19,091 research outputs found
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
Structure and time-dependence of quantum breathers
Quantum states of a discrete breather are studied in two ways. One method
involves numerical diagonalization of the Hamiltonian, the other uses the path
integral to examine correlations in the eigenstates. In both cases only the
central nonlinearity is retained. To reduce truncation effects in the numerical
diagonalization, a basis is used that involves a quadratic local mode. A
similar device is used in the path integral method for deducing localization.
Both approaches lead to the conclusion that aside from quantum tunneling the
quantized discrete breather is stable.Comment: 33 pages, 20 figures, to appear in J. Chem. Phy
Websterisms: In Search of Noah\u27s Headwords
Noah Webster\u27s An American Dictionary of the English Language (1828) is a browser\u27s paradise, revealing many words whose meaning has changed since Noah\u27s time and others that lie idiosyncratically defined. I offer fifty of Webster\u27s definitions below, and challenge the reader to guess the headwords that Webster was trying to define. To make the task more approachable, wordlengths are provided for the to-be-discovered headwords, which are listed in alphabetical order of their appearance in the dictionary. All of these headwords, if not Webster\u27s definitions, should prove to be familiar to readers of Word Ways
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
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
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
Five dimensional relativity and two times
It is possible that null paths in 5D appear as the timelike paths of massive
particles in 4D, where there is an oscillation in the fifth dimension around
the hypersurface we call spacetime. A particle in 5D may be regarded as
multiply imaged in 4D, and the 4D weak equivalence principle may be regarded as
a symmetry of the 5D metric.Comment: 15 pages, in press in Phys. Lett.
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
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