Scholarlink

<p>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)&#xa0;—&#xa0;without resorting to the so-called adiabatic approximation often used in applications. By ascertaining uniqueness for all <i>n</i>-body densities, we ensure that the proof&#xa0;—&#xa0;and the physical conclusions drawn from it&#xa0;—&#xa0;hold for general <i>superadiabatic</i> dynamics of interacting systems even in the presence of (known) non-conservative forces.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Foundation of classical dynamical density functional theory: uniqueness of time-dependent density–potential mappings

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年5月18日

查看全文
  • Michael Andreas Klatt,
  • Christian Bair,
  • Hartmut Löwen,
  • René Wittmann

摘要

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.