Force balance in thermal quantum many-body systems from Noether’s theorem

Title data

Hermann, Sophie ; Schmidt, Matthias:
Force balance in thermal quantum many-body systems from Noether’s theorem.
In: Journal of Physics A: Mathematical and Theoretical. Vol. 55 (2022) Issue 46 . - 464003.
ISSN 1751-8113
DOI: https://doi.org/10.1088/1751-8121/aca12d

Official URL:

Abstract in another language

We address the consequences of invariance properties of the free energy of spatially inhomogeneous quantum many-body systems. We consider a specific position-dependent transformation of the system that consists of a spatial deformation and a corresponding locally resolved change of momenta. This operator transformation is canonical and hence equivalent to a unitary transformation on the underlying Hilbert space of the system. As a consequence, the free energy is an invariant under the transformation. Noether’s theorem for invariant variations then allows to derive an exact sum rule, which we show to be the locally resolved equilibrium one-body force balance. For the special case of homogeneous shifting, the sum rule states that the average global external force vanishes in thermal equilibrium.

Further data

Item Type:	Article in a journal
Refereed:	Yes
Keywords:	force balance; quantum statistical mechanics; YBG equation; density functional theory; Noether’s theorem
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
Result of work at the UBT:	Yes
DDC Subjects:	500 Science > 530 Physics
Date Deposited:	15 Jul 2023 21:15
Last Modified:	17 Jul 2023 09:39
URI:	https://eref.uni-bayreuth.de/id/eprint/86111