3,457 research outputs found
Collective motion of binary self-propelled particle mixtures
In this study, we investigate the phenomenon of collective motion in binary
mixtures of self-propelled particles. We consider two particle species, each of
which consisting of pointlike objects that propel with a velocity of constant
magnitude. Within each species, the particles try to achieve polar alignment of
their velocity vectors, whereas we analyze the cases of preferred polar,
antiparallel, as well as perpendicular alignment between particles of different
species. Our focus is on the effect that the interplay between the two species
has on the threshold densities for the onset of collective motion and on the
nature of the solutions above onset. For this purpose, we start from suitable
Langevin equations in the particle picture, from which we derive mean field
equations of the Fokker-Planck type and finally macroscopic continuum field
equations. We perform particle simulations of the Langevin equations, linear
stability analyses of the Fokker-Planck and macroscopic continuum equations,
and we numerically solve the Fokker-Planck equations. Both, spatially
homogeneous and inhomogeneous solutions are investigated, where the latter
correspond to stripe-like flocks of collectively moving particles. In general,
the interaction between the two species reduces the threshold density for the
onset of collective motion of each species. However, this interaction also
reduces the spatial organization in the stripe-like flocks. The most
interesting behavior is found for the case of preferred perpendicular alignment
between different species. There, a competition between polar and truly nematic
orientational ordering of the velocity vectors takes place within each particle
species. Finally, depending on the alignment rule for particles of different
species and within certain ranges of particle densities, identical and inverted
spatial density profiles can be found for the two particle species.Comment: 16 pages, 10 figure
The effect of Coulombic friction on spatial displacement statistics
The phenomenon of Coulombic friction enters the stochastic description of dry
friction between two solids and the statistic characterization of vibrating
granular media. Here we analyze the corresponding Fokker-Planck equation
including both velocity and spatial components, exhibiting a formal connection
to a quantum mechanical harmonic oscillator in the presence of a delta
potential. Numerical solutions for the resulting spatial displacement
statistics show a crossover from exponential to Gaussian displacement
statistics. We identify a transient intermediate regime that exhibits
multiscaling properties arising from the contribution of Coulombic friction.
The possible role of these effects during observations in diffusion experiments
is shortly discussed.Comment: 11 pages, 9 figure
Dual-path state reconstruction scheme for propagating quantum microwaves and detector noise tomography
Quantum state reconstruction involves measurement devices that are usually
described by idealized models, but not known in full detail in experiments. For
weak propagating microwaves, the detection process requires linear amplifiers
which obscure the signal with random noise. Here, we introduce a theory which
nevertheless allows one to use these devices for measuring all quadrature
moments of propagating quantum microwaves based on cross-correlations from a
dual-path amplification setup. Simultaneously, the detector noise properties
are determined, allowing for tomography. We demonstrate the feasibility of our
novel concept by proof-of-principle experiments with classical mixtures of weak
coherent microwaves.Comment: 11 pages, 3 figure
Two-resonator circuit QED: Dissipative Theory
We present a theoretical treatment for the dissipative two-resonator circuit
quantum electrodynamics setup referred to as quantum switch. There, switchable
coupling between two superconducting resonators is mediated by a
superconducting qubit operating in the dispersive regime, where the qubit
transition frequency is far detuned from those of the resonators. We derive an
effective Hamiltonian for the quantum switch beyond the rotating wave
approximation and study the dissipative dynamics within a Bloch-Redfield
quantum master equation approach. We derive analytically how the qubit affects
the quantum switch even if the qubit has no dynamics, and we estimate the
strength of this influence. The analytical results are corroborated by
numerical calculations, where coherent oscillations between the resonators, the
decay of coherent and Fock states, and the decay of resonator-resonator
entanglement are studied. Finally, we suggest an experimental protocol for
extracting the damping constants of qubit and resonators by measuring the
quadratures of the resonator fields.Comment: 17 pages, 9 figure
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