882 research outputs found
Symmetric path integrals for stochastic equations with multiplicative noise
A Langevin equation with multiplicative noise is an equation schematically of
the form dq/dt = - F(q) + e(q) xi, where e(q) xi is Gaussian white noise whose
amplitude e(q) depends on q itself. I show how to convert such equations into
path integrals. The definition of the path integral depends crucially on the
convention used for discretizing time, and I specifically derive the correct
path integral when the convention used is the natural, time-symmetric one that
time derivatives are (q_t - q_{t-\Delta t}) / \Delta t and coordinates are (q_t
+ q_{t-\Delta t}) / 2. [This is the convention that permits standard
manipulations of calculus on the action, like naive integration by parts.] It
has sometimes been assumed in the literature that a Stratanovich Langevin
equation can be quickly converted to a path integral by treating time as
continuous but using the rule \theta(t=0) = 1/2. I show that this prescription
fails when the amplitude e(q) is q-dependent.Comment: 8 page
Nonequilibrium dynamics in the O(N) model to next-to-next-to-leading order in the 1/N expansion
Nonequilibrium dynamics in quantum field theory has been studied extensively
using truncations of the 2PI effective action. Both 1/N and loop expansions
beyond leading order show remarkable improvement when compared to mean-field
approximations. However, in truncations used so far, only the leading-order
parts of the self energy responsible for memory loss, damping and equilibration
are included, which makes it difficult to discuss convergence systematically.
For that reason we derive the real and causal evolution equations for an O(N)
model to next-to-next-to-leading order in the 2PI-1/N expansion. Due to the
appearance of internal vertices the resulting equations appear intractable for
a full-fledged 3+1 dimensional field theory. Instead, we solve the closely
related three-loop approximation in the auxiliary-field formalism numerically
in 0+1 dimensions (quantum mechanics) and compare to previous approximations
and the exact numerical solution of the Schroedinger equation.Comment: 29 pages, minor changes, references added; to appear in PR
Higher-Order Corrections to Instantons
The energy levels of the double-well potential receive, beyond perturbation
theory, contributions which are non-analytic in the coupling strength; these
are related to instanton effects. For example, the separation between the
energies of odd- and even-parity states is given at leading order by the
one-instanton contribution. However to determine the energies more accurately
multi-instanton configurations have also to be taken into account. We
investigate here the two-instanton contributions. First we calculate
analytically higher-order corrections to multi-instanton effects. We then
verify that the difference betweeen numerically determined energy eigenvalues,
and the generalized Borel sum of the perturbation series can be described to
very high accuracy by two-instanton contributions. We also calculate
higher-order corrections to the leading factorial growth of the perturbative
coefficients and show that these are consistent with analytic results for the
two-instanton effect and with exact data for the first 200 perturbative
coefficients.Comment: 7 pages, LaTe
Non-universal Critical Quantities from Variational Perturbation Theory and Their Application to the BEC Temperature Shift
For an O(N) symmetric scalar field theory with Euclidean action integral d^3x
[1/2 |nabla phi|^2 + 1/2 r phi^2 + 1/4! u phi^4], where phi = (phi_1,...,phi_N)
is a vector of N real field components, variational perturbation theory through
seven loops is employed for N = 0,1,2,3,4 to compute the renormalized value of
r/(N+2)u^2 at the phase transition. Its exact large-N limit is determined as
well. We also extend an earlier computation of the interaction-induced shift
Delta/Nu for N = 1,2,4 to N = 0,3. For N = 2, the results for the two
quantities are used to compute the second-order shift of the condensation
temperature of a dilute Bose gas, both in the homogenous case and for the wide
limit of a harmonic trap. Our results are in agreement with earlier Monte Carlo
simulations for N = 1,2,4. The appendix contains previously unpublished
numerical seven-loop data provided to us by B.Nickel.Comment: 19 page
Dominant Reaction Pathways in High Dimensional Systems
This paper is devoted to the development of a theoretical and computational
framework to efficiently sample the statistically significant thermally
activated reaction pathways, in multi-dimensional systems obeying Langevin
dynamics. We show how to obtain the set of most probable reaction pathways and
compute the corrections due to quadratic thermal fluctuations around such
trajectories. We discuss how to obtain predictions for the evolution of
arbitrary observables and how to generate conformations which are
representative of the transition state ensemble. We present an illustrative
implementation of our method by studying the diffusion of a point particle in a
2-dimensional funneled external potential.Comment: 18 pages, 7 figures. Improvement in the text and in the figures.
Version submitted for publicatio
Power law in a gauge-invariant cut-off regularisation
We study one-loop quantum corrections of a compactified Abelian 5d gauge
field theory. We use a cut-off regularisation procedure which respects the
symmetries of the model, i.e. gauge invariance, exhibits the expected
power-like divergences and therefore allows the derivation of power-law
behavior of the effective 4d gauge coupling in a coherent manner.Comment: 5 pages, 1 figure, 5 graphs, few references added, to appear in
Phys.Rev. Rapid Communication
Influence of quark boundary conditions on the pion mass in finite volume
We calculate the mass shift for the pion in a finite volume with
renormalization group (RG) methods in the framework of the quark-mesons model.
In particular, we investigate the importance of the quark effects on the pion
mass. As in lattice gauge theory, the choice of quark boundary conditions has a
noticeable effect on the pion mass shift in small volumes, in addition to the
shift due to pion interactions. We compare our results to chiral perturbation
theory calculations and find differences due to the fact that chiral
perturbation theory only considers pion effects in the finite volume.Comment: 24 pages, 5 figures, RevTex4, published version, discussion of
lattice results extende
Superfluid transitions in bosonic atom-molecule mixtures near Feshbach resonance
We study bosonic atoms near a Feshbach resonance, and predict that in
addition to a standard normal and atomic superfluid phases, this system
generically exhibits a distinct phase of matter: a molecular superfluid, where
molecules are superfluid while atoms are not. We explore zero- and
finite-temperature properties of the molecular superfluid (a bosonic,
strong-coupling analog of a BCS superconductor), and study quantum and
classical phase transitions between the normal, molecular superfluid and atomic
superfluid states.Comment: 4 revtex pages, 3 eps figures; submitted to PR
Thermally-Assisted Current-Driven Domain Wall Motion
Starting from the stochastic Landau-Lifschitz-Gilbert equation, we derive
Langevin equations that describe the nonzero-temperature dynamics of a rigid
domain wall. We derive an expression for the average drift velocity of the
domain wall as a function of the applied current, and find qualitative
agreement with recent magnetic semiconductor experiments. Our model implies
that at any nonzero temperature the average domain-wall velocity initially
varies linearly with current, even in the absence of non-adiabatic spin
torques.Comment: 4 pages, 2 figure
Temperature driven structural phase transition for trapped ions and its experimental detection
A Wigner crystal formed with trapped ion can undergo structural phase
transition, which is determined only by the mechanical conditions on a
classical level. Instead of this classical result, we show that through
consideration of quantum and thermal fluctuation, a structural phase transition
can be solely driven by change of the system's temperature. We determine a
finite-temperature phase diagram for trapped ions using the renormalization
group method and the path integral formalism, and propose an experimental
scheme to observe the predicted temperature-driven structural phase transition,
which is well within the reach of the current ion trap technology.Comment: 4 pages, 5 figure
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