907 research outputs found
Lie conformal algebra cohomology and the variational complex
We find an interpretation of the complex of variational calculus in terms of
the Lie conformal algebra cohomology theory. This leads to a better
understanding of both theories. In particular, we give an explicit construction
of the Lie conformal algebra cohomology complex, and endow it with a structure
of a g-complex. On the other hand, we give an explicit construction of the
complex of variational calculus in terms of skew-symmetric poly-differential
operators.Comment: 56 page
A convenient criterion under which Z_2-graded operators are Hamiltonian
We formulate a simple and convenient criterion under which skew-adjoint
Z_2-graded total differential operators are Hamiltonian, provided that their
images are closed under commutation in the Lie algebras of evolutionary vector
fields on the infinite jet spaces for vector bundles over smooth manifolds.Comment: J.Phys.Conf.Ser.: Mathematical and Physical Aspects of Symmetry.
Proc. 28th Int. colloq. on group-theoretical methods in Physics (July 26-30,
2010; Newcastle-upon-Tyne, UK), 6 pages (in press
Field dependent collision frequency of the two-dimensional driven random Lorentz gas
In the field-driven, thermostatted Lorentz gas the collision frequency
increases with the magnitude of the applied field due to long-time
correlations. We study this effect with computer simulations and confirm the
presence of non-analytic terms in the field dependence of the collision
frequency as predicted by kinetic theory.Comment: 6 pages, 2 figures. Submitted to Phys. Rev.
Leading Pollicott-Ruelle Resonances and Transport in Area-Preserving Maps
The leading Pollicott-Ruelle resonance is calculated analytically for a
general class of two-dimensional area-preserving maps. Its wave number
dependence determines the normal transport coefficients. In particular, a
general exact formula for the diffusion coefficient D is derived without any
high stochasticity approximation and a new effect emerges: The angular
evolution can induce fast or slow modes of diffusion even in the high
stochasticity regime. The behavior of D is examined for three particular cases:
(i) the standard map, (ii) a sawtooth map, and (iii) a Harper map as an example
of a map with nonlinear rotation number. Numerical simulations support this
formula.Comment: 5 pages, 1 figur
Wave packet autocorrelation functions for quantum hard-disk and hard-sphere billiards in the high-energy, diffraction regime
We consider the time evolution of a wave packet representing a quantum
particle moving in a geometrically open billiard that consists of a number of
fixed hard-disk or hard-sphere scatterers. Using the technique of multiple
collision expansions we provide a first-principle analytical calculation of the
time-dependent autocorrelation function for the wave packet in the high-energy
diffraction regime, in which the particle's de Broglie wave length, while being
small compared to the size of the scatterers, is large enough to prevent the
formation of geometric shadow over distances of the order of the particle's
free flight path. The hard-disk or hard-sphere scattering system must be
sufficiently dilute in order for this high-energy diffraction regime to be
achievable. Apart from the overall exponential decay, the autocorrelation
function exhibits a generally complicated sequence of relatively strong peaks
corresponding to partial revivals of the wave packet. Both the exponential
decay (or escape) rate and the revival peak structure are predominantly
determined by the underlying classical dynamics. A relation between the escape
rate, and the Lyapunov exponents and Kolmogorov-Sinai entropy of the
counterpart classical system, previously known for hard-disk billiards, is
strengthened by generalization to three spatial dimensions. The results of the
quantum mechanical calculation of the time-dependent autocorrelation function
agree with predictions of the semiclassical periodic orbit theory.Comment: 24 pages, 13 figure
Classification of integrable hydrodynamic chains and generating functions of conservation laws
New approach to classification of integrable hydrodynamic chains is
established. Generating functions of conservation laws are classified by the
method of hydrodynamic reductions. N parametric family of explicit hydrodynamic
reductions allows to reconstruct corresponding hydrodynamic chains. Plenty new
hydrodynamic chains are found
Why nonlocal recursion operators produce local symmetries: new results and applications
It is well known that integrable hierarchies in (1+1) dimensions are local
while the recursion operators that generate them usually contain nonlocal
terms. We resolve this apparent discrepancy by providing simple and universal
sufficient conditions for a (nonlocal) recursion operator in (1+1) dimensions
to generate a hierarchy of local symmetries. These conditions are satisfied by
virtually all known today recursion operators and are much easier to verify
than those found in earlier work.
We also give explicit formulas for the nonlocal parts of higher recursion
operators, Poisson and symplectic structures of integrable systems in (1+1)
dimensions.
Using these two results we prove, under some natural assumptions, the
Maltsev--Novikov conjecture stating that higher Hamiltonian, symplectic and
recursion operators of integrable systems in (1+1) dimensions are weakly
nonlocal, i.e., the coefficients of these operators are local and these
operators contain at most one integration operator in each term.Comment: 10 pages, LaTeX 2e, final versio
Physical descriptions of the bacterial nucleoid at large scales, and their biological implications.
Recent experimental and theoretical approaches have attempted to quantify the physical organization (compaction and geometry) of the bacterial chromosome with its complement of proteins (the nucleoid). The genomic DNA exists in a complex and dynamic protein-rich state, which is highly organized at various length scales. This has implications for modulating (when not directly enabling) the core biological processes of replication, transcription and segregation. We overview the progress in this area, driven in the last few years by new scientific ideas and new interdisciplinary experimental techniques, ranging from high space- and time-resolution microscopy to high-throughput genomics employing sequencing to map different aspects of the nucleoid-related interactome. The aim of this review is to present the wide spectrum of experimental and theoretical findings coherently, from a physics viewpoint. In particular, we highlight the role that statistical and soft condensed matter physics play in describing this system of fundamental biological importance, specifically reviewing classic and more modern tools from the theory of polymers. We also discuss some attempts toward unifying interpretations of the current results, pointing to possible directions for future investigation
Hamiltonian evolutions of twisted gons in \RP^n
In this paper we describe a well-chosen discrete moving frame and their
associated invariants along projective polygons in \RP^n, and we use them to
write explicit general expressions for invariant evolutions of projective
-gons. We then use a reduction process inspired by a discrete
Drinfeld-Sokolov reduction to obtain a natural Hamiltonian structure on the
space of projective invariants, and we establish a close relationship between
the projective -gon evolutions and the Hamiltonian evolutions on the
invariants of the flow. We prove that {any} Hamiltonian evolution is induced on
invariants by an evolution of -gons - what we call a projective realization
- and we give the direct connection. Finally, in the planar case we provide
completely integrable evolutions (the Boussinesq lattice related to the lattice
-algebra), their projective realizations and their Hamiltonian pencil. We
generalize both structures to -dimensions and we prove that they are
Poisson. We define explicitly the -dimensional generalization of the planar
evolution (the discretization of the -algebra) and prove that it is
completely integrable, providing also its projective realization
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