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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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| _version_ | 1866912281614352384 |
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| author | Klatt, Michael Andreas Bair, Christian Löwen, Hartmut Wittmann, René |
| author_facet | Klatt, Michael Andreas Bair, Christian Löwen, Hartmut Wittmann, René |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_10526 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Foundation of classical dynamical density functional theory: uniqueness of time-dependent density-potential mappings Klatt, Michael Andreas Bair, Christian Löwen, Hartmut Wittmann, René Mathematical Physics Soft Condensed Matter 82C03, 82C05 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. |
| title | Foundation of classical dynamical density functional theory: uniqueness of time-dependent density-potential mappings |
| topic | Mathematical Physics Soft Condensed Matter 82C03, 82C05 |
| url | https://arxiv.org/abs/2304.10526 |