312 research outputs found
A Graph Model for Imperative Computation
Scott's graph model is a lambda-algebra based on the observation that
continuous endofunctions on the lattice of sets of natural numbers can be
represented via their graphs. A graph is a relation mapping finite sets of
input values to output values.
We consider a similar model based on relations whose input values are finite
sequences rather than sets. This alteration means that we are taking into
account the order in which observations are made. This new notion of graph
gives rise to a model of affine lambda-calculus that admits an interpretation
of imperative constructs including variable assignment, dereferencing and
allocation.
Extending this untyped model, we construct a category that provides a model
of typed higher-order imperative computation with an affine type system. An
appropriate language of this kind is Reynolds's Syntactic Control of
Interference. Our model turns out to be fully abstract for this language. At a
concrete level, it is the same as Reddy's object spaces model, which was the
first "state-free" model of a higher-order imperative programming language and
an important precursor of games models. The graph model can therefore be seen
as a universal domain for Reddy's model
Quantum information in the Posner model of quantum cognition
Matthew Fisher recently postulated a mechanism by which quantum phenomena
could influence cognition: Phosphorus nuclear spins may resist decoherence for
long times, especially when in Posner molecules. The spins would serve as
biological qubits. We imagine that Fisher postulates correctly. How adroitly
could biological systems process quantum information (QI)? We establish a
framework for answering. Additionally, we construct applications of biological
qubits to quantum error correction, quantum communication, and quantum
computation. First, we posit how the QI encoded by the spins transforms as
Posner molecules form. The transformation points to a natural computational
basis for qubits in Posner molecules. From the basis, we construct a quantum
code that detects arbitrary single-qubit errors. Each molecule encodes one
qutrit. Shifting from information storage to computation, we define the model
of Posner quantum computation. To illustrate the model's quantum-communication
ability, we show how it can teleport information incoherently: A state's
weights are teleported. Dephasing results from the entangling operation's
simulation of a coarse-grained Bell measurement. Whether Posner quantum
computation is universal remains an open question. However, the model's
operations can efficiently prepare a Posner state usable as a resource in
universal measurement-based quantum computation. The state results from
deforming the Affleck-Kennedy-Lieb-Tasaki (AKLT) state and is a projected
entangled-pair state (PEPS). Finally, we show that entanglement can affect
molecular-binding rates, boosting a binding probability from 33.6% to 100% in
an example. This work opens the door for the QI-theoretic analysis of
biological qubits and Posner molecules.Comment: Published versio
Single photoeffect on helium-like ions in the non-relativistic region
We present a generalization of the pioneering results obtained for single
K-shell photoionization of H-like ions by M. Stobbe [Ann. Phys. 7 (1930) 661]
to the case of the helium isoelectronic sequence. The total cross section of
the process is calculated, taking into account the correlation corrections to
first order of the perturbation theory with respect to the electron-electron
interaction. Predictions are made for the entire non-relativistic energy
domain. The phenomenon of dynamical suppression of correlation effects in the
ionization cross section is discussed.Comment: to be published in Physics Letters
Tuning of tunneling current noise spectra singularities by localized states charging
We report the results of theoretical investigations of tunneling current
noise spectra in a wide range of applied bias voltage. Localized states of
individual impurity atoms play an important role in tunneling current noise
formation. It was found that switching "on" and "off" of Coulomb interaction of
conduction electrons with two charged localized states results in power law
singularity of low-frequency tunneling current noise spectrum ()
and also results on high frequency component of tunneling current spectra
(singular peaks appear).Comment: 7 pages, 4 figure
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