Spinless particle in rapidly fluctuating random magnetic field

Abstract

We study a two-dimensional spinless particle in a disordered gaussian magnetic field with short time fluctuations, by means of the evolution equation for the density matrix $<x^{(1)}|\hat{\rho }(t)|x^{(2)}>$; in this description the two coordinates are associated with the retarded and advanced paths respectively. The static part of the vector potential correlator is assumed to grow with distance with a power $h$; the case $h=0$ corresponds to a $\delta$-correlated magnetic field, and $h=2$ to free massless field. The value $h=2$ separates two different regimes, diffusion and logarithmic growth respectively. When $h<2$ the baricentric coordinate $r=(1/2)(x^{(1)}+x^{(2)})$ diffuses with a coefficient $D_r$ proportional to $x^{-h}$, where $x$ is the relative coordinate: $x=x^{(1)}-x^{(2)}$. As $h>2$ the correlator of the magnetic field is a power of distance with positive exponent; then the coefficient $D_r$ scales as $x^{-2}$. The density matrix is a function of $r$ and $x^2/t$,and its width in $r$ grows for large times proportionally to $log(t/x^2)$.

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References in corpus (1)

• Quantum Disordered Systems with a Direction