## Bosons in a Random Potential

Lectures at the summer school on "Fundamental
Problems in Statistical Mechanics VIII"
Altenberg, Germany, June 1993).

A.P. Young

Published by Elsevier (1994).
**Abstract**

These lectures discuss a quantum transition at zero temperature
between the Bose-glass and superfluid phase of bosons moving
in a random potential in two-dimensions. This problem illustrates
the methods used to study quantum transitions {\em in general},
and the difficulties
which arise when the system is disordered. This problem should also
describe
the observed superconductor-insulator transition in disordered thin films.
After introducing a suitable model Hamiltonian, the boson Hubbard model,
I discuss the path integral representation of it followed by scaling theory,
including arguments that the conductivity is universal at the critical
point. The last part of the lectures describes Monte Carlo simulations,
which give predictions for universal quantities at the transition.

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