728,225 research outputs found
Higher Dimensional Transition Systems
We introduce the notion of higher dimensional transition systems as a model of concurrency providing an elementary, set-theoretic formalisation of the idea of higher dimensional transition. We show an embedding of the category of higher dimensional transition systems into that of higher dimensional automata which cuts down to an equivalence when we restrict to non-degenerate automata. Moreover, we prove that the natural notion of bisimulation for such structures is a generalisation of the strong history preserving bisimulation, and provide an abstract categorical account of it via open maps. Finally, we define a notion of unfolding for higher dimensional transition systems and characterise the structures so obtained as a generalisation of event structures
Instanton correlators and phase transitions in two- and three-dimensional logarithmic plasmas
The existence of a discontinuity in the inverse dielectric constant of the
two-dimensional Coulomb gas is demonstrated on purely numerical grounds. This
is done by expanding the free energy in an applied twist and performing a
finite-size scaling analysis of the coefficients of higher-order terms. The
phase transition, driven by unbinding of dipoles, corresponds to the
Kosterlitz-Thouless transition in the 2D XY model. The method developed is also
used for investigating the possibility of a Kosterlitz-Thouless phase
transition in a three-dimensional system of point charges interacting with a
logarithmic pair-potential, a system related to effective theories of
low-dimensional strongly correlated systems. We also contrast the finite-size
scaling of the fluctuations of the dipole moments of the two-dimensional
Coulomb gas and the three-dimensional logarithmic system to those of the
three-dimensional Coulomb gas.Comment: 15 pages, 16 figure
From Luttinger to Fermi liquids in organic conductors
This chapter reviews the effects of interactions in quasi-one dimensional
systems, such as the Bechgaard and Fabre salts, and in particular the Luttinger
liquid physics. It discusses in details how transport measurements both d.c.
and a.c. allow to probe such a physics. It also examine the dimensional
crossover and deconfinement transition occurring between the one dimensional
case and the higher dimensional one resulting from the hopping of electrons
between chains in the quasi-one dimensional structure.Comment: To be published In the book "The Physics of Organic Conductors and
Superconductors", Springer, 2007, ed. A. Lebe
Model-Checking the Higher-Dimensional Modal mu-Calculus
The higher-dimensional modal mu-calculus is an extension of the mu-calculus
in which formulas are interpreted in tuples of states of a labeled transition
system. Every property that can be expressed in this logic can be checked in
polynomial time, and conversely every polynomial-time decidable problem that
has a bisimulation-invariant encoding into labeled transition systems can also
be defined in the higher-dimensional modal mu-calculus. We exemplify the latter
connection by giving several examples of decision problems which reduce to
model checking of the higher-dimensional modal mu-calculus for some fixed
formulas. This way generic model checking algorithms for the logic can then be
used via partial evaluation in order to obtain algorithms for theses problems
which may benefit from improvements that are well-established in the field of
program verification, namely on-the-fly and symbolic techniques. The aim of
this work is to extend such techniques to other fields as well, here
exemplarily done for process equivalences, automata theory, parsing, string
problems, and games.Comment: In Proceedings FICS 2012, arXiv:1202.317
Phase transitions in ensembles of solitons induced by an optical pumping or a strong electric field
The latest trend in studies of modern electronically and/or optically active
materials is to provoke phase transformations induced by high electric fields
or by short (femtosecond) powerful optical pulses. The systems of choice are
cooperative electronic states whose broken symmetries give rise to topological
defects. For typical quasi-one-dimensional architectures, those are the
microscopic solitons taking from electrons the major roles as carriers of
charge or spin. Because of the long-range ordering, the solitons experience
unusual super-long-range forces leading to a sequence of phase transitions in
their ensembles: the higher-temperature transition of the confinement and the
lower one of aggregation into macroscopic walls. Here we present results of an
extensive numerical modeling for ensembles of both neutral and charged solitons
in both two- and three-dimensional systems. We suggest a specific Monte Carlo
algorithm preserving the number of solitons, which substantially facilitates
the calculations, allows to extend them to the three-dimensional case and to
include the important long-range Coulomb interactions. The results confirm the
first confinement transition, except for a very strong Coulomb repulsion, and
demonstrate a pattern formation at the second transition of aggregation.Comment: 16 pages, 16 figure
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