On some mathematical problems for open quantum systems with varying particle number

We derive the effective Hamiltonian $H - \mu N$ for open quantum systems with varying particle number from first principles within the framework of non-relativistic quantum statistical mechanics. We prove that under physically motivated assumptions regarding the size of the system and the range of the interaction, this form of the Hamiltonian is unique up to a constant. Our argument relies firstly on establishing a rigorous version of the surface-to-volume ratio approximation, which is routinely used in an empirical form in statistical mechanics, and secondly on showing that the Hilbert space for systems with varying particle number must be isomorphic to Fock space. Together, these findings provide a rigorous mathematical justification for the standard grand canonical formalism employed in statistical physics.

• Publication year

  2026

• Venue

  Unknown venue

• Publication date

  2026-02-25

• Fields of study

  Mathematics, Physics

• Identifiers
  arXiv 2602.21781
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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