270 research outputs found
Locally Optimal Load Balancing
This work studies distributed algorithms for locally optimal load-balancing:
We are given a graph of maximum degree , and each node has up to
units of load. The task is to distribute the load more evenly so that the loads
of adjacent nodes differ by at most .
If the graph is a path (), it is easy to solve the fractional
version of the problem in communication rounds, independently of the
number of nodes. We show that this is tight, and we show that it is possible to
solve also the discrete version of the problem in rounds in paths.
For the general case (), we show that fractional load balancing
can be solved in rounds and discrete load
balancing in rounds for some function , independently of the
number of nodes.Comment: 19 pages, 11 figure
Few-Body States in Fermi-Systems and Condensation Phenomena
Residual interactions in many particle systems lead to strong correlations. A
multitude of spectacular phenomenae in many particle systems are connected to
correlation effects in such systems, e.g. pairing, superconductivity,
superfluidity, Bose-Einstein condensation etc. Here we focus on few-body bound
states in a many-body surrounding.Comment: 10 pages, proceedings 1st Asian-Pacific Few-Body Conference, needs
fbssuppl.sty of Few-Body System
Superconducting properties of the attractive Hubbard model
A self-consistent set of equations for the one-electron self-energy in the
ladder approximation is derived for the attractive Hubbard model in the
superconducting state. The equations provide an extension of a T-matrix
formalism recently used to study the effect of electron correlations on
normal-state properties. An approximation to the set of equations is solved
numerically in the intermediate coupling regime, and the one-particle spectral
functions are found to have four peaks. This feature is traced back to a peak
in the self-energy, which is related to the formation of real-space bound
states. For comparison we extend the moment approach to the superconducting
state and discuss the crossover from the weak (BCS) to the intermediate
coupling regime from the perspective of single-particle spectral densities.Comment: RevTeX format, 8 figures. Accepted for publication in Z.Phys.
Momentum relaxation from the fluid/gravity correspondence
We provide a hydrodynamical description of a holographic theory with broken
translation invariance. We use the fluid/gravity correspondence to
systematically obtain both the constitutive relations for the currents and the
Ward identity for momentum relaxation in a derivative expansion. Beyond leading
order in the strength of momentum relaxation, our results differ from a model
previously proposed by Hartnoll et al. As an application of these techniques we
consider charge and heat transport in the boundary theory. We derive the low
frequency thermoelectric transport coefficients of the holographic theory from
the linearised hydrodynamics.Comment: 19 pages + appendix, v2: references added, typos corrected, v3:
version published in JHE
Correlations and Equilibration in Relativistic Quantum Systems
In this article we study the time evolution of an interacting field
theoretical system, i.e. \phi^4-field theory in 2+1 space-time dimensions, on
the basis of the Kadanoff-Baym equations for a spatially homogeneous system
including the self-consistent tadpole and sunset self-energies. We find that
equilibration is achieved only by inclusion of the sunset self-energy.
Simultaneously, the time evolution of the scalar particle spectral function is
studied for various initial states. We also compare associated solutions of the
corresponding Boltzmann equation to the full Kadanoff-Baym theory. This
comparison shows that a consistent inclusion of the spectral function has a
significant impact on the equilibration rates only if the width of the spectral
function becomes larger than 1/3 of the particle mass. Furthermore, based on
these findings, the conventional transport of particles in the on-shell
quasiparticle limit is extended to particles of finite life time by means of a
dynamical spectral function A(X,\vec{p},M^2). The off-shell propagation is
implemented in the Hadron-String-Dynamics (HSD) transport code and applied to
the dynamics of nucleus-nucleus collisions.Comment: 20 pages, 7 figures to appear in "Nonequilibrium at short time scales
- Formation of correlations", edited by K. Morawetz, Springer, Berlin (2003),
p16
Quantizing higher-spin gravity in free-field variables
We study the formulation of massless higher-spin gravity on AdS in a
gauge in which the fundamental variables satisfy free field Poisson brackets.
This gauge choice leaves a small portion of the gauge freedom unfixed, which
should be further quotiented out. We show that doing so leads to a bulk version
of the Coulomb gas formalism for CFT's: the generators of the residual
gauge symmetries are the classical limits of screening charges, while the
gauge-invariant observables are classical charges. Quantization in these
variables can be carried out using standard techniques and makes manifest a
remnant of the triality symmetry of . This symmetry can be
used to argue that the theory should be supplemented with additional matter
content which is precisely that of the Prokushkin-Vasiliev theory. As a further
application, we use our formulation to quantize a class of conical surplus
solutions and confirm the conjecture that these are dual to specific degenerate
primaries, to all orders in the large central charge expansion.Comment: 31 pages + appendices. V2: typos corrected, reference adde
Spectral renormalization group theory on networks
Discrete amorphous materials are best described in terms of arbitrary
networks which can be embedded in three dimensional space. Investigating the
thermodynamic equilibrium as well as non-equilibrium behavior of such materials
around second order phase transitions call for special techniques.
We set up a renormalization group scheme by expanding an arbitrary scalar
field living on the nodes of an arbitrary network, in terms of the eigenvectors
of the normalized graph Laplacian. The renormalization transformation involves,
as usual, the integration over the more "rapidly varying" components of the
field, corresponding to eigenvectors with larger eigenvalues, and then
rescaling. The critical exponents depend on the particular graph through the
spectral density of the eigenvalues.Comment: 17 pages, 3 figures, presented at the Continuum Models and Discrete
Systems (CMDS-12), 21-25 Feb 2011, Saha Institute of Nuclear Physics,
Kolkata, Indi
Conjectures on exact solution of three - dimensional (3D) simple orthorhombic Ising lattices
We report the conjectures on the three-dimensional (3D) Ising model on simple
orthorhombic lattices, together with the details of calculations for a putative
exact solution. Two conjectures, an additional rotation in the fourth curled-up
dimension and the weight factors on the eigenvectors, are proposed to serve as
a boundary condition to deal with the topologic problem of the 3D Ising model.
The partition function of the 3D simple orthorhombic Ising model is evaluated
by spinor analysis, by employing these conjectures. Based on the validity of
the conjectures, the critical temperature of the simple orthorhombic Ising
lattices could be determined by the relation of KK* = KK' + KK'' + K'K'' or
sinh 2K sinh 2(K' + K'' + K'K''/K) = 1. For a simple cubic Ising lattice, the
critical point is putatively determined to locate exactly at the golden ratio
xc = exp(-2Kc) = (sq(5) - 1)/2, as derived from K* = 3K or sinh 2K sinh 6K = 1.
If the conjectures would be true, the specific heat of the simple orthorhombic
Ising system would show a logarithmic singularity at the critical point of the
phase transition. The spontaneous magnetization and the spin correlation
functions of the simple orthorhombic Ising ferromagnet are derived explicitly.
The putative critical exponents derived explicitly for the simple orthorhombic
Ising lattices are alpha = 0, beta = 3/8, gamma = 5/4, delta = 13/3, eta = 1/8
and nu = 2/3, showing the universality behavior and satisfying the scaling
laws. The cooperative phenomena near the critical point are studied and the
results obtained based on the conjectures are compared with those of the
approximation methods and the experimental findings. The 3D to 2D crossover
phenomenon differs with the 2D to 1D crossover phenomenon and there is a
gradual crossover of the exponents from the 3D values to the 2D ones.Comment: 176 pages, 4 figure
Hysteresis phenomenon in turbulent convection
Coherent large-scale circulations of turbulent thermal convection in air have
been studied experimentally in a rectangular box heated from below and cooled
from above using Particle Image Velocimetry. The hysteresis phenomenon in
turbulent convection was found by varying the temperature difference between
the bottom and the top walls of the chamber (the Rayleigh number was changed
within the range of ). The hysteresis loop comprises the one-cell
and two-cells flow patterns while the aspect ratio is kept constant (). We found that the change of the sign of the degree of the anisotropy of
turbulence was accompanied by the change of the flow pattern. The developed
theory of coherent structures in turbulent convection (Elperin et al. 2002;
2005) is in agreement with the experimental observations. The observed coherent
structures are superimposed on a small-scale turbulent convection. The
redistribution of the turbulent heat flux plays a crucial role in the formation
of coherent large-scale circulations in turbulent convection.Comment: 10 pages, 9 figures, REVTEX4, Experiments in Fluids, 2006, in pres
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