Regensburg 2025 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 37: Brownian Motion and Anomalous Diffusion
DY 37.3: Vortrag
Donnerstag, 20. März 2025, 15:30–15:45, H43
Foundation of classical dynamical density functional theory: uniqueness of time-dependent density--potential mappings — Michael Andreas Klatt2,3,1, •Christian Bair1, Hartmut Löwen1, and René Wittmann1,4 — 1Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität, Düsseldorf, Germany — 2Deutsches Zentrum für Luft- und Raumfahrt (DLR), Institut für KI Sicherheit, Ulm, Germany — 3DLR, Institut für Materialphysik im Weltraum, Köln, Germany — 4Institut für Sicherheit und Qualität bei Fleisch, Max Rubner-Institut, Kulmbach, Germany
When can we uniquely map a classical density profile to an external potential? In equilibrium, without time dependence, the one-body density is known to uniquely specify the external potential that is applied to the many-body system. This mapping from a density to the potential is the cornerstone of classical density functional theory (DFT). Here, we consider non-equilibrium, time-dependent many-body systems that evolve from a given initial condition. We derive explicit conditions, for example, no flux at the boundary, that ensure that the mapping from the density to a time-dependent external potential is unique. We thus prove the underlying assertion of dynamical density functional theory (DDFT) - without resorting to the so-called adiabatic approximation often used in applications. By ascertaining uniqueness for all n-body densities, we ensure that the proof - and the physical conclusions drawn from it - hold for general superadiabatic dynamics of interacting systems.
Keywords: classical Dynamical Density Functional Theory; Smoluchowski eqation; rigorous results