14,205 research outputs found
p-topological and p-regular: dual notions in convergence theory
The natural duality between "topological" and "regular," both considered as
convergence space properties, extends naturally to p-regular convergence
spaces, resulting in the new concept of a p-topological convergence space.
Taking advantage of this duality, the behavior of p-topological and p-regular
convergence spaces is explored, with particular emphasis on the former, since
they have not been previously studied. Their study leads to the new notion of a
neighborhood operator for filters, which in turn leads to an especially simple
characterization of a topology in terms of convergence criteria. Applications
include the topological and regularity series of a convergence space.Comment: 12 pages in Acrobat 3.0 PDF forma
A proposal for founding mistrustful quantum cryptography on coin tossing
A significant branch of classical cryptography deals with the problems which
arise when mistrustful parties need to generate, process or exchange
information. As Kilian showed a while ago, mistrustful classical cryptography
can be founded on a single protocol, oblivious transfer, from which general
secure multi-party computations can be built.
The scope of mistrustful quantum cryptography is limited by no-go theorems,
which rule out, inter alia, unconditionally secure quantum protocols for
oblivious transfer or general secure two-party computations. These theorems
apply even to protocols which take relativistic signalling constraints into
account. The best that can be hoped for, in general, are quantum protocols
computationally secure against quantum attack. I describe here a method for
building a classically certified bit commitment, and hence every other
mistrustful cryptographic task, from a secure coin tossing protocol. No
security proof is attempted, but I sketch reasons why these protocols might
resist quantum computational attack.Comment: Title altered in deference to Physical Review's fear of question
marks. Published version; references update
Micromagnetic Simulations of Ferromagnetic Rings
Thin nanomagnetic rings have generated interest for fundamental studies of
magnetization reversal and also for their potential in various applications,
particularly as magnetic memories. They are a rare example of a geometry in
which an analytical solution for the rate of thermally induced magnetic
reversal has been determined, in an approximation whose errors can be estimated
and bounded. In this work, numerical simulations of soft ferromagnetic rings
are used to explore aspects of the analytical solution. The evolution of the
energy near the transition states confirms that, consistent with analytical
predictions, thermally induced magnetization reversal can have one of two
intermediate states: either constant or soliton-like saddle configurations,
depending on ring size and externally applied magnetic field. The results
confirm analytical predictions of a transition in thermally activated reversal
behavior as magnetic field is varied at constant ring size. Simulations also
show that the analytic one dimensional model continues to hold even for wide
rings
Thermal Stability of the Magnetization in Perpendicularly Magnetized Thin Film Nanomagnets
Understanding the stability of thin film nanomagnets with perpendicular
magnetic anisotropy (PMA) against thermally induced magnetization reversal is
important when designing perpendicularly magnetized patterned media and
magnetic random access memories. The leading-order dependence of magnetization
reversal rates are governed by the energy barrier the system needs to surmount
in order for reversal to proceed. In this paper we study the reversal dynamics
of these systems and compute the relevant barriers using the string method of
E, Vanden-Eijnden, and Ren. We find the reversal to be often spatially
incoherent; that is, rather than the magnetization flipping as a rigid unit,
reversal proceeds instead through a soliton-like domain wall sweeping through
the system. We show that for square nanomagnetic elements the energy barrier
increases with element size up to a critical length scale, beyond which the
energy barrier is constant. For circular elements the energy barrier continues
to increase indefinitely, albeit more slowly beyond a critical size. In both
cases the energy barriers are smaller than those expected for coherent
magnetization reversal.Comment: 5 pages, 4 Figure
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