2,884 research outputs found
Charge migration mechanisms in the DNA at finite temperature revisited; from quasi-ballistic to subdiffusive transport
Various charge migration mechanisms in the DNA are studied within the
framework of the Peyrard-Bishop-Holstein model which has been widely used to
address charge dynamics in this macromolecule. To analyze these mechanisms we
consider characteristic size and time scales of the fluctuations of the
electronic and vibrational subsystems. It is shown, in particular, that due to
substantial differences in these timescales polaron formation is unlikely
within a broad range of temperatures. We demonstrate that at low temperatures
electronic transport can be quasi-ballistic. For high temperatures, we propose
an alternative to polaronic charge migration mechanism: the
fluctuation-assisted one, in which the electron dynamics is governed by
relatively slow fluctuations of the vibrational subsystem. We argue also that
the discussed methods and mechanisms can be relevant for other organic
macromolecular systems, such as conjugated polymers and molecular aggregates
KMS states on Quantum Grammars
We consider quantum (unitary) continuous time evolution of spins on a lattice
together with quantum evolution of the lattice itself. In physics such
evolution was discussed in connection with quantum gravity. It is also related
to what is called quantum circuits, one of the incarnations of a quantum
computer. We consider simpler models for which one can obtain exact
mathematical results. We prove existence of the dynamics in both Schroedinger
and Heisenberg pictures, construct KMS states on appropriate C*-algebras. We
show (for high temperatures) that for each system where the lattice undergoes
quantum evolution, there is a natural scaling leading to a quantum spin system
on a fixed lattice, defined by a renormalized Hamiltonian.Comment: 22 page
Dynamics of Triangulations
We study a few problems related to Markov processes of flipping
triangulations of the sphere. We show that these processes are ergodic and
mixing, but find a natural example which does not satisfy detailed balance. In
this example, the expected distribution of the degrees of the nodes seems to
follow the power law
On the functions counting walks with small steps in the quarter plane
Models of spatially homogeneous walks in the quarter plane
with steps taken from a subset of the set of jumps to the eight
nearest neighbors are considered. The generating function of the numbers of such walks starting at the origin and
ending at after steps is studied. For all
non-singular models of walks, the functions and are continued as multi-valued functions on having
infinitely many meromorphic branches, of which the set of poles is identified.
The nature of these functions is derived from this result: namely, for all the
51 walks which admit a certain infinite group of birational transformations of
, the interval of variation of splits into
two dense subsets such that the functions and are shown to be holonomic for any from the one of them and
non-holonomic for any from the other. This entails the non-holonomy of
, and therefore proves a conjecture of
Bousquet-M\'elou and Mishna.Comment: 40 pages, 17 figure
Charge transfer mechanisms in DNA at finite temperatures: from quasiballistic to anomalous subdiffusive charge transfer
We address various regimes of charge transfer in DNA within the framework of the Peyrard-Bishop-Holstein model and analyze them from the standpoint of the characteristic size and timescales of the electronic and vibrational subsystems. It is demonstrated that a polaron is an unstable configuration within a broad range of temperatures and therefore polaronic contribution to the charge transport is irrelevant. We put forward an alternative fluctuation-governed charge transfer mechanism and show that the charge transfer can be quasi -ballistic at low temperatures, diffusive or mixed at intermediate temperatures, and subdiffusive close to the DNA denaturation transition point. Dynamic fluctuations in the vibrational subsystem is the key ingredient of our proposed mechanism which allows for explanation of all charge transfer regimes at finite temperatures. In particular, we demonstrate that in the most relevant regime of high temperatures (above the aqueous environment freezing point), the electron dynamics is completely governed by relatively slow fluctuations of the mechanical subsystem. We argue also that our proposed analysis methods and mechanisms can be relevant for the charge transfer in other organic systems, such as conjugated polymers, molecular aggregates, alpha-helices, etc
Binary Collisions and the Slingshot Effect
We derive the equations for the gravity assist manoeuvre in the general 2D
case without the constraints of circular planetary orbits or widely different
masses as assumed by Broucke, and obtain the slingshot conditions and maximum
energy gain for arbitrary mass ratios of two colliding rigid bodies. Using the
geometric view developed in an earlier paper by the authors the possible
trajectories are computed for both attractive or repulsive interactions
yielding a further insight on the slingshot mechanics and its parametrization.
The general slingshot manoeuvre for arbitrary masses is explained as a
particular case of the possible outcomes of attractive or repulsive binary
collisions, and the correlation between asymptotic information and orbital
parameters is obtained in general.Comment: 12 pages, 7 figures, accepted for publication Dec'07, Celestial
Mechanics and Dynamical Astronom
Growth of uniform infinite causal triangulations
We introduce a growth process which samples sections of uniform infinite
causal triangulations by elementary moves in which a single triangle is added.
A relation to a random walk on the integer half line is shown. This relation is
used to estimate the geodesic distance of a given triangle to the rooted
boundary in terms of the time of the growth process and to determine from this
the fractal dimension. Furthermore, convergence of the boundary process to a
diffusion process is shown leading to an interesting duality relation between
the growth process and a corresponding branching process.Comment: 27 pages, 6 figures, small changes, as publishe
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