URN to cite this document: urn:nbn:de:bvb:703-epub-8154-8
Title data
Hermann, Sophie ; Sammüller, Florian ; Schmidt, Matthias:
Noether invariance theory for the equilibrium force structure of soft matter.
In: Journal of Physics A: Mathematical and Theoretical.
Vol. 57
(2024)
Issue 17
.
- 175001.
ISSN 1751-8113
DOI der Verlagsversion: https://doi.org/10.1088/1751-8121/ad3ab2
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Abstract
We give details and derivations for the Noether invariance theory that characterizes the spatial equilibrium structure of inhomogeneous classical many-body systems, as recently proposed and investigated for bulk systems (Sammüller et al 2023 Phys. Rev. Lett. 130 268203). Thereby an intrinsic thermal symmetry against a local shifting transformation on phase space is exploited on the basis of the Noether theorem for invariant variations. We consider the consequences of the shifting that emerge at second order in the displacement field that parameterizes the transformation. In a natural way the standard two-body density distribution is generated. Its second spatial derivative is thereby balanced by two further and different two-body correlation functions, which respectively introduce thermally averaged force correlations and force gradients in a systematic and microscopically sharp way into the framework. Separate exact self and distinct sum rules express this balance. We exemplify the validity of the theory on the basis of computer simulations for the Lennard–Jones gas, liquid, and crystal, the Weeks–Chandler–Andersen fluid, monatomic Molinero–Moore water at ambient conditions, a three-body-interacting colloidal gel former, the Yukawa and soft-sphere dipolar fluids, and for isotropic and nematic phases of Gay–Berne particles. We describe explicitly the derivation of the sum rules based on Noether’s theorem and also give more elementary proofs based on partial phase space integration following Yvon’s theorem.
Further data
Item Type: | Article in a journal |
---|---|
Keywords: | Noether-constrained correlations; pair correlation function;
classical statistical mechanics; YBG equation; density functional theory; Noether’s theorem; Brownian dynamics simulations |
DDC Subjects: | 500 Science > 530 Physics |
Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Chair Theoretical Physics II > Chair Theoretical Physics II - Univ.-Prof. Dr. Matthias Schmidt Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Chair Theoretical Physics II |
Language: | English |
Originates at UBT: | Yes |
URN: | urn:nbn:de:bvb:703-epub-8154-8 |
Date Deposited: | 24 Jan 2025 08:46 |
Last Modified: | 24 Jan 2025 08:47 |
URI: | https://epub.uni-bayreuth.de/id/eprint/8154 |