Calculating energy shifts in terms of phase shifts

Yu Zhenhua; G. Baym; C. J. Pethick

doi:10.1088/0953-4075/44/19/195207

Calculating energy shifts in terms of phase shifts

Yu Zhenhua, G. Baym, C. J. Pethick

Kvanteoptik

3 Citationer (Scopus)

Abstract

We clarify the relation in interacting systems, and in particular ultracold atomic gases, between energy shifts arising from interparticle interactions and scattering phase shifts. A principle result of this paper is an expression for the energy levels of an atom in a container of arbitrary shape in the presence of a short-range scatterer, generalizing the result of Lüscher to containers of shapes other than cubic. We show that, while the energy shifts for a spherical container are under many conditions proportional to the phase shift, those for a cubic container have a more complicated structure. The general relation is extended to problems of particles in traps with smoothly varying potentials, including, e.g., the interaction of a small neutral atom with a Rydberg atom. Finally, we discuss why, even though individual energy levels are very sensitive to boundary conditions, the energies of many-body systems are not.

Originalsprog	Engelsk
Tidsskrift	Journal of Physics B: Atomic, Molecular and Optical Physics
Vol/bind	44
Udgave nummer	19
Sider (fra-til)	195207
ISSN	0953-4075
DOI	https://doi.org/10.1088/0953-4075/44/19/195207
Status	Udgivet - 14 nov. 2011

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10.1088/0953-4075/44/19/195207

Citationsformater

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abstract = "We clarify the relation in interacting systems, and in particular ultracold atomic gases, between energy shifts arising from interparticle interactions and scattering phase shifts. A principle result of this paper is an expression for the energy levels of an atom in a container of arbitrary shape in the presence of a short-range scatterer, generalizing the result of L{\"u}scher to containers of shapes other than cubic. We show that, while the energy shifts for a spherical container are under many conditions proportional to the phase shift, those for a cubic container have a more complicated structure. The general relation is extended to problems of particles in traps with smoothly varying potentials, including, e.g., the interaction of a small neutral atom with a Rydberg atom. Finally, we discuss why, even though individual energy levels are very sensitive to boundary conditions, the energies of many-body systems are not.",

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T1 - Calculating energy shifts in terms of phase shifts

AU - Zhenhua, Yu

AU - Baym, G.

AU - Pethick, C. J.

PY - 2011/11/14

Y1 - 2011/11/14

N2 - We clarify the relation in interacting systems, and in particular ultracold atomic gases, between energy shifts arising from interparticle interactions and scattering phase shifts. A principle result of this paper is an expression for the energy levels of an atom in a container of arbitrary shape in the presence of a short-range scatterer, generalizing the result of Lüscher to containers of shapes other than cubic. We show that, while the energy shifts for a spherical container are under many conditions proportional to the phase shift, those for a cubic container have a more complicated structure. The general relation is extended to problems of particles in traps with smoothly varying potentials, including, e.g., the interaction of a small neutral atom with a Rydberg atom. Finally, we discuss why, even though individual energy levels are very sensitive to boundary conditions, the energies of many-body systems are not.

AB - We clarify the relation in interacting systems, and in particular ultracold atomic gases, between energy shifts arising from interparticle interactions and scattering phase shifts. A principle result of this paper is an expression for the energy levels of an atom in a container of arbitrary shape in the presence of a short-range scatterer, generalizing the result of Lüscher to containers of shapes other than cubic. We show that, while the energy shifts for a spherical container are under many conditions proportional to the phase shift, those for a cubic container have a more complicated structure. The general relation is extended to problems of particles in traps with smoothly varying potentials, including, e.g., the interaction of a small neutral atom with a Rydberg atom. Finally, we discuss why, even though individual energy levels are very sensitive to boundary conditions, the energies of many-body systems are not.

U2 - 10.1088/0953-4075/44/19/195207

DO - 10.1088/0953-4075/44/19/195207

M3 - Journal article

SN - 0953-4075

VL - 44

SP - 195207

JO - Journal of Physics B: Atomic, Molecular and Optical Physics

JF - Journal of Physics B: Atomic, Molecular and Optical Physics

IS - 19

ER -

Calculating energy shifts in terms of phase shifts

Abstract

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