Effective field theories for disordered systems from the logarithmic derivative of the wave-function

Details Effective field theories for disordered systems from the logarithmic derivative of the wave-function Effective field theories for disordered systems from the logarithmic derivative of the wave-function

2001-09-07

arxiv.org/abs/cond-mat/0109138v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

21 pages, 3 figures

Scientific paper

We consider a spinless particle moving in a random potential on a d-dimensional torus. Introducing the gradient of the logarithm of the wave-function transforms the time independent Schroedinger 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 as well as the conductivity for a d-dimensional system. We use the well studied one dimensional system with Gaussian disorder to illustrate that these quantities can be computed reliably in the current formalism by using standard approximation techniques. We also indicate the possibility of including magnetic fields.

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