amplitude of the emission intensity variations can be larger than the actual amplitude of the wave by a factor of two and there is an optimal angle maximizing the observed amplitude. For other angles this effect can also attenuate the observed wave amplitude. The observed amplitude depends upon the ratio of the wave length of kink perturbations to the width of the structure and on the angle between the LOS and the axis of the structure. Sausage modes are always affected negatively from the observational point of view, as the observed amplitude is always less than the actual one. This effect should be taken into account in the interpretation of wave phenomena observed in the corona with space-borne and ground-based imaging telescopes
Time evolution of the chiral phase transition during a spherical expansion
We examine the non-equilibrium time evolution of the hadronic plasma produced
in a relativistic heavy ion collision, assuming a spherical expansion into the
vacuum. We study the linear sigma model to leading order in a large-
expansion. Starting at a temperature above the phase transition, the system
expands and cools, finally settling into the broken symmetry vacuum state. We
consider the proper time evolution of the effective pion mass, the order
parameter , and the particle number distribution. We
examine several different initial conditions and look for instabilities
(exponentially growing long wavelength modes) which can lead to the formation
of disoriented chiral condensates (DCCs). We find that instabilities exist for
proper times which are less than 3 fm/c. We also show that an experimental
signature of domain growth is an increase in the low momentum spectrum of
outgoing pions when compared to an expansion in thermal equilibrium. In
comparison to particle production during a longitudinal expansion, we find that
in a spherical expansion the system reaches the ``out'' regime much faster and
more particles get produced. However the size of the unstable region, which is
related to the domain size of DCCs, is not enhanced.Comment: REVTex, 20 pages, 8 postscript figures embedded with eps
Equilibrium and nonequilibrium properties associated with the chiral phase transition at finite density in the Gross-Neveu Model
We study the dynamics of the chiral phase transition at finite density in the
Gross-Neveu (GN) model in the leading order in large-N approximation. The phase
structure of the GN model in this approximation has the property that there is
a tricritical point at a fixed temperature and chemical potential separating
regions where the chiral transition is first order from that where it is second
order. We consider evolutions starting in local thermal and chemical
equilibrium in the massless unbroken phase for conditions pertaining to
traversing a first or second order phase transition. We assume boost invariant
kinematics and determine the evolution of the order parameter , the
energy density and pressure as well as the effective temperature, chemical
potential and interpolating number densities as a function of the proper time
. We find that before the phase transition, the system behaves as if it
were an ideal fluid in local thermal equilibrium with equation of state
. After the phase transition, the system quickly reaches its true
broken symmetry vacuum value for the fermion mass and for the energy density.
The single particle distribution functions for Fermions and anti-Fermions go
far out of equilibrium as soon as the plasma traverses the chiral phase
transition. We have also determined the spatial dependence of the "pion"
Green's function as a function of the proper time.Comment: 39 pages, 23 figure
Gauge Fields Out-Of-Equilibrium: A Gauge Invariant Formulation and the Coulomb Gauge
We study the abelian Higgs model out-of-equilibrium in two different
approaches, a gauge invariant formulation, proposed by Boyanovsky et al.
\cite{Boyanovsky:1996dc} and in the Coulomb gauge. We show that both approaches
become equivalent in a consistent one loop approximation. Furthermore, we carry
out a proper renormalization for the model in order to prepare the equations
for a numerical implementation. The additional degrees of freedom, which arise
in gauge theories, influence the behavior of the system dramatically. A
comparison with results in the 't Hooft-Feynman background gauge found by us
recently, shows very good agreement.Comment: 32 pages, 8 figure
An O(N) symmetric extension of the Sine-Gordon Equation
We discuss an O(N) exension of the Sine-Gordon (S-G)equation which allows us
to perform an expansion around the leading order in large-N result using
Path-Integral methods. In leading order we show our methods agree with the
results of a variational calculation at large-N. We discuss the striking
differences for a non-polynomial interaction between the form for the effective
potential in the Gaussian approximation that one obtains at large-N when
compared to the N=1 case. This is in contrast to the case when the classical
potential is a polynomial in the field and no such drastic differences occur.
We find for our large-N extension of the Sine-Gordon model that the unbroken
ground state is unstable as one increases the coupling constant (as it is for
the original S-G equation) and we determine the stability criteria.Comment: 21 pages, Latex (Revtex4) v3:minor grammatical changes and addition
Analytic and Numerical Study of Preheating Dynamics
We analyze the phenomenon of preheating,i.e. explosive particle production
due to parametric amplification of quantum fluctuations in the unbroken case,
or spinodal instabilities in the broken phase, using the Minkowski space
vector model in the large limit to study the non-perturbative issues
involved. We give analytic results for weak couplings and times short compared
to the time at which the fluctuations become of the same order as the tree
level,as well as numerical results including the full backreaction.In the case
where the symmetry is unbroken, the analytic results agree spectacularly well
with the numerical ones in their common domain of validity. In the broken
symmetry case, slow roll initial conditions from the unstable minimum at the
origin, give rise to a new and unexpected phenomenon: the dynamical relaxation
of the vacuum energy.That is, particles are abundantly produced at the expense
of the quantum vacuum energy while the zero mode comes back to almost its
initial value.In both cases we obtain analytically and numerically the equation
of state which turns to be written in terms of an effective polytropic index
that interpolates between vacuum and radiation-like domination. We find that
simplified analysis based on harmonic behavior of the zero mode, giving rise to
a Mathieu equation forthe non-zero modes miss important physics. Furthermore,
analysis that do not include the full backreaction do not conserve energy,
resulting in unbound particle production. Our results do not support the recent
claim of symmetry restoration by non-equilibrium fluctuations.Finally estimates
of the reheating temperature are given,as well as a discussion of the
inconsistency of a kinetic approach to thermalization when a non-perturbatively
large number of particles is created.Comment: Latex file, 52 pages and 24 figures in .ps files. Minor changes. To
appear in Physical Review D, 15 December 199
Chaos in Time Dependent Variational Approximations to Quantum Dynamics
Dynamical chaos has recently been shown to exist in the Gaussian
approximation in quantum mechanics and in the self-consistent mean field
approach to studying the dynamics of quantum fields. In this study, we first
show that any variational approximation to the dynamics of a quantum system
based on the Dirac action principle leads to a classical Hamiltonian dynamics
for the variational parameters. Since this Hamiltonian is generically nonlinear
and nonintegrable, the dynamics thus generated can be chaotic, in distinction
to the exact quantum evolution. We then restrict attention to a system of two
biquadratically coupled quantum oscillators and study two variational schemes,
the leading order large N (four canonical variables) and Hartree (six canonical
variables) approximations. The chaos seen in the approximate dynamics is an
artifact of the approximations: this is demonstrated by the fact that its onset
occurs on the same characteristic time scale as the breakdown of the
approximations when compared to numerical solutions of the time-dependent
Schrodinger equation.Comment: 10 pages (12 figures), RevTeX (plus macro), uses epsf, minor typos
correcte
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