Noninteracting trapped Fermions in double-well potentials: inverted parabola kernel
| Autor: | Naftali R. Smith, Pierre Le Doussal, David S. Dean, Satya N. Majumdar, Grégory Schehr |
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| Přispěvatelé: | Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Laboratoire Ondes et Matière d'Aquitaine (LOMA), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique de l'ENS (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics
Condensed Matter::Quantum Gases Statistical Mechanics (cond-mat.stat-mech) [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] Parabola FOS: Physical sciences Fermi energy Disjoint sets Fermion Mathematical Physics (math-ph) Space (mathematics) 01 natural sciences [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] 010305 fluids & plasmas Matter waves and collective properties of cold atoms and molecules Position (vector) Quantum Gases (cond-mat.quant-gas) Kernel (statistics) Quantum mechanics 0103 physical sciences 010306 general physics Condensed Matter - Quantum Gases Condensed Matter - Statistical Mechanics Mathematical Physics Fermi Gamma-ray Space Telescope |
| Zdroj: | Phys.Rev.A Phys.Rev.A, 2020, 101 (5), pp.053602. ⟨10.1103/PhysRevA.101.053602⟩ |
| Popis: | We study a system of $N$ noninteracting spinless fermions in a confining, double-well potential in one dimension. When the Fermi energy is close to the value of the potential at its local maximum we show that 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 new 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 $L$. Finally, we discuss the possibility of observing our results in experiments, as well as the extensions to nonzero temperature and to higher space dimensions. 16 pages, 8 figures |
| Databáze: | OpenAIRE |
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