1,261 research outputs found
Simulating nonequilibrium quantum fields with stochastic quantization techniques
We present lattice simulations of nonequilibrium quantum fields in
Minkowskian space-time. Starting from a non-thermal initial state, the
real-time quantum ensemble in 3+1 dimensions is constructed by a stochastic
process in an additional (5th) ``Langevin-time''. For the example of a
self-interacting scalar field we show how to resolve apparent unstable Langevin
dynamics, and compare our quantum results with those obtained in classical
field theory. Such a direct simulation method is crucial for our understanding
of collision experiments of heavy nuclei or other nonequilibrium phenomena in
strongly coupled quantum many-body systems.Comment: 4 pages, 4 figures, PRL version, minor change
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
Asymptotically free four-fermion interactions and electroweak symmetry breaking
We investigate the fermions of the standard model without a Higgs scalar.
Instead, we consider a non-local four-quark interaction in the tensor channel
which is characterized by a single dimensionless coupling . Quantization
leads to a consistent perturbative expansion for small . The running of
is asymptotically free and therefore induces a non-perturbative scale
, in analogy to the strong interactions. We argue that
spontaneous electroweak symmetry breaking is triggered at a scale where
grows large and find the top quark mass of the order of . We also
present a first estimate of the effective Yukawa coupling of a composite Higgs
scalar to the top quark, as well as the associated mass ratio between the top
quark and the W boson.Comment: 24 page
A unified picture of ferromagnetism, quasi-long range order and criticality in random field models
By applying the recently developed nonperturbative functional renormalization
group (FRG) approach, we study the interplay between ferromagnetism, quasi-long
range order (QLRO) and criticality in the -dimensional random field O(N)
model in the whole (, ) diagram. Even though the "dimensional reduction"
property breaks down below some critical line, the topology of the phase
diagram is found similar to that of the pure O(N) model, with however no
equivalent of the Kosterlitz-Thouless transition. In addition, we obtain that
QLRO, namely a topologically ordered "Bragg glass" phase, is absent in the
3--dimensional random field XY model. The nonperturbative results are
supplemented by a perturbative FRG analysis to two loops around .Comment: 4 pages, 4 figure
Lattice simulations of real-time quantum fields
We investigate lattice simulations of scalar and nonabelian gauge fields in
Minkowski space-time. For SU(2) gauge-theory expectation values of link
variables in 3+1 dimensions are constructed by a stochastic process in an
additional (5th) ``Langevin-time''. A sufficiently small Langevin step size and
the use of a tilted real-time contour leads to converging results in general.
All fixed point solutions are shown to fulfil the infinite hierarchy of
Dyson-Schwinger identities, however, they are not unique without further
constraints. For the nonabelian gauge theory the thermal equilibrium fixed
point is only approached at intermediate Langevin-times. It becomes more stable
if the complex time path is deformed towards Euclidean space-time. We analyze
this behavior further using the real-time evolution of a quantum anharmonic
oscillator, which is alternatively solved by diagonalizing its Hamiltonian.
Without further optimization stochastic quantization can give accurate
descriptions if the real-time extend of the lattice is small on the scale of
the inverse temperature.Comment: 36 pages, 15 figures, Late
Linking the Quark Meson Model with QCD at High Temperature
We model the transition of a system of quarks and gluons at high energies to
a system of quarks and mesons at low energies in a consistent renormalization
group approach. Flow equations interpolate between the physics of the
high-temperature degrees of freedom and the low-temperature dynamics at a scale
of 1 GeV. We also discuss the dependence of the equation of state on baryon
density and compare our results with recent lattice gauge simulations.Comment: 11 pages, 4 figures additional discussion of the second order phase
transitio
Bosonic effective action for interacting fermions
We compare different versions of a bosonic description for systems of
interacting fermions, with particular emphasis on the free energy functional.
The bosonic effective action makes the issue of symmetries particularly
transparent and we present for the Hubbard model an exact mapping between
repulsive and attractive interactions. A systematic expansion for the bosonic
effective action starts with a solution to the lowest order Schwinger-Dyson or
gap equation. We propose a two particle irreducible formulation of an exact
functional renormalization group equation for computations beyond leading
order. On this basis we suggest a renormalized gap equation. This approach is
compared with functional renormalization in a partially bosonized setting.Comment: new sections on exact mapping between attractive and repulsive
Hubbard model and relation between two-particle-irreducible formalism, 32
pages,1 figure,LaTe
Numerical investigation of friction in inflaton equations of motion
The equation of motion for the expectation value of a scalar quantum field
does not have the local form that is commonly assumed in studies of
inflationary cosmology. We have recently argued that the true, temporally
non-local equation of motion does not possess a time-derivative expansion and
that the conversion of inflaton energy into particles is not, in principle,
described by the friction term estimated from linear response theory. Here, we
use numerical methods to investigate whether this obstacle to deriving a local
equation of motion is purely formal, or of some quantitative importance. Using
a simple scalar-field model, we find that, although the non-equilibrium
evolution can exhibit significant damping, this damping is not well described
by the local equation of motion obtained from linear response theory. It is
possible that linear response theory does not apply to the situation we study
only because thermalization turns out to be slow, but we argue that that the
large discrepancies we observe indicate a failure of the local approximation at
a more fundamental level.Comment: 13 pages, 7 figure
Bottom-up isotropization in classical-statistical lattice gauge theory
We compute nonequilibrium dynamics for classical-statistical SU(2) pure gauge
theory on a lattice. We consider anisotropic initial conditions with high
occupation numbers in the transverse plane on a characteristic scale ~ Q_s.
This is used to investigate the very early stages of the thermalization process
in the context of heavy-ion collisions. We find Weibel or "primary"
instabilities with growth rates similar to those obtained from previous
treatments employing anisotropic distributions of hard modes (particles) in the
weak coupling limit. We observe "secondary" growth rates for higher-momentum
modes reaching substantially larger values and we analyse them in terms of
resummed loop diagrams beyond the hard-loop approximation. We find that a
coarse grained pressure isotropizes "bottom-up" with a characteristic inverse
rate of gamma^{-1} ~ 1 - 2 fm/c for coarse graining momentum scales of p < 1
GeV choosing an initial energy density for RHIC of epsilon = 30 GeV/fm^3. The
nonequilibrium spatial Wilson loop is found to exhibit an area law and to
become isotropic on a similar time scale.Comment: 22 pages, 12 figures. Phys. Rev. D version, appendix on insensitivity
to volume and cutoff effects adde
Functional renormalization for trion formation in ultracold fermion gases
The energy spectrum for three species of identical fermionic atoms close to a
Feshbach resonance is computed by use of a nonperturbative flow equation.
Already a simple truncation shows that for large scattering length the
lowest energy state is a "trion" (or trimer) bound state of three atoms. At the
location of the resonance, for , we find an infinite set of
trimer bound states, with exponentially decreasing binding energy. This feature
was pointed out by Efimov. It arises from limit cycle scaling, which also leads
to a periodic dependence of the three body scattering coupling on .
Extending our findings by continuity to nonzero density and temperature we find
that a "trion phase" separates a BEC and a BCS phase, with interesting quantum
phase transitions for T=0.Comment: 9 pages, 4 figures, minor changes, reference adde
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