Quantum fluctuations and glassy behavior: The case of a quantum particle in a random potential

In this paper we expand our previous investigation of a quantum particle subject to the action of a random potential plus a fixed harmonic potential at a finite temperature T. In the classical limit the system reduces to a well-known ‘‘toy’’ model for an interface in a random medium. It also applies to a single quantum particle such as an electron subject to random interactions, where the harmonic potential can be tuned to mimic the effect of a finite box. Using the variational approximation, or alternatively, the limit of large spatial dimensions, together with the use of the replica method, we are able to solve the model and obtain its phase diagram in the T-(ħ²/m) plane, where m is the particle’s mass. The phase diagram is similar to that of a quantum spin glass in a transverse field, where the variable ħ²/m plays the role of the transverse field. The glassy phase is characterized by replica symmetry breaking. The quantum transition at zero temperature is also discussed. © 1996 The American Physical Society.