60 research outputs found
Network Evolution Induced by the Dynamical Rules of Two Populations
We study the dynamical properties of a finite dynamical network composed of
two interacting populations, namely; extrovert () and introvert (). In
our model, each group is characterized by its size ( and ) and
preferred degree ( and ). The network dynamics
is governed by the competing microscopic rules of each population that consist
of the creation and destruction of links. Starting from an unconnected network,
we give a detailed analysis of the mean field approach which is compared to
Monte Carlo simulation data. The time evolution of the restricted degrees
\moyenne{k_{bb}} and \moyenne{k_{ab}} presents three time regimes and a non
monotonic behavior well captured by our theory. Surprisingly, when the
population size are equal , the ratio of the restricted degree
\theta_0=\moyenne{k_{ab}}/\moyenne{k_{bb}} appears to be an integer in the
asymptotic limits of the three time regimes. For early times (defined by
) the total number of links presents a linear evolution, where
the two populations are indistinguishable and where .
Interestingly, in the intermediate time regime (defined for
and for which ), the system reaches a
transient stationary state, where the number of contacts among introverts
remains constant while the number of connections is increasing linearly in the
extrovert population. Finally, due to the competing dynamics, the network
presents a frustrated stationary state characterized by a ratio .Comment: 21 pages, 6 figure
Fourier's law on a one-dimensional optical random lattice
We study the transport properties of a one-dimensional hard-core bosonic
lattice gas coupled to two particle reservoirs at different chemical potentials
which generate a current flow through the system. In particular, the influence
of random fluctuations of the underlying lattice on the stationary-state
properties is investigated. We show analytically that the steady-state density
presents a linear profile. The local steady-state current obeys the Fourier law
where is a typical timescale of the lattice
fluctuations and the density gradient imposed by the reservoirs.Comment: 9 pages, 2 figure
Relaxation in the XX quantum chain
We present the results obtained on the magnetisation relaxation properties of
an XX quantum chain in a transverse magnetic field. We first consider an
initial thermal kink-like state where half of the chain is initially
thermalized at a very high temperature while the remaining half, called
the system, is put at a lower temperature . From this initial state, we
derive analytically the Green function associated to the dynamical behaviour of
the transverse magnetisation. Depending on the strength of the magnetic field
and on the temperature of the system, different regimes are obtained for the
magnetic relaxation. In particular, with an initial droplet-like state, that is
a cold subsystem of finite size in contact at both ends with an infinite
temperature environnement, we derive analytically the behaviour of the
time-dependent system magnetisation
Dynamical phase transition of a 1D transport process including death
Motivated by biological aspects related to fungus growth, we consider the
competition of growth and corrosion. We study a modification of the totally
asymmetric exclusion process, including the probabilities of injection
and death of the last particle . The system presents a phase transition
at , where the average position of the last particle
grows as . For , a non equilibrium stationary state
exists while for the asymptotic state presents a low density
and max current phases. We discuss the scaling of the density and current
profiles for parallel and sequential updates.Comment: 4 pages, 5 figure
Entanglement evolution after connecting finite to infinite quantum chains
We study zero-temperature XX chains and transverse Ising chains and join an
initially separate finite piece on one or on both sides to an infinite
remainder. In both critical and non-critical systems we find a typical increase
of the entanglement entropy after the quench, followed by a slow decay towards
the value of the homogeneous chain. In the critical case, the predictions of
conformal field theory are verified for the first phase of the evolution, while
at late times a step structure can be observed.Comment: 15 pages, 11 figure
Quantum repeated interactions and the chaos game
Inspired by the algorithm of Barnsley's chaos game, we construct an open
quantum system model based on the repeated interaction process. We shown that
the quantum dynamics of the appropriate fermionic/bosonic system (in
interaction with an environment) provides a physical model of the chaos game.
When considering fermionic operators, we follow the system's evolution by
focusing on its reduced density matrix. The system is shown to be in a Gaussian
state (at all time ) and the average number of particles is shown to obey
the chaos game equation. Considering bosonic operators, with a system initially
prepared in coherent states, the evolution of the system can be tracked by
investigating the dynamics of the eigenvalues of the annihilation operator.
This quantity is governed by a chaos game-like equation from which different
scenarios emerge.Comment: 21 pages, 8 figue
A matrix product solution for a nonequilibrium steady state of an XX chain
A one dimensional XX spin chain of finite length coupled to reservoirs at
both ends is solved exactly in terms of a matrix product state ansatz. An
explicit representation of matrices of fixed dimension 4 independent of the
chain length is found. Expectations of all observables are evaluated, showing
that all connected correlations, apart from nearest neighbor z-z, are zero.Comment: 11 page
Critical dynamics in trapped particle systems
We discuss the effects of a trapping space-dependent potential on the
critical dynamics of lattice gas models. Scaling arguments provide a dynamic
trap-size scaling framework to describe how critical dynamics develops in the
large trap-size limit. We present numerical results for the relaxational
dynamics of a two-dimensional lattice gas (Ising) model in the presence of a
harmonic trap, which support the dynamic trap-size scaling scenario.Comment: 7 page
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