Electron self-trapping at quantum and classical critical points

Details Electron self-trapping at quantum and classical critical points Electron self-trapping at quantum and classical critical points

2006-02-21

arxiv.org/abs/cond-mat/0602500v1

Annals of Physics, Vol 321, No 8 pp 1762-1789 (2006)

Physics

Condensed Matter

Statistical Mechanics

45 pages, 1 eps figure, elsart, submitted to Annals of Physics

Scientific paper

10.1016/j.aop.2006.02.012

Using Feynman path integral technique estimations of the ground state energy have been found for a conduction electron interacting with order parameter fluctuations near quantum critical points. In some cases only \textit{singular} perturbation theory in the coupling constant emerges for the electron ground state energy. It is shown that an autolocalized state (quantum fluctuon) can be formed and its characteristics have been calculated depending on critical exponents for both weak and strong coupling regimes. The concept of fluctuon is considered also for the classical critical point (at finite temperatures) and the difference between quantum and classical cases has been investigated. It is shown that, whereas the quantum fluctuon energy is connected with a true boundary of the energy spectrum, for classical fluctuon it is just a saddle-point solution for the chemical potential in the exponential density of states fluctuation tail.

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