arXiv subjects

Tanja Schilling

Publications and source records attributed to Tanja Schilling.

At least 19 recordsLinked to original sources

arXiv2026

Ultrafast configuration changes and anomalous diffusion of an aromatic adsorbate on rare-gas nanoparticles

Nanoparticles (NPs) exhibit tunable catalytic properties and serve as nanoreactors for controlled multimolecular chemistry. The kinetics and reactivity of such systems are critically governed by the surface binding configurations of adsorbates, their stochastic fluctuations, and the adsorbate mobility across the nanosurface. However, resolving these properties with sufficient structural, spatial, and temporal resolution remains a major experimental challenge. Here, we study phthalocyanine adsorbates on rare-gas clusters as a test case. By combining high-resolution two-dimensional electronic spectroscopy and molecular dynamics simulations, we reveal the configurational dynamics of the adsorbates and establish a direct relation between these dynamics and the nanoscale properties of the clusters. Our findings indicate sub-diffusive surface motion and trapping of the adsorbate within single surface facets. Such dynamical behavior seems unexpected considering the weak adsorbate-surface interaction and cluster temperatures close to the sublimation point. These results provide direct insight into the ultrafast binding dynamics of molecular adsorbates on nanoscale objects, which is critical for our understanding of the chemistry of such systems.

physics.chem-ph↗

arXiv2026

How wrong is too wrong: A numerical study on the relevance of positional memory in the generalized Langevin equation

If a generalized Langevin equation contains a potential of mean force, it cannot at the same time contain a linear memory kernel and a fluctuating force that obeys a second fluctuation dissipation theorem in the sense of Kubo, and be exact. As modelers often prefer to use generalized Langevin equations that have the first three properties, one needs to ask how close the model dynamics is to the dynamics of the underlying microscopic system. To test this, we analyze a simple model system in which the potential of mean force can be well approximated by a polynomial of low order. The exact generalized Langevin equation of this model contains memory terms in addition to the linear one. We show that these additional terms, at least for the model system regarded in this article, are important for the dynamics and cannot be neglected if one intends to model core aspects of the underlying system correctly.

cond-mat.stat-mech↗

arXiv2026

On the generalized Langevin equation and the Mori projection operator technique

In statistical physics, the Nakajima-Mori-Zwanzig projection operator formalism is used to derive an integro-differential equation for observables in a Hilbert space, the generalized Langevin equation (GLE). This technique relies on the splitting of the dynamics into a projected and an orthogonal part. However, the well-posedness of the abstract Cauchy problem for the orthogonal dynamics remains an open problem. Moreover, it is rarely discussed under which assumptions the Dyson identity, which is used to derive the GLE, holds. In this article, we address this issue for rank-one projections (Mori's projection). For the Mori projection, the orthogonal dynamics is obtained from the bounded perturbation theorem. The variation of constants formula for strongly continuous semigroups then yields the GLE and the second fluctuation dissipation theorem (2FDT). We show that the variation of constants can be replaced by a limiting process in order to give a general proof of the GLE and 2FDT that does not require the differentiability of the fluctuating forces. In addition, we offer an alternative approach that does not require the bounded perturbation theorem. Our starting point is the observation that the GLE and 2FDT uniquely determine the fluctuating forces as well as the memory kernel. Furthermore, the orbit maps for the orthogonal dynamics can be directly defined via solutions of linear Volterra equations. All desired properties of the orthogonal dynamics are then proven directly from this definition. In particular, the orthogonal dynamics is a strongly continuous semigroup generated by $\overline{\mathcal{QL}}\mathcal{Q}=\mathcal{QLQ}$, where $\mathcal{L}$ is the generator of the time evolution operator, and $\mathcal{P}=1-\mathcal{Q}$ is the Mori projection operator. Our results apply to general autonomous dynamical systems whose time evolution is given by a strongly continuous semigroup.

math-ph↗

arXiv2026

Generalised Langevin Dynamics: Significance and Limitations of the Projection Operator Formalism

We discuss some mathematical aspects of the Mori-Zwanzig projection operator formalism. The core of the Mori-Zwanzig formalism is the generalised Langevin equation, which is typically derived from the Dyson-Duhamel identity. We derive the projection operator formalism for Mori's projection by means of semigroup theory, and we illustrate where rigorous methods fail for the case of Zwanzig's projection. For bounded perturbations of the time-evolution operator (e.g. for Mori's projection), the Dyson-Duhamel identity coincides with the variation of constants formula. For unbounded perturbations (e.g. for Zwanzigs's projection), the Dyson-Duhamel identity should be considered an equation for the orthogonal dynamics, for which the existence of unique solutions has yet to be established. Then we recall that all properties of Mori's generalised Langevin equation follow directly from the well-posedness of Volterra equations, irrespective of the projection operator formalism. Further, we discuss the use of Mori's generalised Langevin equation as a coarse-grained model. Finally, we illustrate that the memory term is a coupling term that is not necessarily related to memory. To this end, we introduce projections onto subspaces of 'fast' and 'slow' variables that are associated with the spectral decomposition of skew-adjoint operators. For these projections, the memory term vanishes.

math-ph↗

arXiv2026

Why life is hot

The process of evolution by natural selection leads to phenotypes of increasing fitness. For cellular chemical reaction networks, this means optimising a variety of fitness functions such as robustness, precision, or sensitivity to external stimuli. We argue that these diverse goals can be achieved by a versatile, generic mechanism: coupling chemical reaction networks to reservoirs that are strongly out of equilibrium. Using theory and numerics we show that this mechanism of optimization comes at the price of significant heat dissipation. We compute the heat flux caused by kinetic proofreading in {\it Escherichia coli} and show that it constitutes a significant fraction of the total heat flux experimentally measured in this model organism. We then demonstrate that the degree of optimality achievable saturates, and that Nature appears to operate near saturation despite high energetic costs. We conclude that `life is hot' largely because of the need for a versatile mechanism to optimise a variety of fitness functions.

cond-mat.soft↗

arXiv2025

Relevance of Aggregate Anisotropy in Sheared Suspensions of Carbon Black

Carbon Black is a filler frequently used in conductive suspensions or nanocomposites, in which it forms networks supporting electric conductivity. Although Carbon Black aggregates originate from a presumably isotropic aggregation process, the resulting particles are inherently anisotropic. Therefore, they can be expected to interact with shear flow, which significantly influences material properties. In this study, we investigate sheared suspensions of Carbon Black aggregates to elucidate the impact of aggregate anisotropy on the rheological properties. We aim at concentrations below and above the conductivity percolation threshold and comprehensively characterize particle behavior under flow conditions. Aggregates assembled by a diffusion-limited aggregation process are simulated with Langevin dynamics in simple shear flow. The simulations reveal a clear alignment of the aggregates' long axis with the flow direction, an increase in tumbling frequency with higher shear rates, and a shear-thinning response. This behavior closely parallels that of rod-like particles and underlines the significance of the anisotropic nature of Carbon Black aggregates. These findings will facilitate the optimization of nanocomposite precursor processing and the tailoring of Carbon Black-based conductive suspensions.

cond-mat.soft↗

arXiv2025

Snap, Crackle, and Pop: This is why the potential of mean force clashes with the fluctuation dissipation relation

We analyze the non-linear generalized Langevin equation which contains a thermodynamic force. We show that even for systems in thermal equilibrium the presence of the thermodynamic force implies that the auto-correlation function of the fluctuating force becomes non-stationary. We further illustrate that a standard coarse-graining procedure that neglects this fact predicts waiting-time distributions incompatible with the original, microscopic process. We conclude that one needs to proceed with care when adding thermodynamic driving forces to the Langevin equation.

cond-mat.stat-mech↗

arXiv2025

The concept of minimal dissipation and the identification of work in autonomous systems: A view from classical statistical physics

Recently, the concept of minimal dissipation has been brought forward as a means to define work performed on open quantum systems [Phys. Rev. A 105, 052216 (2022)]. We discuss this concept from the point of view of projection operator formalisms in classical statistical physics. We analyse an autonomous composite system which consists of a system and an environment in the most general sense (i.e. we neither impose conditions on the coupling between system and environment nor on the properties of the environment). One condition any useful definition of work needs to fulfill is that it reproduces the thermodynamic notion of work in the limit of weak coupling to an environment that has infinite heat capacity. We propose a projection operator route to a definition of work that reaches this limit and we discuss its relation to minimal dissipation.

quant-ph↗

arXiv2025

A universally applicable approach to connectivity percolation

Percolation problems appear in a large variety of different contexts ranging from the design of composite materials to vaccination strategies on community networks. The key observable for many applications is the percolation threshold. Unlike the universal critical exponents, the percolation threshold depends explicitly on the specific system properties. As a consequence, theoretical approaches to the percolation threshold are rare and generally tailored to the specific application. Yet, any percolating cluster forms a discrete network the emergence of which can be cast as a graph problem and analyzed using branching processes. We propose a general mapping of any kind of percolation problem onto a branching process which provides rigorous lower bounds of the percolation threshold. These bounds progressively tighten as we incorporate more information into the theory. We showcase our approach for different continuum problems finding accurate predictions with almost no effort. Our approach is based on first principles and does not require fitting parameters. As such it offers an important theoretical reference in a field that is dominated by simulation studies and heuristic fit functions.

cond-mat.stat-mech↗

arXiv2025

Polydispersity in Percolation

Every realistic instance of a percolation problem is faced with some degree of polydispersity, e.g., the pore-size distribution of an inhomogeneous medium, the size distribution of filler particles in composite materials, or the vertex degree of agents in a social network. Studies on different classes of systems have independently found very similar conceptual results for the percolation problem, i.e., that the percolation threshold is insensitive to the particular distribution controlling the polydispersity. Rather, the percolation threshold depends only on the first few moments of the distribution. In this article, we explain this frequently observed pattern using branching processes. The key observation is that a reasonable degree of polydispersity effectively does not alter the structure of the network that forms at the percolation threshold. As a consequence, the critical parameters of the monodisperse system can be analytically continued to account for polydispersity.

cond-mat.stat-mech↗

arXiv2024

Flow-induced anisotropy in a carbon black-filled silicone elastomer: electromechanical properties and structure

Carbon black (CB)-elastomers can serve as low-cost, highly deformable sensor materials, but hardly any work exists on their structure-property relationships. We report on flow-induced anisotropy, considering CB-silicone films generated via doctor blade coating. Cured films showed slight electrical anisotropy, with conductivity parallel to the coating direction being lower than perpendicular to it. Furthermore, piezoresistive sensitivity was much larger for stretch perpendicular to the coating direction than for parallel stretch. Structural analysis for length scales up to the CB agglomerate level yielded only weak evidence of anisotropy. Based on this evidence and insight from CB network simulations, we hypothesize that shear flow during coating fragments the CB network and then induces a preferential aggregate alignment, as well as increased inter-particle distances, parallel to the coating direction. As a practical conclusion, already weak anisotropic structuration suffices to cause significant electric anisotropy.

cond-mat.mtrl-sci↗

arXiv2024

Tracer dynamics in polymer networks: generalized Langevin description

Tracer diffusion in polymer networks and hydrogels is relevant in biology and technology, while it also constitutes an interesting model process for the dynamics of molecules in fluctuating, heterogeneous soft matter. Here, we study systematically the time-dependent dynamics and (non-Markovian) memory effects of tracers in polymer networks based on (Markovian) implicit-solvent Langevin simulations. In particular, we consider spherical tracer solutes at high dilution in regular, tetrafunctional bead-spring polymer networks, and control the tracer-network Lennard-Jones (LJ) interactions and the polymer density. Based on the analysis of the memory (friction) kernels, we recover the expected long-time transport coefficients, and demonstrate how the short-time tracer dynamics, polymer fluctuations, and the viscoelastic response are interlinked. Further, we fit the characteristic memory modes of the tracers with damped harmonic oscillations and identify LJ contributions, bond vibrations, and slow network relaxations, which enter the kernel with an almost linear scaling with the LJ attractions. This procedure proposes a reduced functional form for the tracer memory, allowing for a convenient inter- and extrapolation of the memory kernels. This leads eventually to highly efficient simulations utilizing the generalized Langevin equation (GLE), in which the polymer network acts as an additional thermal bath with tuneable intensity.

cond-mat.soft↗

arXiv2023

The non-equilibrium solvent response force: What happens if you push a Brownian particle

In this letter we discuss how to add forces to the Langevin equation. We derive the exact generalized Langevin equation for the dynamics of one particle subject to an external force embedded in a system of many interacting particles. The external force may depend on time and/or on the phase-space coordinates of the system. We construct a projection operator such that the drift coefficient, the memory kernel, and the fluctuating force of the generalized Langevin equation are the same as for the system without external driving. We show that the external force then enters the generalized Langevin equation additively. In addition we obtain one term which, to our knowledge, has up to now been overlooked. We analyze this additional term for an exemplary system.

cond-mat.stat-mech↗

arXiv2023

Work, Heat and Internal Energy in Open Quantum Systems: A Comparison of Four Approaches from the Autonomous System Framework

We compare definitions of the internal energy of an open quantum system and strategies to split the internal energy into work and heat contributions as given by four different approaches from autonomous system framework. Our discussion focuses on methods that allow for arbitrary environments (not just heat baths) and driving by a quantum mechanical system. As a simple application we consider an atom as the system of interest and an oscillator field mode as the environment. Three different types of coupling are analyzed. We discuss ambiguities in the definitions and highlight differences that appear if one aims at constructing environments that act as pure heat or work reservoirs. Further, we identify different sources of work (e.g. coherence, correlations, or frequency offset), depending on the underlying framework. Finally, we give arguments to favour the approach based on minimal dissipation.

quant-ph↗

arXiv2023

Optimizing the Structure of Acene Clusters

We present a study of the potential energy surface (PES) of anthracene, tetracene and pentacene clusters with up to 30 molecules. We have applied the basin-hopping Monte Carlo (BHMC) algorithm to clusters of acene molecules in order to find their lowest energy states. The acene molecules are described by the polymer-consistent force field - interface force field (PCFF-IFF). We present the structures with the lowest observed energy, and we discuss the relative stability and accessibility of structures corresponding to local energy minima.

physics.atm-clus↗

arXiv2022

Generalized Langevin dynamics simulation with non-stationary memory kernels: How to make noise

We present a numerical method to produce stochastic dynamics according to the generalized Langevin equation with a non-stationary memory kernel. This type of dynamics occurs when a microscopic system with an explicitly time-dependent Liouvillian is coarse-grained by means of a projection operator formalism. We show how to replace the deterministic fluctuating force in the generalized Langevin equation by a stochastic process, such that the distributions of the observables are reproduced up to moments of a given order. Thus, in combination with a method to extract the memory kernel from simulation data of the underlying microscopic model, the method introduced here allows to construct and simulate a coarse-grained model for a driven process.

cond-mat.stat-mech↗

arXiv2022

Hard sphere crystal nucleation rates: Reconciliation of simulation and experiment

Over the past two decades, a large number of studies addressed the topic of crystal nucleation in suspensions of hard spheres. The shared result of all these efforts is that, at low super-saturations, experimentally observed nucleation rates and numerically computed ones differ by more than ten orders of magnitude. We present precise simulation results of crystal nucleation rate densities in the meta-stable hard sphere liquid. To compare these rate densities to experimentally measured ones, we propose an interpretation of the experimental data as a combination of nucleation and crystal growth processes (rather than purely the nucleation process). This interpretation may resolve the long standing dispute about the differing rates.

cond-mat.soft↗

arXiv2022

The Interplay between Memory and Potentials of Mean Force: A Discussion on the Structure of Equations of Motion for Coarse Grained Observables

The underdamped, non-linear, generalized Langevin equation is widely used to model coarse-grained dynamics of soft and biological materials. By means of a projection operator formalism, we show under which approximations this equation can be obtained from the Hamiltonian dynamics of the underlying microscopic system and in which cases it makes sense to introduce a potential of mean force. We discuss shortcomings of previous derivations presented in the literature and demonstrate the implications of our derivation for the structure of memory terms and their connection to generalized fluctuation-dissipation relations. We show, in particular, that the widely used, simple structure which contains a potential of mean force, a memory term which is linear in the observable, and a fluctuating force which is related to the memory term by a fluctuation-dissipation relation, is neither exact nor can it, in general, be derived as a controlled approximation to the exact dynamics.

cond-mat.soft↗