Noninteracting trapped fermions in double-well potentials: Inverted-parabola kernel

Naftali R. Smith, David S. Dean, Pierre Le Doussal, Satya N. Majumdar, Grégory Schehr

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We study a system of N noninteracting spinless fermions in a confining double-well potential in one dimension. We show that when the Fermi energy is close to the value of the potential at its local maximum, physical properties, such as the average density and the fermion position correlation functions, display a universal behavior that depends only on the local properties of the potential near its maximum. This behavior describes the merging of two Fermi gases, which are disjoint at sufficiently low Fermi energies. We describe this behavior in terms of a correlation kernel that we compute analytically and we call it the inverted parabola kernel. As an application, we calculate the mean and variance of the number of particles in an interval of size 2L centered around the position of the local maximum, for sufficiently small L. We discuss the possibility of observing our results in experiments, as well as extensions to nonzero temperature and to higher space dimensions.

Original languageEnglish
Article number053602
JournalPhysical Review A
Issue number5
StatePublished - 1 May 2020
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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