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Effective Field Theories for Disordered Systems from a Generalized Phase Formulation

✍ Scribed by A.J. van Biljon; F.G. Scholtz

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 113 KB
Volume: 302
Category: Article
ISSN: 0003-4916
DOI: 10.1006/aphy.2002.6311

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✦ Synopsis

We consider a spinless particle moving in a d-dimensional box, subject to periodic boundary conditions, and in the presence of a random potential. Introducing the logarithm of the wave function transforms the time-independent Schrödinger equation into a stochastic differential equation with the random potential acting as the source. Using this as our starting point we write functional integral representations for the disorder averaged density of states, the two point correlator of the absolute value of the wave function, and inverse participation ratios. We also show how a deterministic or random magnetic field can be included in the formalism.

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