380 research outputs found
Fourier's Law from Closure Equations
We give a rigorous derivation of Fourier's law from a system of closure
equations for a nonequilibrium stationary state of a Hamiltonian system of
coupled oscillators subjected to heat baths on the boundary. The local heat
flux is proportional to the temperature gradient with a temperature dependent
heat conductivity and the stationary temperature exhibits a nonlinear profile
Properties of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz Gas II: The many point particles system
We study the stationary nonequilibrium states of N point particles moving
under the influence of an electric field E among fixed obstacles (discs) in a
two dimensional torus. The total kinetic energy of the system is kept constant
through a Gaussian thermostat which produces a velocity dependent mean field
interaction between the particles. The current and the particle distribution
functions are obtained numerically and compared for small E with analytic
solutions of a Boltzmann type equation obtained by treating the collisions with
the obstacles as random independent scatterings. The agreement is surprisingly
good for both small and large N. The latter system in turn agrees with a self
consistent one particle evolution expected to hold in the limit of N going to
infinity.Comment: 14 pages, 9 figure
Intriguing Heat Conduction of a Polymer Chain
We study heat conduction in a one-dimensional chain of particles with
longitudinal as well as transverse motions. The particles are connected by
two-dimensional harmonic springs together with bending angle interactions.
Using equilibrium and nonequilibrium molecular dynamics, three types of thermal
conducting behaviors are found: a logarithmic divergence with system sizes for
large transverse coupling, 1/3 power-law at intermediate coupling, and 2/5
power-law at low temperatures and weak coupling. The results are consistent
with a simple mode-coupling analysis of the same model. The 1/3 power-law
divergence should be a generic feature for models with transverse motions.Comment: 4 page
Heat Conduction in One-Dimensional chain of Hard Discs with Substrate Potential
Heat conduction of one-dimensional chain of equivalent rigid particles in the
field of external on-site potential is considered. Zero diameters of the
particles correspond to exactly integrable case with divergent heat conduction
coefficient. By means of simple analytical model it is demonstrated that for
any nonzero particle size the integrability is violated and the heat conduction
coefficient converges. The result of the analytical computation is verified by
means of numerical simulation in a plausible diapason of parameters and good
agreement is observedComment: 14 pages, 7 figure
Fluctuation relation for a L\'evy particle
We study the work fluctuations of a particle subjected to a deterministic
drag force plus a random forcing whose statistics is of the L\'evy type. In the
stationary regime, the probability density of the work is found to have ``fat''
power-law tails which assign a relatively high probability to large
fluctuations compared with the case where the random forcing is Gaussian. These
tails lead to a strong violation of existing fluctuation theorems, as the ratio
of the probabilities of positive and negative work fluctuations of equal
magnitude behaves in a non-monotonic way. Possible experiments that could probe
these features are proposed.Comment: 5 pages, 2 figures, RevTeX4; v2: minor corrections and references
added; v3: typos corrected, new conclusion, close to published versio
Quantum Phase Transition in an Interacting Fermionic Chain
We rigorously analyze the quantum phase transition between a metallic and an insulating phase in (non-solvable) interacting spin chains or one-dimensional fermionic systems. In particular, we prove the persistence of Luttinger liquid behavior in the presence of an interaction even arbitrarily close to the critical point, where the Fermi velocity vanishes and the two Fermi points coalesce. The analysis is based on two different multiscale analysis; the analysis of the first regime provides gain factors which compensate the small divisors due to the vanishing Fermi velocity
Incommensurate Charge Density Waves in the adiabatic Hubbard-Holstein model
The adiabatic, Holstein-Hubbard model describes electrons on a chain with
step interacting with themselves (with coupling ) and with a classical
phonon field \f_x (with coupling \l). There is Peierls instability if the
electronic ground state energy F(\f) as a functional of \f_x has a minimum
which corresponds to a periodic function with period , where
is the Fermi momentum. We consider irrational so that
the CDW is {\it incommensurate} with the chain. We prove in a rigorous way in
the spinless case, when \l,U are small and {U\over\l} large, that a)when
the electronic interaction is attractive there is no Peierls instability
b)when the interaction is repulsive there is Peierls instability in the
sense that our convergent expansion for F(\f), truncated at the second order,
has a minimum which corresponds to an analytical and periodic
\f_x. Such a minimum is found solving an infinite set of coupled
self-consistent equations, one for each of the infinite Fourier modes of
\f_x.Comment: 16 pages, 1 picture. To appear Phys. Rev.
Noninvasive positive pressure ventilation (NPPV) in critically ill patients: preliminary experience
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