Persistent correlations in colloidal suspension

Thomas Franosch (Univ. Innsbruck)

Transport properties  of a hard-sphere colloidal fluid are investigated by Brownian dynamics simulations. We implement a novel algorithm for the time-dependent velocity-autocorrelation function (VACF) essentially eliminating the noise of the bare random motion. The measured VACF reveals  persistent  anti-correlations manifested by a negative algebraic power-law tail \(t^{-5/2}\) at all densities. At small packing fractions the simulations fully agree with the analytic low-density prediction, yet  the amplitude of the tail becomes dramatically suppressed as the  packing fraction is increased. The mode-coupling theory of the glass transition provides a qualitative explanation for the strong variation   in terms of the static compressibility as well as the  slowing down of the structural relaxation.

In the second part of the presentation, I will discuss a microrheological set-up where a single probe particle is immersed in a complex fluid and exposed to a strong external force driving the system out of equilibrium. The time-dependent response of a probe particlein a dilute suspension of Brownian particles to a large step-force is derived analytically, exact in first order of the density of the bath particles. The time-dependent drift velocity approaches its stationary state value exponentially fast for arbitrarily small driving in striking contrast to the power-law prediction of linear response encoded in the long-time tails of the velocity autocorrelation function. We show that the stationary-state behavior depends nonanalytically on the driving force and connect this behavior to the persistent correlations in the equilibrium state.

A tale of Pfaffian persistence tails told by a Painlevé VI transcendent

Ivan Dornic (SPEC CEA Saclay)

We identify the persistence probability for the zero-temperature non-equilibrium Glauber dynamics of the half-space Ising chain as a particular Painlevé VI transcendent, with monodromy exponents (1/2,1/2,0,0). Among other things, this characterization a la Tracy-Widom permits to relate our specific Bonnet-Painlevé VI to the one found by Jimbo & Miwa and characterizing the lattice diagonal correlation functions at all temperatures for the planar static Ising model. In particular, in terms of the standard critical exponents eta=1/4 and beta=1/8 for the latter, this implies that the probability that the limiting Gaussian real Kac's polynomial has no real root decays with an exponent 4(eta+beta)=3/4.

Pressure and forces in active matter

Alexandre Solon (LPTMC)

Active matter, composed of self-propelling entities, is found across scales in nature, from cellular tissues to animal groups. Such systems, as well as engineered active materials, exhibit many types of collective behaviors and unusual mechanical properties. In this talk, I will focus on different aspects of the interactions between active fluids and boundaries or passive objects, and show that they lead to intriguing effects, specific to active systems. In particular, I will discuss the absence of equation of state for the pressure of active fluids, the instability of a filament in an active bath, long-range interactions mediated by an active fluid and the localization of active particles in a random potential.

Emergent phenomena from correlation and competition: a case of figure from high temperature superconductivity

Marcello Civelli (LPS Orsay)

Emergent phenomena are common in correlated systems. For instance, in correlated quantum materials novel phases appear displaying remarkable properties, like e.g. colossal magneto-resistance, exotic charge and magnetic order, quantum criticality, unconventional superconductivity….Tuning the system from one phase to another via the application of an external parameter, like temperature, pressure, doping, or by manipulating intrinsic parameters via, for example, light-matter interaction, offer the possibility to exploit a large variety of different functionalities on the same device and opens the route to the development of novel technologies.

Two main concepts that frame the emergence of novel phenomena from correlation have been at the front stage. On one side the competition between quantum phases, famously advocated for example in the case of quantum critical phase transitions in heavy fermion compounds. On the other side, the idea that “more is different” (P.W. Anderson), i.e. that our understanding of these new quantum phenomena require a new quantum state of matter, sharply different from the ones that we have known so far.

We shall show how these two concepts merge in the most known exotic state of matter rising from correlation, the high-temperature superconductivity in cuprates. The scenario that we propose is obtained by resolving the Hubbard Model, which is the simplest model capturing the salient features of cuprates. In particular we shall show that an unprecedented form of superconducting pairing arises from correlation, requiring to go beyond the main concepts of unconventional superconductivity developed so far.