Effective equilibrium picture in xy−xy-model with exponentially correlated noise

We study the effect of exponentially correlated noise on $xy-$model in the limit of small correlation time discussing the order-disorder transition in mean-field and the topological transition in two dimensions. We map the steady states of the non-equilibrium dynamics into an effective equilibrium theory. In mean-field, the critical temperature increases with the noise correlation time $\tau$ indicating that memory effects promote ordering. This finding is confirmed by numerical simulations. The topological transition temperature in two dimensions remains untouched. However, finite size effects induce a crossover in the vortices proliferation that is confirmed by numerical simulations

Heat, temperature and Clausius inequality in a model for active brownian particles

Methods of stochastic thermodynamics and hydrodynamics are applied to the a recently introduced model of active particles. The model consists of an overdamped particle subject to Gaussian coloured noise. Inspired by stochastic thermodynamics, we derive from the system's Fokker-Planck equation the average exchanges of heat and work with the active bath and the associated entropy production. We show that a Clausius inequality holds, with the local (non-uniform) temperature of the active bath replacing the uniform temperature usually encountered in equilibrium systems. Furthermore, by restricting the dynamical space to the first velocity moments of the local distribution function we derive a hydrodynamic description where local pressure, kinetic temperature and internal heat fluxes appear and are consistent with the previous thermodynamic analysis. The procedure also shows under which conditions one obtains the unified coloured noise approximation (UCNA): such an approximation neglects the fast relaxation to the active bath and therefore yields detailed balance and zero entropy production. In the last part, by using multiple time-scale analysis, we provide a constructive method (alternative to UCNA) to determine the solution of the Kramers equation and go beyond the detailed balance condition determining negative entropy production.Comment: 19 pages, 1 figure. Major changes in the text. 1 figure has been replace

Pressure and surface tension of an active simple liquid: a comparison between kinetic, mechanical and free-energy based approaches

We discuss different definitions of pressure for a system of active spherical particles driven by a non-thermal coloured noise. We show that mechanical, kinetic and free-energy based approaches lead to the same result up to first order in the non-equilibrium expansion parameter. The first prescription is based on a generalisation of the kinetic mesoscopic virial equation and expresses the pressure exerted on the walls in terms of the average of the virial of the inter-particle forces. In the second approach, the pressure and the surface tension are identified with the volume and area derivatives, respectively, of the partition function associated with the known stationary non-equilibrium distribution of the model. The third method is a mechanical approach and is related to the work necessary to deform the system. The pressure is obtained by comparing the expression of the work in terms of local stress and strain with the corresponding expression in terms of microscopic distribution. This is determined from the force balance encoded in the Born-Green-Yvon equation. Such a method has the advantage of giving a formula for the local pressure tensor and the surface tension even in inhomogeneous situations. By direct inspection, we show that the three procedures lead to the same values of the pressure, and give support to the idea that the partition function, obtained via the unified coloured noise approximation, is more than a formal property of the system, but determines the stationary non-equilibrium thermodynamics of the model

Effective potential method for active particles

We investigate the steady state properties of an active fluid modeled as an assembly of soft repulsive spheres subjected to Gaussian colored noise. Such a noise captures one of the salient aspects of active particles, namely the persistence of their motion and determines a variety of novel features with respect to familiar passive fluids. We show that within the so-called multidimensional unified colored noise approximation, recently introduced in the field of active matter, the model can be treated by methods similar to those employed in the study of standard molecular fluids. The system shows a tendency of the particles to aggregate even in the presence of purely repulsive forces because the combined action of colored noise and interactions enhances the the effective friction between nearby particles. We also discuss whether an effective two-body potential approach, which would allow to employ methods similar to those of density functional theory, is appropriate. The limits of such an approximation are discussed.Comment: 14 pages, 6 figures in Molecular Physics, 11 march 2016. arXiv admin note: text overlap with arXiv:cond-mat/0605094 by other author

Multidimensional Stationary Probability Distribution for Interacting Active Particles

We derive the stationary probability distribution for a non-equilibrium system composed by an arbitrary number of degrees of freedom that are subject to Gaussian colored noise and a conservative potential. This is based on a multidimensional version of the Unified Colored Noise Approximation. By comparing theory with numerical simulations we demonstrate that the theoretical probability density quantitatively describes the accumulation of active particles around repulsive obstacles. In particular, for two particles with repulsive interactions, the probability of close contact decreases when one of the two particle is pinned. Moreover, in the case of isotropic confining potentials, the radial density profile shows a non trivial scaling with radius. Finally we show that the theory well approximates the "pressure" generated by the active particles allowing to derive an equation of state for a system of non-interacting colored noise-driven particles.Comment: 5 pages, 2 figure

Speeding up the solution of the Bethe-Salpeter equation by a double-grid method and Wannier interpolation

The Bethe-Salpeter equation is a widely used approach to describe optical excitations in bulk semiconductors. It leads to spectra that are in very good agreement with experiment, but the price to pay for such accuracy is a very high computational burden. One of the main bottlenecks is the large number of k-points required to obtain converged spectra. In order to circumvent this problem we propose a strategy to solve the Bethe-Salpeter equation based on a double-grid technique coupled to a Wannier interpolation of the Kohn-Sham band structure. This strategy is then benchmarked for a particularly difficult case, the calculation of the absorption spectrum of GaAs, and for the well studied case of Si. The considerable gains observed in these cases fully validate our approach, and open the way for the application of the Bethe-Salpeter equation to large and complex systems.Comment: 5 pages, 3 figures. Accepted for Phys. Rev.

Multipolar terahertz absorption spectroscopy ignited by graphene plasmons

AbstractTerahertz absorption spectroscopy plays a key role in physical, chemical and biological systems as a powerful tool to identify molecular species through their rotational spectrum fingerprint. Owing to the sub-nanometer scale of molecules, radiation-matter coupling is typically dominated by dipolar interaction. Here we show that multipolar rotational spectroscopy of molecules in proximity of localized graphene structures can be accessed through the extraordinary enhancement of their multipolar transitions provided by terahertz plasmons. In particular, specializing our calculations to homonuclear diatomic molecules, we demonstrate that a micron-sized graphene ring with a nano-hole at the core combines a strong near-field enhancement and an inherently pronounced field localization enabling the enhancement of the dipole-forbidden terahertz absorption cross-section of $${{\rm{H}}}_{2}^{+}$$ H 2 + by 8 orders of magnitude. Our results shed light on the strong potential offered by nano-structured graphene as a robust and electrically tunable platform for multipolar terahertz absorption spectroscopy at the nanoscale

Collision quenching in the ultrafast dynamics of plasmonic materials

We explore the nonlinear response of plasmonic materials driven by ultrashort pulses of electromagnetic radiation with temporal duration of few femtoseconds and high peak intensity. By developing the Fokker-Planck-Landau theory of electron collisions, we solve analytically the collisional integral and derive a novel set of hydrodynamical equations accounting for plasma dynamics at ultrashort time scales. While in the limit of small light intensities we recover the well established Drude model of plasmas, in the high intensity limit we observe nonlinear quenching of collision-induced damping leading to absorption saturation. Our results provide a general background to understand electron dynamics in plasmonic materials with promising photonic applications in the manipulation of plasma waves with reduced absorption at the femtosecond time scale