671 research outputs found
Thermal conductance through molecular wires
We consider phononic heat transport through molecular chains connecting two
thermal reservoirs. For relatively short molecules at normal temperatures heat
conduction is dominated by the harmonic part of the molecular force-field. We
develop a general theory for the heat conduction through harmonic chains in
3-dimensions. A Landauer-type expression for the heat conduction is obtained,
in agreement with other recent studies. We use this formalism to study the heat
conduction properties of alkanes. For relatively short (1-30 carbon atoms)
chains the length and temperature dependence of the molecular heat conduction
result from the balance of three factors: (i) The molecular frequency spectrum
in relation to the frequency cutoff of the thermal reservoirs, (ii) the degree
of localization of the molecular normal modes and (iii) the molecule-heat
reservoirs coupling. The fact that molecular modes at different frequency
regimes have different localization properties gives rise to intricate
dependence of the heat conduction on molecular length at different
temperatures. For example, the heat conduction increases with molecular length
for short molecular chains at low temperatures. Similar considerations apply
for isotopically substituted disordered chains. Finally, we compare the heat
conduction obtained from this microscopic calculation to that estimated by
considering the molecule as a cylinder characterized by a macroscopic heat
conduction typical to organic solids. We find that this classical model
overestimates the heat conduction of single alkane molecules by about an order
of magnitude at room temperature. Implications of the present study to the
problem of heating in electrically conducting molecular junctions are pointed
out.Comment: 40 pages, 11 figures. J. Chem. Phys. Submitte
From a kinetic equation to a diffusion under an anomalous scaling
A linear Boltzmann equation is interpreted as the forward equation for the
probability density of a Markov process (K(t), i(t), Y(t)), where (K(t), i(t))
is an autonomous reversible jump process, with waiting times between two jumps
with finite expectation value but infinite variance, and Y(t) is an additive
functional of K(t). We prove that under an anomalous rescaling Y converges in
distribution to a two-dimensional Brownian motion. As a consequence, the
appropriately rescaled solution of the Boltzmann equation converges to a
diffusion equation
Transport in the XX chain at zero temperature: Emergence of flat magnetization profiles
We study the connection between magnetization transport and magnetization
profiles in zero-temperature XX chains. The time evolution of the transverse
magnetization, m(x,t), is calculated using an inhomogeneous initial state that
is the ground state at fixed magnetization but with m reversed from -m_0 for
x0. In the long-time limit, the magnetization evolves into a
scaling form m(x,t)=P(x/t) and the profile develops a flat part (m=P=0) in the
|x/t|1/2 while it
expands with the maximum velocity, c_0=1, for m_0->0. The states emerging in
the scaling limit are compared to those of a homogeneous system where the same
magnetization current is driven by a bulk field, and we find that the
expectation values of various quantities (energy, occupation number in the
fermionic representation) agree in the two systems.Comment: RevTex, 8 pages, 3 ps figure
Existence of temperature on the nanoscale
We consider a regular chain of quantum particles with nearest neighbour
interactions in a canonical state with temperature . We analyse the
conditions under which the state factors into a product of canonical density
matrices with respect to groups of particles each and under which these
groups have the same temperature . In quantum mechanics the minimum group
size depends on the temperature , contrary to the classical case.
We apply our analysis to a harmonic chain and find that for
temperatures above the Debye temperature and below.Comment: Version that appeared in PR
Anomalous thermal conductivity and local temperature distribution on harmonic Fibonacci chains
The harmonic Fibonacci chain, which is one of a quasiperiodic chain
constructed with a recursion relation, has a singular continuous
frequency-spectrum and critical eigenstates. The validity of the Fourier law is
examined for the harmonic Fibonacci chain with stochastic heat baths at both
ends by investigating the system size N dependence of the heat current J and
the local temperature distribution. It is shown that J asymptotically behaves
as (ln N)^{-1} and the local temperature strongly oscillates along the chain.
These results indicate that the Fourier law does not hold on the harmonic
Fibonacci chain. Furthermore the local temperature exhibits two different
distribution according to the generation of the Fibonacci chain, i.e., the
local temperature distribution does not have a definite form in the
thermodynamic limit. The relations between N-dependence of J and the
frequency-spectrum, and between the local temperature and critical eigenstates
are discussed.Comment: 10 pages, 4 figures, submitted to J. Phys.: Cond. Ma
Energy transport through rare collisions
We study a one-dimensional hamiltonian chain of masses perturbed by an energy
conserving noise. The dynamics is such that, according to its hamiltonian part,
particles move freely in cells and interact with their neighbors through
collisions, made possible by a small overlap of size between
near cells. The noise only randomly flips the velocity of the particles. If
, and if time is rescaled by a factor ,
we show that energy evolves autonomously according to a stochastic equation,
which hydrodynamic limit is known in some cases. In particular, if only two
different energies are present, the limiting process coincides with the simple
symmetric exclusion process.Comment: 24 pages, 2 figure
Heat conduction in the diatomic Toda lattice revisited
The problem of the diverging thermal conductivity in one-dimensional (1-D)
lattices is considered. By numerical simulations, it is confirmed that the
thermal conductivity of the diatomic Toda lattice diverges, which is opposite
to what one has believed before. Also the diverging exponent is found to be
almost the same as the FPU chain. It is reconfirmed that the diverging thermal
conductivity is universal in 1-D systems where the total momentum preserves.Comment: 3 pages, 3 figures. To appear in Phys. Rev.
Thermal conductivity of one-dimensional lattices with self-consistent heat baths: a heuristic derivation
We derive the thermal conductivities of one-dimensional harmonic and
anharmonic lattices with self-consistent heat baths (BRV lattice) from the
Single-Mode Relaxation Time (SMRT) approximation. For harmonic lattice, we
obtain the same result as previous works. However, our approach is heuristic
and reveals phonon picture explicitly within the heat transport process. The
results for harmonic and anharmonic lattices are compared with numerical
calculations from Green-Kubo formula. The consistency between derivation and
simulation strongly supports that effective (renormalized) phonons are energy
carriers in anharmonic lattices although there exist some other excitations
such as solitons and breathers.Comment: 4 pages, 3 figures. accepted for publication in JPS
A Symmetry Property of Momentum Distribution Functions in the Nonequilibrium Steady State of Lattice Thermal Conduction
We study a symmetry property of momentum distribution functions in the steady
state of heat conduction. When the equation of motion is symmetric under change
of signs for all dynamical variables, the distribution function is also
symmetric. This symmetry can be broken by introduction of an asymmetric term in
the interaction potential or the on-site potential, or employing the thermal
walls as heat reservoirs. We numerically find differences of behavior of the
models with and without the on-site potential.Comment: 13 pages. submitted to JPS
Correlations and scaling in one-dimensional heat conduction
We examine numerically the full spatio-temporal correlation functions for all
hydrodynamic quantities for the random collision model introduced recently. The
autocorrelation function of the heat current, through the Kubo formula, gives a
thermal conductivity exponent of 1/3 in agreement with the analytical
prediction and previous numerical work. Remarkably, this result depends
crucially on the choice of boundary conditions: for periodic boundary
conditions (as opposed to open boundary conditions with heat baths) the
exponent is approximately 1/2. This is expected to be a generic feature of
systems with singular transport coefficients. All primitive hydrodynamic
quantities scale with the dynamic critical exponent predicted analytically.Comment: 7 pages, 11 figure
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