7,922 research outputs found
Hawking from Catalan
The Virasoro algebra determines all `graviton' matrix elements in
AdS/CFT. We study the explicit exchange of any number of Virasoro
gravitons between heavy and light CFT operators at large central charge.
These graviton exchanges can be written in terms of new on-shell tree diagrams,
organized in a perturbative expansion in , the heavy operator dimension
divided by the central charge. The Virasoro vacuum conformal block, which is
the sum of all the tree diagrams, obeys a differential recursion relation
generalizing that of the Catalan numbers. We use this recursion relation to sum
the on-shell diagrams to all orders, computing the Virasoro vacuum block.
Extrapolating to large determines the Hawking temperature of a BTZ
black hole in dual AdS theories.Comment: 19+8 pages, 5 figure
Chaotic Field Theory - a Sketch
Spatio-temporally chaotic dynamics of a classical field can be described by
means of an infinite hierarchy of its unstable spatio-temporally periodic
solutions. The periodic orbit theory yields the global averages characterizing
the chaotic dynamics, as well as the starting semiclassical approximation to
the quantum theory. New methods for computing corrections to the semiclassical
approximation are developed; in particular, a nonlinear field transformation
yields the perturbative corrections in a form more compact than the Feynman
diagram expansions.Comment: 22 pp, 24 figs, uses elsart.cl
Self-Consistent Approximations to Non-Equilibrium Many-Body Theory
Within the non-equilibrium Green's function technique on the real time
contour, the Phi-functional method of Baym is reviewed and generalized to
arbitrary non-equilibrium many-particle systems. The scheme may be closed at
any desired order in the number of loops or vertices of the generating
functional. It defines effective theories, which provide a closed set of
coupled classical field and Dyson equations, which are self-consistent,
conserving and thermodynamically consistent. The approach permits to include
unstable particles and therefore unifies the description of resonances with all
other particles, which obtain a mass width by collisions, decays or creation
processes in dense matter. The inclusion of classical fields enables the
treatment of soft modes and phase instabilities. The method can be taken as a
starting point for adequate and consistent quantum improvements of the
in-medium rates in transport theories.Comment: 31 pages, Latex elsart-styl
Expansion of the effective action around non-Gaussian theories
This paper derives the Feynman rules for the diagrammatic perturbation
expansion of the effective action around an arbitrary solvable problem. The
perturbation expansion around a Gaussian theory is well known and composed of
one-line irreducible diagrams only. For the expansions around an arbitrary,
non-Gaussian problem, we show that a more general class of irreducible diagrams
remains in addition to a second set of diagrams that has no analogue in the
Gaussian case. The effective action is central to field theory, in particular
to the study of phase transitions, symmetry breaking, effective equations of
motion, and renormalization. We exemplify the method on the Ising model, where
the effective action amounts to the Gibbs free energy, recovering the
Thouless-Anderson-Palmer mean-field theory in a fully diagrammatic derivation.
Higher order corrections follow with only minimal effort compared to existing
techniques. Our results show further that the Plefka expansion and the
high-temperature expansion are special cases of the general formalism presented
here.Comment: 37 pages, published versio
Loschmidt Echo and Lyapunov Exponent in a Quantum Disordered System
We investigate the sensitivity of a disordered system with diffractive
scatterers to a weak external perturbation. Specifically, we calculate the
fidelity M(t) (also called the Loschmidt echo) characterizing a return
probability after a propagation for a time followed by a backward
propagation governed by a slightly perturbed Hamiltonian. For short-range
scatterers we perform a diagrammatic calculation showing that the fidelity
decays first exponentially according to the golden rule, and then follows a
power law governed by the diffusive dynamics. For long-range disorder (when the
diffractive scattering is of small-angle character) an intermediate regime
emerges where the diagrammatics is not applicable. Using the path integral
technique, we derive a kinetic equation and show that M(t) decays exponentially
with a rate governed by the classical Lyapunov exponent.Comment: 9 pages, 7 figure
Semiclassical Approach to Orbital Magnetism of Interacting Diffusive Quantum Systems
We study interaction effects on the orbital magnetism of diffusive mesoscopic
quantum systems. By combining many-body perturbation theory with semiclassical
techniques, we show that the interaction contribution to the ensemble averaged
quantum thermodynamic potential can be reduced to an essentially classical
operator. We compute the magnetic response of disordered rings and dots for
diffusive classical dynamics. Our semiclassical approach reproduces the results
of previous diagrammatic quantum calculations.Comment: 8 pages, revtex, includes 1 postscript fi
A Renormalization-Group approach to the Coulomb Gap
The free energy of the Coulomb Gap problem is expanded as a set of Feynman
diagrams, using the standard diagrammatic methods of perturbation theory. The
gap in the one-particle density of states due to long-ranged interactions
corresponds to a renormalization of the two-point vertex function. By
collecting the leading order logarithmic corrections we have derived the
standard result for the density of states in the critical dimension, d=1. This
method, which is shown to be identical to the approach of Thouless, Anderson
and Palmer to spin glasses, allows us to derive the strong-disorder behaviour
of the density of states. The use of the renormalization group allows this
derivation to be extended to all disorders, and the use of an epsilon-expansion
allows the method to be extended to d=2 and d=3. We speculate that the
renormalization group equations can also be derived diagrammatically, allowing
a simple derivation of the crossover behaviour observed in the case of weak
disorder.Comment: 16 pages, LaTeX. Diagrams available on request from
[email protected]. Changes to figure 4 and second half of section
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