60 research outputs found
Gauge Field Fluctuations and First-Order Phase Transition in Color Superconductivity
We study the gauge field fluctuations in dense quark matter and determine the
temperature of the induced first-order phase transition to the
color-superconducting phase in weak coupling. We find that the local
approximation of the coupling between the gauge potential and the order
parameter, employed in the Ginzburg-Landau theory, has to be modified by
restoring the full momentum dependence of the polarization function of gluons
in the superconducting phase.Comment: 5 pages, 1 figure, Revtex, we have modified our conclusions for the
metallic superconducto
Ward Identities in Non-equilibrium QED
We verify the QED Ward identity for the two- and three -point functions at
non-equilibrium in the HTL limit. We use the Keldysh formalism of real time
finite temperature field theory. We obtain an identity of the same form as the
Ward identity for a set of one loop self-energy and one loop three-point vertex
diagrams which are constructed from HTL effective propagators and vertices.Comment: 19 pages, RevTex, 4 PostScript figures, revised version to be
published in Phys. Rev.
Absence of the London limit for the first-order phase transition to a color superconductor
We study the effects of gauge-field fluctuations on the free energy of a
homogeneous color superconductor in the color-flavor-locked (CFL) phase.
Gluonic fluctuations induce a strong first-order phase transition, in contrast
to electronic superconductors where this transition is weakly first order. The
critical temperature for this transition is larger than the one corresponding
to the diquark pairing instability. The physical reason is that the gluonic
Meissner masses suppress long-wavelength fluctuations as compared to the normal
conducting phase where gluons are massless, which stabilizes the
superconducting phase. In weak coupling, we analytically compute the
temperatures associated with the limits of metastability of the normal and
superconducting phases, as well as the latent heat associated with the
first-order phase transition. We then extrapolate our results to intermediate
densities and numerically evaluate the temperature of the fluctuation-induced
first-order phase transition, as well as the discontinuity of the diquark
condensate at the critical point. We find that the London limit of magnetic
interactions is absent in color superconductivity.Comment: 14 pages, 5 figure
Shear viscosity in theory from an extended ladder resummation
We study shear viscosity in weakly coupled hot theory using the CTP
formalism . We show that the viscosity can be obtained as the integral of a
three-point function. Non-perturbative corrections to the bare one-loop result
can be obtained by solving a decoupled Schwinger-Dyson type integral equation
for this vertex. This integral equation represents the resummation of an
infinite series of ladder diagrams which contribute to the leading order
result. It can be shown that this integral equation has exactly the same form
as the Boltzmann equation. We show that the integral equation for the viscosity
can be reexpressed by writing the vertex as a combination of polarization
tensors. An expression for this polarization tensor can be obtained by solving
another Schwinger-Dyson type integral equation. This procedure results in an
expression for the viscosity that represents a non-perturbative resummation of
contributions to the viscosity which includes certain non-ladder graphs, as
well as the usual ladders. We discuss the motivation for this resummation. We
show that these resummations can also be obtained by writing the viscosity as
an integral equation involving a single four-point function. Finally, we show
that when the viscosity is expressed in terms of a four-point function, it is
possible to further extend the set of graphs included in the resummation by
treating vertex and propagator corrections self-consistently. We discuss the
significance of such a self-consistent resummation and show that the integral
equation contains cancellations between vertex and propagator corrections.Comment: Revtex 40 pages with 29 figures, version to appear in Phys. Rev.
KMS conditions for 4-point Green functions at finite temperature
We study the 4-point function in the Keldysh formalism of the closed time
path formulation of real time finite temperature field theory.
We derive the KMS conditions for these functions and discuss the number of
4-point functions that are independent. We define a set of `physical' functions
which are linear combinations of the usual Keldysh functions. We show that
these functions satisfy simple KMS conditions. In addition, we consider a set
of integral equations which represent a resummation of ladder graphs. We show
that these integral equations decouple when one uses the physical functions
that we have defined. We discuss the generalization of these results to QED.Comment: 17 pages in Revtex with 2 figure
A Hybrid Simulated Annealing Algorithm for Container Loading Problem
This paper presents a hybrid simulated annealing algorithm for container loading problem with boxes of different sizes and single container for loading. A basic heuristic algorithm is introduced to generate feasible solution from a special structure called packing sequence. The hybrid algorithm uses basic heuristic to encode feasible packing solution as packing sequence, and searches in the encoding space to find an approximated optimal solution. The computational experiments on 700 weakly heterogeneous benchmark show that our algorithm outperforms all previous methods in average
The Boltzmann equation for colourless plasmons in hot QCD plasma. Semiclassical approximation
Within the framework of the semiclassical approximation, we derive the
Boltzmann equation describing the dynamics of colorless plasmons in a hot QCD
plasma. The probability of the plasmon-plasmon scattering at the leading order
in the coupling constant is obtained. This probability is gauge-independent at
least in the class of the covariant and temporal gauges. It is noted that the
structure of the scattering kernel possesses important qualitative difference
from the corresponding one in the Abelian plasma, in spite of the fact that we
focused our study on the colorless soft excitations. It is shown that
four-plasmon decay is suppressed by the power of relative to the process of
nonlinear scattering of plasmons by thermal particles at the soft momentum
scale. It is stated that the former process becomes important in going to the
ultrasoft region of the momentum scale.Comment: 41, LaTeX, minor changes, identical to published versio
Out of Equilibrium Thermal Field Theories - Finite Time after Switching on the Interaction - Wigner Transforms of Projected Functions
We study out of equilibrium thermal field theories with switching on the
interaction occurring at finite time using the Wigner transforms (in relative
space-time) of two-point functions.
For two-point functions we define the concept of projected function: it is
zero if any of times refers to the time before switching on the interaction,
otherwise it depends only on the relative coordinates. This definition includes
bare propagators, one-loop self-energies, etc. For the infinite-average-time
limit of the Wigner transforms of projected functions we define the analyticity
assumptions: (1) The function of energy is analytic above (below) the real
axis. (2) The function goes to zero as the absolute value of energy approaches
infinity in the upper (lower) semiplane.
Without use of the gradient expansion, we obtain the convolution product of
projected functions. We sum the Schwinger-Dyson series in closed form. In the
calculation of the Keldysh component (both, resummed and single self-energy
insertion approximation) contributions appear which are not the Wigner
transforms of projected functions, signaling the limitations of the method.
In the Feynman diagrams there is no explicit energy conservation at vertices,
there is an overall energy-smearing factor taking care of the uncertainty
relations.
The relation between the theories with the Keldysh time path and with the
finite time path enables one to rederive the results, such as the cancellation
of pinching, collinear, and infrared singularities, hard thermal loop
resummation, etc.Comment: 23 pages + 1 figure, Latex, corrected version, improved presentation,
version accepted for publication in Phys. Rev.
A clique-based algorithm for constructing feasible timetables
Constructing a feasible solution, where the focus is on “hard ” constraints only, is an important part of solving timetabling problems. For the University Course Timetabling Problem (UCTP), we propose a heuristic algorithm to schedule events to timeslots based on cliques, each representing a set of events that could be scheduled in the same timeslot, which the algorithm constructs. Our algorithm has been tested on a set of well-known instances, and the experimental results show that our algorithm compares favorably with other effective algorithms
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