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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.10526 |
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Table of Contents:
- When can we map a classical density profile to an external potential? In equilibrium, without time dependence, the one-body density is known to 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 even in the presence of (known) non-conservative forces.