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ON THE GROUND STATE OF SPIN-1 BOSE–EINSTEIN CONDENSATES WITH AN EXTERNAL IOFFE–PITCHARD MAGNETIC FIELD

Part of: Partial differential equations Elliptic equations and systems

Published online by Cambridge University Press:  28 May 2012

WEI LUO ,
ZHONGXUE LÜ  and
ZUHAN LIU
WEI LUO
Affiliation:
School of Mathematical Sciences, Xuzhou Normal University, Xuzhou, 221116, PR China
ZHONGXUE LÜ*
Affiliation:
School of Mathematical Sciences, Xuzhou Normal University, Xuzhou, 221116, PR China (email: lvzx1@tom.com)
ZUHAN LIU
Affiliation:
School of Mathematical Sciences, Xuzhou Normal University, Xuzhou, 221116, PR China
*
✉For correspondence; e-mail: lvzx1@tom.com
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Abstract

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In this paper, we prove the existence of the ground state for the spinor Bose–Einstein condensates with an external Ioffe–Pitchard magnetic field in the one-dimensional case. We also characterise the ground states of spin-1 Bose–Einstein condensates with an external Ioffe–Pitchard magnetic field; that is, for ferromagnetic systems, we show that, under some condition, searching for the ground state of ferromagnetic spin-1 Bose–Einstein condensates with an external Ioffe–Pitchard magnetic field can be reduced to a ‘one-component’ minimisation problem.

Keywords

ground statesspin-1 Bose–Einstein condensatethe external Ioffe–Pitchard magnetic field

MSC classification

Secondary: 35J65: Nonlinear boundary value problems for linear elliptic equations 35B45: A priori estimates
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 3 , December 2012 , pp. 356 - 369
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

Footnotes

Research is supported by the Natural Science Foundation of China (No. 10771181; 11071206), NSF of Jiangsu Province (No. BK2010172), the Postgraduate Innovation Project of Jiangsu Province (No. CXZZ11-0901) and Foundation of Xuzhou Normal University (No. 2011YLA003).

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