Convergence of matrices under random conjugation: wave packet scattering without kinematic entanglement

In previous work, it was shown numerically that under successive scattering events, a collection of particles with Gaussian wavefunctions retains the Gaussian property, with the spread of the Gaussian ('Δx') tending to a value inversely proportional to the square root of each particle's mass. We prove this convergence in all dimensions ≥3

Wave-packet scattering without kinematic entanglement: convergence of expectation values

The wave packet spread of a particle in a collection of different mass particles, all with Gaussian wave functions, evolves to a value that is inversely proportional to the mass of the particle. The assumptions underlying this result and its derivation are reviewed. A mathematical demonstration of the convergence of an iteration central to this assertion is presented. Finally, the question of in-principle measurement of wave packet spread is taken up

Cryptography from tensor problems

We describe a new proposal for a trap-door one-way function. The new proposal belongs to the "multivariate quadratic" family but the trap-door is different from existing methods, and is simpler

The quantifier semigroup for bipartite graphs

In a bipartite graph there are two widely encountered monotone mappings from subsets of one side of the graph to subsets of the other side: one corresponds to the quantifier "there exists a neighbor in the subset" and the other to the quantifier "all neighbors are in the subset." These mappings generate a partially ordered semigroup which we characterize in terms of "run-unimodal" words

Imaging geometry through dynamics: the observable representation

For many stochastic processes there is an underlying coordinate space, $V$, with the process moving from point to point in $V$ or on variables (such as spin configurations) defined with respect to $V$. There is a matrix of transition probabilities (whether between points in $V$ or between variables defined on $V$) and we focus on its ``slow'' eigenvectors, those with eigenvalues closest to that of the stationary eigenvector. These eigenvectors are the ``observables,'' and they can be used to recover geometrical features of $V$

Signal Propagation, with Application to a Lower Bound on the Depth of Noisy Formulas

We study the decay of an information signal propagating through a series of noisy channels. We obtain exact bounds on such decay, and as a result provide a new lower bound on the depth of formulas with noisy components. This improves upon previous work of N. Pippenger and significantly decreases the gap between his lower bound and the classical upper bound of von Neumann. We also discuss connections between our work and the study of mixing rates of Markov chains

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

Universal immersion spaces for edge-colored graphs and nearest-neighbor metrics

There exist finite universal immersion spaces for the following: (a) Edge-colored graphs of bounded degree and boundedly many colors. (b) Nearest-neighbor metrics of bounded degree and boundedly many edge lengths