1,735 research outputs found
Renormalized thermodynamics from the 2PI effective action
High-temperature resummed perturbation theory is plagued by poor convergence
properties. The problem appears for theories with bosonic field content such as
QCD, QED or scalar theories. We calculate the pressure as well as other
thermodynamic quantities at high temperature for a scalar one-component field
theory, solving a three-loop 2PI effective action numerically without further
approximations. We present a detailed comparison with the two-loop
approximation. One observes a strongly improved convergence behavior as
compared to perturbative approaches. The renormalization employed in this work
extends previous prescriptions, and is sufficient to determine all counterterms
required for the theory in the symmetric as well as the spontaneously broken
phase.Comment: 20 pages, 7 figures; PRD version, references added, very minor
change
Perturbative and Nonperturbative Kolmogorov Turbulence in a Gluon Plasma
In numerical simulations of nonabelian plasma instabilities in the hard-loop
approximation, a turbulent spectrum has been observed that is characterized by
a phase-space density of particles with exponent , which is larger than expected from relativistic
scatterings. Using the approach of Zakharov, L'vov and Falkovich, we analyse
possible Kolmogorov coefficients for relativistic -particle
processes, which give at most perturbatively for an energy cascade.
We discuss nonperturbative scenarios which lead to larger values. As an extreme
limit we find the result generically in an inherently nonperturbative
effective field theory situation, which coincides with results obtained by
Berges et al.\ in large- scalar field theory. If we instead assume that
scaling behavior is determined by Schwinger-Dyson resummations such that the
different scaling of bare and dressed vertices matters, we find that
intermediate values are possible. We present one simple scenario which would
single out .Comment: published versio
Critical phenomena from the two-particle irreducible 1/N expansion
The 1/N expansion of the two-particle irreducible (2PI) effective action is
employed to compute universal properties at the second-order phase transition
of an O(N)-symmetric N-vector model directly in three dimensions. At
next-to-leading order the approach cures the spurious small-N divergence of the
standard (1PI) 1/N expansion for a computation of the critical anomalous
dimension eta(N), and leads to improved estimates already for moderate values
of N.Comment: 18 pages, 3 figure
Turning a First Order Quantum Phase Transition Continuous by Fluctuations: General Flow Equations and Application to d-Wave Pomeranchuk Instability
We derive renormalization group equations which allow us to treat order
parameter fluctuations near quantum phase transitions in cases where an
expansion in powers of the order parameter is not possible. As a prototypical
application, we analyze the nematic transition driven by a d-wave Pomeranchuk
instability in a two-dimensional electron system. We find that order parameter
fluctuations suppress the first order character of the nematic transition
obtained at low temperatures in mean-field theory, so that a continuous
transition leading to quantum criticality can emerge
Results from the 4PI Effective Action in 2- and 3-dimensions
We consider a symmetric scalar theory with quartic coupling and solve the
equations of motion from the 4PI effective action in 2- and 3-dimensions using
an iterative numerical lattice method. For coupling less than 10 (in
dimensionless units) good convergence is obtained in less than 10 iterations.
We use lattice size up to 16 in 2-dimensions and 10 in 3-dimensions and
demonstrate the convergence of the results with increasing lattice size. The
self-consistent solutions for the 2-point and 4-point functions agree well with
the perturbative ones when the coupling is small and deviate when the coupling
is large.Comment: 14 pages, 11 figures; v5: added numerical calculations in 3D; version
accepted for publication in EPJ
Non-equilibrium dynamics of a Bose-Einstein condensate in an optical lattice
The dynamical evolution of a Bose-Einstein condensate trapped in a
one-dimensional lattice potential is investigated theoretically in the
framework of the Bose-Hubbard model. The emphasis is set on the
far-from-equilibrium evolution in a case where the gas is strongly interacting.
This is realized by an appropriate choice of the parameters in the Hamiltonian,
and by starting with an initial state, where one lattice well contains a
Bose-Einstein condensate while all other wells are empty. Oscillations of the
condensate as well as non-condensate fractions of the gas between the different
sites of the lattice are found to be damped as a consequence of the collisional
interactions between the atoms. Functional integral techniques involving
self-consistently determined mean fields as well as two-point correlation
functions are used to derive the two-particle-irreducible (2PI) effective
action. The action is expanded in inverse powers of the number of field
components N, and the dynamic equations are derived from it to next-to-leading
order in this expansion. This approach reaches considerably beyond the
Hartree-Fock-Bogoliubov mean-field theory, and its results are compared to the
exact quantum dynamics obtained by A.M. Rey et al., Phys. Rev. A 69, 033610
(2004) for small atom numbers.Comment: 9 pages RevTeX, 3 figure
Quantum simulation of lattice gauge theories using Wilson fermions
Quantum simulators have the exciting prospect of giving access to real-time
dynamics of lattice gauge theories, in particular in regimes that are difficult
to compute on classical computers. Future progress towards scalable quantum
simulation of lattice gauge theories, however, hinges crucially on the
efficient use of experimental resources. As we argue in this work, due to the
fundamental non-uniqueness of discretizing the relativistic Dirac Hamiltonian,
the lattice representation of gauge theories allows for an optimization that up
to now has been left unexplored. We exemplify our discussion with lattice
quantum electrodynamics in two-dimensional space-time, where we show that the
formulation through Wilson fermions provides several advantages over the
previously considered staggered fermions. Notably, it enables a strongly
simplified optical lattice setup and it reduces the number of degrees of
freedom required to simulate dynamical gauge fields. Exploiting the optimal
representation, we propose an experiment based on a mixture of ultracold atoms
trapped in a tilted optical lattice. Using numerical benchmark simulations, we
demonstrate that a state-of-the-art quantum simulator may access the Schwinger
mechanism and map out its non-perturbative onset.Comment: 19 pages, 11 figure
Transport coefficients from the 2PI effective action
We show that the lowest nontrivial truncation of the two-particle irreducible
(2PI) effective action correctly determines transport coefficients in a weak
coupling or 1/N expansion at leading (logarithmic) order in several
relativistic field theories. In particular, we consider a single real scalar
field with cubic and quartic interactions in the loop expansion, the O(N) model
in the 2PI-1/N expansion, and QED with a single and many fermion fields.
Therefore, these truncations will provide a correct description, to leading
(logarithmic) order, of the long time behavior of these systems, i.e. the
approach to equilibrium. This supports the promising results obtained for the
dynamics of quantum fields out of equilibrium using 2PI effective action
techniques.Comment: 5 pages, explanation in introduction expanded, summary added; to
appear in PR
Low-energy properties of two-dimensional quantum triangular antiferromagnets: Non-perturbative renormalization group approach
We explore low temperature properties of quantum triangular Heisenberg
antiferromagnets in two dimension in the vicinity of the quantum phase
transition at zero temperature. Using the effective field theory described by
the matrix Ginzburg-Landau-Wilson model and the
non-perturbative renormalization group method, we clarify how quantum and
thermal fluctuations affect long-wavelength behaviors in the parameter region
where the systems exhibit a fluctuation-driven first order transition to a
long-range ordered state. We show that at finite temperatures the crossover
from a quantum theory to a renormalized two-dimensional classical
nonlinear sigma model region appears, and in this crossover region, massless
fluctuation modes with linear dispersion a la spin waves govern low-energy
physics. Our results are in good agreement with the recent experimental
observations for the two-dimensional triangular Heisenberg spin system,
NiGaS.Comment: 14 pages,7 figures, version accepted for publication in Physical
Review
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