2,237 research outputs found
Renormalized effective actions for the O(N) model at next-to-leading order of the 1/N expansion
A fully explicit renormalized quantum action functional is constructed for
the O(N)-model in the auxiliary field formulation at next-to-leading order
(NLO) of the 1/N expansion. Counterterms are consistently and explicitly
derived for arbitrary constant vacuum expectation value of the scalar and
auxiliary fields. The renormalized NLO pion propagator is exact at this order
and satisfies Goldstone's theorem. Elimination of the auxiliary field sector at
the level of the functional provides with order N^0 accuracy the renormalized
effective action of the model in terms of the original variables. Alternative
elimination of the pion and sigma propagators provides the renormalized NLO
effective potential for the expectation values of the N-vector and of the
auxiliary field with the same accuracy.Comment: RevTeX4, 19 pages, 3 figures. Version published Phys. Rev.
Classical Physics and Quantum Loops
The standard picture of the loop expansion associates a factor of h-bar with
each loop, suggesting that the tree diagrams are to be associated with
classical physics, while loop effects are quantum mechanical in nature. We
discuss examples wherein classical effects arise from loop contributions and
display the relationship between the classical terms and the long range effects
of massless particles.Comment: 15 pages, 3 figure
Local Approximations for Effective Scalar Field Equations of Motion
Fluctuation and dissipation dynamics is examined at all temperature ranges
for the general case of a background time evolving scalar field coupled to
heavy intermediate quantum fields which in turn are coupled to light quantum
fields. The evolution of the background field induces particle production from
the light fields through the action of the intermediate catalyzing heavy
fields. Such field configurations are generically present in most particle
physics models, including Grand Unified and Supersymmetry theories, with
application of this mechanism possible in inflation, heavy ion collision and
phase transition dynamics. The effective evolution equation for the background
field is obtained and a fluctuation-dissipation theorem is derived for this
system. The effective evolution in general is nonlocal in time. Appropriate
conditions are found for when these time nonlocal effects can be approximated
by local terms. Here careful distinction is made between a local expansion and
the special case of a derivative expansion to all orders, which requires
analytic behavior of the evolution equation in Fourier space.Comment: 14 pages, 2 figures. Replaced with published version. Some extra
typos correcte
Zurek-Kibble Mechanism for the Spontaneous Vortex Formation in Josephson Tunnel Junctions: New Theory and Experiment
New scaling behavior has been both predicted and observed in the spontaneous
production of fluxons in quenched annular Josephson tunnel
junctions as a function of the quench time, . The probability
to trap a single defect during the N-S phase transition clearly follows an
allometric dependence on with a scaling exponent , as
predicted from the Zurek-Kibble mechanism for {\it realistic} JTJs formed by
strongly coupled superconductors. This definitive experiment replaces one
reported by us earlier, in which an idealised model was used that predicted
, commensurate with the then much poorer data. Our experiment
remains the only condensed matter experiment to date to have measured a scaling
exponent with any reliability.Comment: Four pages, one figur
The packing of granular polymer chains
Rigid particles pack into structures, such as sand dunes on the beach, whose
overall stability is determined by the average number of contacts between
particles. However, when packing spatially extended objects with flexible
shapes, additional concepts must be invoked to understand the stability of the
resulting structure. Here we study the disordered packing of chains constructed
out of flexibly-connected hard spheres. Using X-ray tomography, we find long
chains pack into a low-density structure whose mechanical rigidity is mainly
provided by the backbone. On compaction, randomly-oriented, semi-rigid loops
form along the chain, and the packing of chains can be understood as the
jamming of these elements. Finally we uncover close similarities between the
packing of chains and the glass transition in polymers.Comment: 11 pages, 4 figure
Optimized perturbation theory for charged scalar fields at finite temperature and in an external magnetic field
Symmetry restoration in a theory of a self-interacting charged scalar field
at finite temperature and in the presence of an external magnetic field is
examined. The effective potential is evaluated nonperturbatively in the context
of the optimized perturbation theory method. It is explicitly shown that in all
ranges of the magnetic field, from weak to large fields, the phase transition
is second order and that the critical temperature increases with the magnetic
field. In addition, we present an efficient way to deal with the sum over the
Landau levels, which is of interest especially in the case of working with weak
magnetic fields.Comment: 18 pages, 7 eps figures. References added and some small improvements
to the tex
Exactly solvable model of the 2D electrical double layer
We consider equilibrium statistical mechanics of a simplified model for the
ideal conductor electrode in an interface contact with a classical
semi-infinite electrolyte, modeled by the two-dimensional Coulomb gas of
pointlike unit charges in the stability-against-collapse regime of
reduced inverse temperatures . If there is a potential difference
between the bulk interior of the electrolyte and the grounded interface, the
electrolyte region close to the interface (known as the electrical double
layer) carries some nonzero surface charge density. The model is mappable onto
an integrable semi-infinite sine-Gordon theory with Dirichlet boundary
conditions. The exact form-factor and boundary state information gained from
the mapping provide asymptotic forms of the charge and number density profiles
of electrolyte particles at large distances from the interface. The result for
the asymptotic behavior of the induced electric potential, related to the
charge density via the Poisson equation, confirms the validity of the concept
of renormalized charge and the corresponding saturation hypothesis. It is
documented on the non-perturbative result for the asymptotic density profile at
a strictly nonzero that the Debye-H\"uckel limit is a
delicate issue.Comment: 14 page
More on Gribov copies and propagators in Landau-gauge Yang-Mills theory
Fixing a gauge in the non-perturbative domain of Yang-Mills theory is a
non-trivial problem due to the presence of Gribov copies. In particular, there
are different gauges in the non-perturbative regime which all correspond to the
same definition of a gauge in the perturbative domain. Gauge-dependent
correlation functions may differ in these gauges. Two such gauges are the
minimal and absolute Landau gauge, both corresponding to the perturbative
Landau gauge. These, and their numerical implementation, are described and
presented in detail. Other choices will also be discussed.
This investigation is performed, using numerical lattice gauge theory
calculations, by comparing the propagators of gluons and ghosts for the minimal
Landau gauge and the absolute Landau gauge in SU(2) Yang-Mills theory. It is
found that the propagators are different in the far infrared and even at energy
scales of the order of half a GeV. In particular, also the finite-volume
effects are modified. This is observed in two and three dimensions. Some
remarks on the four-dimensional case are provided as well.Comment: 23 pages, 16 figures, 6 tables; various changes throughout most of
the paper; extended discussion on different possibilities to define the
Landau gauge and connection to existing scenarios; in v3: Minor changes,
error in eq. (3) & (4) corrected, version to appear in PR
New Experiments for Spontaneous Vortex Formation in Josephson Tunnel Junctions
It has been argued by Zurek and Kibble that the likelihood of producing
defects in a continuous phase transition depends in a characteristic way on the
quench rate. In this paper we discuss an improved experiment for measuring the
Zurek-Kibble scaling exponent for the production of fluxons in
annular symmetric Josephson Tunnel Junctions. We find .
Further, we report accurate measurements of the junction gap voltage
temperature dependence which allow for precise monitoring of the fast
temperature variations during the quench.Comment: 12 pages, 5 figures, submitted to Phys. Rev.
Quantum Extremism: Effective Potential and Extremal Paths
The reality and convexity of the effective potential in quantum field
theories has been studied extensively in the context of Euclidean space-time.
It has been shown that canonical and path-integral approaches may yield
different results, thus resolving the `convexity problem'. We discuss the
transferral of these treatments to Minkowskian space-time, which also
necessitates a careful discussion of precisely which field configurations give
the dominant contributions to the path integral. In particular, we study the
effective potential for the N=1 linear sigma model.Comment: 11 pages, 4 figure
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