8,490 research outputs found
Non-stationary heat conduction in one-dimensional chains with conserved momentum
The Letter addresses the relationship between hyperbolic equations of heat
conduction and microscopic models of dielectrics. Effects of the non-stationary
heat conduction are investigated in two one-dimensional models with conserved
momentum: Fermi-Pasta-Ulam (FPU) chain and chain of rotators (CR). These models
belong to different universality classes with respect to stationary heat
conduction. Direct numeric simulations reveal in both models a crossover from
oscillatory decay of short-wave perturbations of the temperature field to
smooth diffusive decay of the long-wave perturbations. Such behavior is
inconsistent with parabolic Fourier equation of the heat conduction. The
crossover wavelength decreases with increase of average temperature in both
models. For the FPU model the lowest order hyperbolic Cattaneo-Vernotte
equation for the non-stationary heat conduction is not applicable, since no
unique relaxation time can be determined.Comment: 4 pages, 5 figure
Elliptic operators in odd subspaces
An elliptic theory is constructed for operators acting in subspaces defined
via odd pseudodifferential projections. Subspaces of this type arise as
Calderon subspaces for first order elliptic differential operators on manifolds
with boundary, or as spectral subspaces for self-adjoint elliptic differential
operators of odd order. Index formulas are obtained for operators in odd
subspaces on closed manifolds and for general boundary value problems. We prove
that the eta-invariant of operators of odd order on even-dimesional manifolds
is a dyadic rational number.Comment: 27 page
Nonlinear Breathing-like Localized Modes in C60 Nanocrystals
We study the dynamics of nanocrystals composed of C60 fullerene molecules. We
demonstrate that such structures can support long-lived strongly localized
nonlinear oscillatory modes, which resemble discrete breathers in simple
lattices. We reveal that at room temperatures the lifetime of such nonlinear
localized modes may exceed tens of picoseconds; this suggests that C60
nanoclusters should demonstrate anomalously slow thermal relaxation when the
temperature gradient decays in accord to a power law, thus violating the
Cattaneo-Vernotte law of thermal conductivity.Comment: 6 pages, 6 figure
Properties of short-range and long-range correlation energy density functionals from electron-electron coalescence
The combination of density functional theory with other approaches to the
many-electron problem through the separation of the electron-electron
interaction into a short-range and a long-range contribution is a promising
method, which is raising more and more interest in recent years. In this work
some properties of the corresponding correlation energy functionals are derived
by studying the electron-electron coalescence condition for a modified
(long-range-only) interaction. A general relation for the on-top (zero
electron-electron distance) pair density is derived, and its usefulness is
discussed with some examples. For the special case of the uniform electron gas,
a simple parameterization of the on-top pair density for a long-range only
interaction is presented and supported by calculations within the ``extended
Overhauser model''. The results of this work can be used to build
self-interaction corrected short-range correlation energy functionals.Comment: revised version, to appear in Phys. Rev.
Lattice stretching bistability and dynamic heterogeneity
A simple one-dimensional lattice model is suggested to describe the
experimentally observed plateau in force-stretching diagrams for some
macromolecules. This chain model involves the nearest-neighbor interaction of a
Morse-like potential (required to have a saturation branch) and an harmonic
second-neighbor coupling. Under an external stretching applied t o the chain
ends, the intersite Morse-like potential results in the appearance of a
double-well potential within each chain monomer, whereas the interaction
between the second neighbors provide s a homogeneous bistable (degenerate)
ground state, at least within a certain part of the chain.
As a result, different conformational changes occur in the chain under the
external forcing. The transition regions between these conformations are
described as topological solitons. With a strong second-neighbor interaction,
the solitons describe the transition between the bistable ground states.
However, the key point of the model is the appearance of a heterogenous
structure, when the second-neighbor coupling is sufficiently weak. In this
case, a part of the chain has short bonds with a single-well potential, whereas
the complementary part admits strongly stretched bonds with a double-well
potential. This case allows us to explain the existence of a plateau in the
force-stretching diagram for DNA and alpha-helix protein. Finally, the soliton
dynamics are studied in detail.Comment: Submitted to Phys. Rev. E, 13 figure
System-adapted correlation energy density functionals from effective pair interactions
We present and discuss some ideas concerning an ``average-pair-density
functional theory'', in which the ground-state energy of a many-electron system
is rewritten as a functional of the spherically and system-averaged pair
density. These ideas are further clarified with simple physical examples. We
then show that the proposed formalism can be combined with density functional
theory to build system-adapted correlation energy functionals. A simple
approximation for the unknown effective electron-electron interaction that
enters in this combined approach is described, and results for the He series
and for the uniform electron gas are briefly reviewed.Comment: to appear in Phil. Mag. as part of Conference proceedings for the
"Electron Correlations and Materials Properties", Kos Greece, July 5-9, 200
Long-range/short-range separation of the electron-electron interaction in density functional theory
By splitting the Coulomb interaction into long-range and short-range
components, we decompose the energy of a quantum electronic system into
long-range and short-range contributions. We show that the long-range part of
the energy can be efficiently calculated by traditional wave function methods,
while the short-range part can be handled by a density functional. The analysis
of this functional with respect to the range of the associated interaction
reveals that, in the limit of a very short-range interaction, the short-range
exchange-correlation energy can be expressed as a simple local functional of
the on-top pair density and its first derivatives. This provides an explanation
for the accuracy of the local density approximation (LDA) for the short-range
functional. Moreover, this analysis leads also to new simple approximations for
the short-range exchange and correlation energies improving the LDA.Comment: 18 pages, 14 figures, to be published in Phys. Rev.
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