49 research outputs found
Negative response to an excessive bias by a mixed population of voters
We study an outcome of a vote in a population of voters exposed to an
externally applied bias in favour of one of two potential candidates. The
population consists of ordinary individuals, that are in majority and tend to
align their opinion with the external bias, and some number of contrarians ---
individuals who are always hostile to the bias but are not in a conflict with
ordinary voters. The voters interact among themselves, all with all, trying to
find an opinion reached by the community as a whole. We demonstrate that for a
sufficiently weak external bias, the opinion of ordinary individuals is always
decisive and the outcome of the vote is in favour of the preferential
candidate. On the contrary, for an excessively strong bias, the contrarians
dominate in the population's opinion, producing overall a negative response to
the imposed bias. We also show that for sufficiently strong interactions within
the community, either of two subgroups can abruptly change an opinion of the
other group.Comment: 11 pages, 6 figure
Fourier's Law in a Quantum Spin Chain and the Onset of Quantum Chaos
We study heat transport in a nonequilibrium steady state of a quantum
interacting spin chain. We provide clear numerical evidence of the validity of
Fourier law. The regime of normal conductivity is shown to set in at the
transition to quantum chaos.Comment: 4 pages, 5 figures, RevTe
Memory Effects in Nonequilibrium Transport for Deterministic Hamiltonian Systems
We consider nonequilibrium transport in a simple chain of identical
mechanical cells in which particles move around. In each cell, there is a
rotating disc, with which these particles interact, and this is the only
interaction in the model. It was shown in \cite{eckmann-young} that when the
cells are weakly coupled, to a good approximation, the jump rates of particles
and the energy-exchange rates from cell to cell follow linear profiles. Here,
we refine that study by analyzing higher-order effects which are induced by the
presence of external gradients for situations in which memory effects, typical
of Hamiltonian dynamics, cannot be neglected. For the steady state we propose a
set of balance equations for the particle number and energy in terms of the
reflection probabilities of the cell and solve it phenomenologically. Using
this approximate theory we explain how these asymmetries affect various aspects
of heat and particle transport in systems of the general type described above
and obtain in the infinite volume limit the deviation from the theory in
\cite{eckmann-young} to first-order. We verify our assumptions with extensive
numerical simulations.Comment: Several change
Nonequilibrium dynamics of a stochastic model of anomalous heat transport: numerical analysis
We study heat transport in a chain of harmonic oscillators with random
elastic collisions between nearest-neighbours. The equations of motion of the
covariance matrix are numerically solved for free and fixed boundary
conditions. In the thermodynamic limit, the shape of the temperature profile
and the value of the stationary heat flux depend on the choice of boundary
conditions. For free boundary conditions, they also depend on the coupling
strength with the heat baths. Moreover, we find a strong violation of local
equilibrium at the chain edges that determine two boundary layers of size
(where is the chain length), that are characterized by a
different scaling behaviour from the bulk. Finally, we investigate the
relaxation towards the stationary state, finding two long time scales: the
first corresponds to the relaxation of the hydrodynamic modes; the second is a
manifestation of the finiteness of the system.Comment: Submitted to Journal of Physics A, Mathematical and Theoretica
A stochastic model of anomalous heat transport: analytical solution of the steady state
We consider a one-dimensional harmonic crystal with conservative noise, in
contact with two stochastic Langevin heat baths at different temperatures. The
noise term consists of collisions between neighbouring oscillators that
exchange their momenta, with a rate . The stationary equations for the
covariance matrix are exactly solved in the thermodynamic limit ().
In particular, we derive an analytical expression for the temperature profile,
which turns out to be independent of . Moreover, we obtain an exact
expression for the leading term of the energy current, which scales as
. Our theoretical results are finally found to be consistent
with the numerical solutions of the covariance matrix for finite .Comment: Minor changes in the text. To appear in Journal of Physics
Density dynamics from current auto-correlations at finite time- and length-scales
We consider the increase of the spatial variance of some inhomogeneous,
non-equilibrium density (particles, energy, etc.) in a periodic quantum system
of condensed matter-type. This is done for a certain class of initial quantum
states which is supported by static linear response and typicality arguments.
We directly relate the broadening to some current auto-correlation function at
finite times. Our result is not limited to diffusive behavior, however, in that
case it yields a generalized Einstein relation. These findings facilitate the
approximation of diffusion constants/conductivities on the basis of current
auto-correlation functions at finite times for finite systems. Pursuing this,
we quantitatively confirm the magnetization diffusion constant in a spin chain
which was recently found from non-equilibrium bath scenarios.Comment: 4 pages, 1 figure, accepted for publication in Europhys. Let
A non-perturbative renormalization group study of the stochastic Navier--Stokes equation
We study the renormalization group flow of the average action of the
stochastic Navier--Stokes equation with power-law forcing. Using Galilean
invariance we introduce a non-perturbative approximation adapted to the zero
frequency sector of the theory in the parametric range of the H\"older exponent
of the forcing where real-space local interactions are
relevant. In any spatial dimension , we observe the convergence of the
resulting renormalization group flow to a unique fixed point which yields a
kinetic energy spectrum scaling in agreement with canonical dimension analysis.
Kolmogorov's -5/3 law is, thus, recovered for as also predicted
by perturbative renormalization. At variance with the perturbative prediction,
the -5/3 law emerges in the presence of a \emph{saturation} in the
-dependence of the scaling dimension of the eddy diffusivity at
when, according to perturbative renormalization, the velocity
field becomes infra-red relevant.Comment: RevTeX, 18 pages, 5 figures. Minor changes and new discussion
Current in coherent quantum systems connected to mesoscopic Fermi reservoirs
We study particle current in a recently proposed model for coherent quantum transport. In this model, a system connected to mesoscopic Fermi reservoirs (meso-reservoir) is driven out of equilibrium by the action of super-reservoirs thermalized to prescribed temperatures and chemical potentials by a simple dissipative mechanism described by the Lindblad equation. We compare exact (numerical) results with theoretical expectations based on the Landauer formula