5 research outputs found
Self-trapping transition for nonlinear impurities embedded in a Cayley tree
The self-trapping transition due to a single and a dimer nonlinear impurity
embedded in a Cayley tree is studied. In particular, the effect of a perfectly
nonlinear Cayley tree is considered. A sharp self-trapping transition is
observed in each case. It is also observed that the transition is much sharper
compared to the case of one-dimensional lattices. For each system, the critical
values of for the self-trapping transitions are found to obey a
power-law behavior as a function of the connectivity of the Cayley tree.Comment: 6 pages, 7 fig
Does a Computer have an Arrow of Time?
In [Sch05a], it is argued that Boltzmann's intuition, that the psychological
arrow of time is necessarily aligned with the thermodynamic arrow, is correct.
Schulman gives an explicit physical mechanism for this connection, based on the
brain being representable as a computer, together with certain thermodynamic
properties of computational processes. [Haw94] presents similar, if briefer,
arguments. The purpose of this paper is to critically examine the support for
the link between thermodynamics and an arrow of time for computers. The
principal arguments put forward by Schulman and Hawking will be shown to fail.
It will be shown that any computational process that can take place in an
entropy increasing universe, can equally take place in an entropy decreasing
universe. This conclusion does not automatically imply a psychological arrow
can run counter to the thermodynamic arrow. Some alternative possible explana-
tions for the alignment of the two arrows will be briefly discussed.Comment: 31 pages, no figures, publication versio