1,304 research outputs found
Complete Wiener-Hopf Solution of the X-Ray Edge Problem
We present a complete solution of the soft x-ray edge problem within a
field-theoretic approach based on the Wiener-Hopf infinite-time technique. We
derive for the first time within this approach critical asymptotics of all the
relevant quantities for the x-ray problem as well as their nonuniversal
prefactors. Thereby we obtain the most complete field-theoretic solution of the
problem with a number of new experimentally relevant results. We make thorough
comparison of the proposed Wiener-Hopf technique with other approaches based on
finite-time methods. It is proven that the Fredholm, finite-time solution
converges smoothly to the Wiener-Hopf one and that the latter is stable with
respect to perturbations in the long-time limit. Further on we disclose a wide
interval of intermediate times showing quasicritical behavior deviating from
the Wiener-Hopf one. The quasicritical behavior of the core-hole Green function
is derived exactly from the Wiener-Hopf solution and the quasicritical exponent
is shown to match the result of Nozi\`eres and De Dominicis. The reasons for
the quasicritical behavior and the way of a crossover to the infinite-time
solution are expounded and the physical relevance of the Nozi\`eres and De
Dominicis as well as of the Winer-Hopf results are discussed.Comment: 19 pages, RevTex, no figure
Two-particle renormalizations in many-fermion perturbation theory: Importance of the Ward identity
We analyze two-particle renormalizations within many-fermion perturbation
expansion. We show that present diagrammatic theories suffer from lack of a
direct diagrammatic control over the physical two-particle functions. To
rectify this we introduce and prove a Ward identity enabling an explicit
construction of the self-energy from a given two-particle irreducible vertex.
Approximations constructed in this way are causal, obey conservation laws and
offer an explicit diagrammatic control of singularities in dynamical
two-particle functions.Comment: REVTeX4, 4 pages, 2 EPS figure
Replica trick with real replicas: A way to build in thermodynamic homogeneity
We use real replicas to investigate stability of thermodynamic homogeneity of
the free energy of the Sherrington-Kirkpatrick (SK) model of spin glasses.
Within the replica trick with the replica symmetric ansatz we show that the
averaged free energy at low temperatures is not thermodynamically homogeneous.
The demand of minimization of the inhomogeneity of thermodynamic potentials
leads in a natural way to the hierarchical solution of the Parisi type.
Conditions for the global thermodynamic homogeneity are derived and evaluated
for the SK and -spin infinite range models.Comment: 6 pages, presented at SPDSA2004 Hayama (Japan), to appear in Progr.
Theor. Phy
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