2,246 research outputs found
Courant-Dorfman algebras and their cohomology
We introduce a new type of algebra, the Courant-Dorfman algebra. These are to
Courant algebroids what Lie-Rinehart algebras are to Lie algebroids, or Poisson
algebras to Poisson manifolds. We work with arbitrary rings and modules,
without any regularity, finiteness or non-degeneracy assumptions. To each
Courant-Dorfman algebra (\R,\E) we associate a differential graded algebra
\C(\E,\R) in a functorial way by means of explicit formulas. We describe two
canonical filtrations on \C(\E,\R), and derive an analogue of the Cartan
relations for derivations of \C(\E,\R); we classify central extensions of
\E in terms of H^2(\E,\R) and study the canonical cocycle
\Theta\in\C^3(\E,\R) whose class obstructs re-scalings of the
Courant-Dorfman structure. In the nondegenerate case, we also explicitly
describe the Poisson bracket on \C(\E,\R); for Courant-Dorfman algebras
associated to Courant algebroids over finite-dimensional smooth manifolds, we
prove that the Poisson dg algebra \C(\E,\R) is isomorphic to the one
constructed in \cite{Roy4-GrSymp} using graded manifolds.Comment: Corrected formulas for the brackets in Examples 2.27, 2.28 and 2.29.
The corrections do not affect the exposition in any wa
Pulse radiolysis studies of fast reactions in molecular systems. Progress report, November 1974--October 1975
Work on the reactivity of aryl carbonium ions in solution and single heme reduction in human methemoglobin is summarized. (LK
Information-theoretic equilibration: the appearance of irreversibility under complex quantum dynamics
The question of how irreversibility can emerge as a generic phenomena when
the underlying mechanical theory is reversible has been a long-standing
fundamental problem for both classical and quantum mechanics. We describe a
mechanism for the appearance of irreversibility that applies to coherent,
isolated systems in a pure quantum state. This equilibration mechanism requires
only an assumption of sufficiently complex internal dynamics and natural
information-theoretic constraints arising from the infeasibility of collecting
an astronomical amount of measurement data. Remarkably, we are able to prove
that irreversibility can be understood as typical without assuming decoherence
or restricting to coarse-grained observables, and hence occurs under distinct
conditions and time-scales than those implied by the usual decoherence point of
view. We illustrate the effect numerically in several model systems and prove
that the effect is typical under the standard random-matrix conjecture for
complex quantum systems.Comment: 15 pages, 7 figures. Discussion has been clarified and additional
numerical evidence for information theoretic equilibration is provided for a
variant of the Heisenberg model as well as one and two-dimensional random
local Hamiltonian
Power-law tail distributions and nonergodicity
We establish an explicit correspondence between ergodicity breaking in a
system described by power-law tail distributions and the divergence of the
moments of these distributions.Comment: 4 pages, 1 figure, corrected typo
Macroscopic detection of the strong stochasticity threshold in Fermi-Pasta-Ulam chains of oscillators
The largest Lyapunov exponent of a system composed by a heavy impurity
embedded in a chain of anharmonic nearest-neighbor Fermi-Pasta-Ulam oscillators
is numerically computed for various values of the impurity mass . A
crossover between weak and strong chaos is obtained at the same value
of the energy density (energy per degree of freedom)
for all the considered values of the impurity mass . The threshold \epsi
lon_{_T} coincides with the value of the energy density at which a
change of scaling of the relaxation time of the momentum autocorrelation
function of the impurity ocurrs and that was obtained in a previous work ~[M.
Romero-Bastida and E. Braun, Phys. Rev. E {\bf65}, 036228 (2002)]. The complete
Lyapunov spectrum does not depend significantly on the impurity mass . These
results suggest that the impurity does not contribute significantly to the
dynamical instability (chaos) of the chain and can be considered as a probe for
the dynamics of the system to which the impurity is coupled. Finally, it is
shown that the Kolmogorov-Sinai entropy of the chain has a crossover from weak
to strong chaos at the same value of the energy density that the crossover
value of largest Lyapunov exponent. Implications of this result
are discussed.Comment: 6 pages, 5 figures, revtex4 styl
Velocity Tails for Inelastic Maxwell Models
We study the velocity distribution function for inelastic Maxwell models,
characterized by a Boltzmann equation with constant collision rate, independent
of the energy of the colliding particles. By means of a nonlinear analysis of
the Boltzmann equation, we find that the velocity distribution function decays
algebraically for large velocities, with exponents that are analytically
calculated.Comment: 4 pages, 2 figure
Quantum macrostatistical picture of nonequilibrium steady states
We employ a quantum macrostatistical treatment of irreversible processes to
prove that, in nonequilibrium steady states, (a) the hydrodynamical observables
execute a generalised Onsager-Machlup process and (b) the spatial correlations
of these observables are generically of long range. The key assumptions behind
these results are a nonequilibrium version of Onsager's regression hypothesis,
together with certain hypotheses of chaoticity and local equilibrium for
hydrodynamical fluctuations.Comment: TeX, 13 page
Hierarchy of piecewise non-linear maps with non-ergodicity behavior
We study the dynamics of hierarchy of piecewise maps generated by
one-parameter families of trigonometric chaotic maps and one-parameter families
of elliptic chaotic maps of and types, in detail.
We calculate the Lyapunov exponent and Kolmogorov-Sinai entropy of the these
maps with respect to control parameter. Non-ergodicity of these piecewise maps
is proven analytically and investigated numerically . The invariant measure of
these maps which are not equal to one or zero, appears to be characteristic of
non-ergodicity behavior. A quantity of interest is the Kolmogorov-Sinai
entropy, where for these maps are smaller than the sum of positive Lyapunov
exponents and it confirms the non-ergodicity of the maps.Comment: 18 pages, 8 figure
Generalized Haldane Equation and Fluctuation Theorem in the Steady State Cycle Kinetics of Single Enzymes
Enyzme kinetics are cyclic. We study a Markov renewal process model of
single-enzyme turnover in nonequilibrium steady-state (NESS) with sustained
concentrations for substrates and products. We show that the forward and
backward cycle times have idential non-exponential distributions:
\QQ_+(t)=\QQ_-(t). This equation generalizes the Haldane relation in
reversible enzyme kinetics. In terms of the probabilities for the forward
() and backward () cycles, is shown to be the
chemical driving force of the NESS, . More interestingly, the moment
generating function of the stochastic number of substrate cycle ,
follows the fluctuation theorem in the form of
Kurchan-Lebowitz-Spohn-type symmetry. When $\lambda$ = $\Delta\mu/k_BT$, we
obtain the Jarzynski-Hatano-Sasa-type equality:
1 for all , where is the fluctuating chemical work
done for sustaining the NESS. This theory suggests possible methods to
experimentally determine the nonequilibrium driving force {\it in situ} from
turnover data via single-molecule enzymology.Comment: 4 pages, 3 figure
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