Schulman Replies

This is a reply to a comment of Casati, Chirikov and Zhirov (PRL 85, 896 (2000)) on PRL 83, 5419 (1999). The suitability of the particlar two-time boundary value problem used in the earlier PRL is argued

Bounds on Decoherence and Error

When a confined system interacts with its walls (treated quantum mechanically), there is an intertwining of degrees of freedom. We show that this need not lead to entanglement, hence decoherence. It will generally lead to error. The wave function optimization required to avoid decoherence is also examined.Comment: 10 pages, plain TeX, no figure

Opposite Thermodynamic Arrows of Time

A model in which two weakly coupled systems maintain opposite running thermodynamic arrows of time is exhibited. Each experiences its own retarded electromagnetic interaction and can be seen by the other. The possibility of opposite-arrow systems at stellar distances is explored and a relation to dark matter suggested.Comment: To appear in Phys. Rev. Let

Ratcheting up energy by means of measurement

The destruction of quantum coherence can pump energy into a system. For our examples this is paradoxical since the destroyed correlations are ordinarily considered negligible. Mathematically the explanation is straightforward and physically one can identify the degrees of freedom supplying this energy. Nevertheless, the energy input can be calculated without specific reference to those degrees of freedom.Comment: To appear in Phys. Rev. Let

Multiple phases in stochastic dynamics: geometry and probabilities

Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multi-dimensional space the phases (in the sense of phase transitions) of the underlying system become manifest as extremal points. This geometrical construction, which we call an \textit{observable-representation of state space}, can allow hierarchical structure to be observed. It also provides a method for the calculation of the probability that an initial points ends in one or another asymptotic state