Generalized Langevin Equation and non-Markovian fluctuation-dissipation theorem for particle-bath systems in external oscillating fields

The Generalized Langevin Equation (GLE) can be derived from a particle-bath Hamiltonian, in both classical and quantum dynamics, and provides a route to the (both Markovian and non-Markovian) fluctuation-dissipation theorem (FDT). All previous studies have focused either on particle-bath systems with time-independent external forces only, or on the simplified case where only the tagged particle is subject to the external time-dependent oscillatory field. Here we extend the GLE and the corresponding FDT for the more general case where both the tagged particle and the bath oscillators respond to an external oscillatory field. This is the example of a charged or polarisable particle immersed in a bath of other particles that are also charged or polarizable, under an external AC electric field. For this Hamiltonian, we find that the ensemble average of the stochastic force is not zero, but proportional to the AC field. The associated FDT reads as $\langle F_P(t)F_P(t')\rangle=mk_BT\nu(t-t')+(\gamma e)^2E(t)E(t')$, where $F_{p}$ is the random force, $\nu(t-t')$ is the friction memory function, and $\gamma$ is a numerical prefactor

Single-molecule force spectroscopy with photoluminescent semiconducting polymers: Harnessing entropy

We discuss implications of a recent experimental breakthrough which uses a fluorescence-doped flexible semiconducting polymer to construct a single-molecule sensor which can detect ultra-weak forces in the molecular environment, with a grey scale down to 300 femtonewtons

General theory of the viscosity of liquids and solids from nonaffine particle motions

A new microscopic formula for the viscosity of liquids and solids is derived rigorously from a first-principles (microscopically reversible) Hamiltonian for particle-bath atomistic motion. The derivation is done within the framework of nonaffine linear response theory. The new formula may lead to a valid alternative to the Green-Kubo approach to describe the viscosity of condensed matter systems from molecular simulations without having to fit long-time tails. Furthermore, it provides a direct link between the viscosity, the vibrational density of states of the system, and the zero-frequency limit of the memory kernel

Theory of vanishing heavy-quarks contribution to quark-gluon plasma viscosity

The shear viscosity of strongly interacting dense heavy-quarks plasma is evaluated analytically using a methodology valid for strongly-correlated nonequilibrium dense matter. The shear viscosity turns out to be directly proportional to the zero-frequency limit of the spectral function. By evaluating the latter using lattice QCD data from the literature, the vanishing of interaction-dominated viscosity contribution of heavy quarks to the QGP plasma is demonstrated.Comment: arXiv admin note: substantial text overlap with arXiv:2306.0577

On a Coarse-Graining Concept in Colloidal Physics with Application to Fluid and Arrested Colloidal Suspensions in Shearing Fields

We poorly understand the macroscopic properties of complex fluids and of amorphous bodies in general. This is mainly due to the interplay between phenomena at different levels and length-scales. In particular, it is not necessarily true that the microscopic level (dominated by direct interactions) coincides with the level where the continuum description comes into play. This is typically the case in the presence of structural inhomogeneities which are inherent to all structurally disordered states of matter below close packing. As a consequence, the macroscopic response to external fields of either fluid or arrested disordered states is not well understood. In order to disentangle this complexity, in this work we build upon a simple yet seemingly powerful concept. This can be summarized as follows: the mesoscopic length-scale of structural inhomogeneities is assumed to be the characteristic length-scale of the effective building blocks, while the degrees of freedom of the primary particles are integrated out. Theoretical results are derived, in the present work, for the macroscopic response of fluid and dynamically arrested model colloidal states in fields of shear. The predictions of the coarse-grained theories and the applicability of the principle are tested in comparison with original simulation and experimental data

Theory of activated-rate processes under shear with application to shear-induced aggregation of colloids

Using a novel approximation scheme within the convective diffusion (two body Smoluchowski) equation framework, we unveil the shear-driven aggregation mechanism at the origin of structure-formation in sheared colloidal systems. The theory, verified against numerics and experiments, explains the induction time followed by explosive (irreversible) rise of viscosity observed in charge-stabilized colloidal and protein systems under steady shear. The Arrhenius-type equation with shear derived here, extending Kramers theory in the presence of shear, is the first analytical result clearly showing the important role of shear-drive in activated-rate processes as they are encountered in soft condensed matter