From classical to quantum stochastic processes.

In this paper, we construct quantum analogs starting from classical stochastic processes, by replacing random "which path" decisions with superpositions of all paths. This procedure typically leads to nonunitary quantum evolution, where coherences are continuously generated and destroyed. In spite of their transient nature, these coherences can change the scaling behavior of classical observables. Using the zero temperature Glauber dynamics in a linear Ising spin chain, we find quantum analogs with different domain growth exponents. In some cases, this exponent is even smaller than for the original classical process, which means that coherence can play an important role to speed up the relaxation process.

Decoherence of an n-qubit quantum memory.

We analyze decoherence of a quantum register in the absence of nonlocal operations, i.e., n noninteracting qubits coupled to an environment. The problem is solved in terms of a sum rule which implies linear scaling in the number of qubits. Each term involves a single qubit and its entanglement with the remaining ones. Two conditions are essential: first, decoherence must be small, and second, the coupling of different qubits must be uncorrelated in the interaction picture. We apply the result to a random matrix model, and illustrate its reach considering a Greenberger-Horne-Zeilinger state coupled to a spin bath.

Low-rank perturbations and the spectral statistics of pseudointegrable billiards.

We present an efficient method to solve Schrödinger's equation for perturbations of low rank. The method is ideally suited for systems with short range interactions or quantum billiards. It involves a secular equation of low dimension, which directly returns the level counting function. For illustration, we calculate the number variance for two pseudointegrable quantum billiards: the barrier billiard and a right triangle billiard. In this way, we obtain precise estimates for the level compressibility in the semiclassical (high energy) limit. In both cases, our results confirm recent theoretical predictions, based on periodic orbit summation, disregarding diffractive orbits.