计算自旋轨道耦合 Spin-2 BEC 基态的带拉格朗日乘子的正规梯度流法

Abstract

Abstract:

In this paper, a normalized gradient flow with Lagrange multipliers is designed to compute ground states of spin-orbit coupled Spin-2 Bose-Einstein condensates. By excavating the implicit relation between projection coefficients, the difficult that the existed conditions (the conservation of total mass and magnetization) of the model problem is insufficient to determine all the projection coefficients, is overcome. Extensive numerical experiments are done to compute the ground states of spin-orbit coupled Spin-2 BECs with cyclic/ferromagenetic interactions. As a result, the effectiveness of the two algorithms is verified, and the phase transformation law about how the stripe pattern ground states and the square-lattice pattern ground states of spin-orbit coupled Spin-2 BECs change to each other with the spin-orbit coupling parameter,are revealed.

Key words: Bose-Einstein condensate, Ground state, Normalized gradient flow, Lagrange multiplier

CLC Number:

O242.1

Yuan Yongjun. A Normalized Gradient Flow with Lagrange Multipliers for Computing Ground States of Spin-Orbit Coupled Spin-2 Bose-Einstein Condensates[J].Acta mathematica scientia,Series A, 2023, 43(5): 1607-1619.

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[1]	Anderson M H, Ensher J R, Matthewa M R, et al. Observation of Bose-Einstein condensation in a dilute atomic vapor. Science, 1995, 269: 198-201 pmid: 17789847
[2]	Antoine X, Levitt A, Tang Q. Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods. Journal of Computational Physics, 2017, 343:92-109
[3]	Bao W, Cai Y. Mathematical models and numerical methods for spinor Bose-Einstein condensates. Communications in Computational Physics, 2018, 24: 899-965
[4]	Bao W, Du Q. Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow. SIAM Journal on Scientific Computing, 2004, 25: 1674-1697 doi: 10.1137/S1064827503422956
[5]	Bao W, Lim F. Computing ground states of spin-1 Bose-Einstein condensates by the normalized gradient flow. SIAM Journal on Scientific Computing, 2008, 30 1925-1948 doi: 10.1137/070698488
[6]	Bao W, Tang W. Ground state solution of Bose-Einstein condensate by directly minimizing the energy functional. Journal of Computational Physics, 2003, 187: 230-254 doi: 10.1016/S0021-9991(03)00097-4
[7]	Bao W, Wang H. A mass and magnetization conservervative and energy-diminishing numerical method for computing ground state of spin-1 Bose-Einstein condensates. SIAM Journal on Numerical Analysis, 2007, 45(5): 2177-2200 doi: 10.1137/070681624
[8]	Bao W, Wang H, Markowich P A. Ground, symmetric and central vortex states in rotating Bose-Einstein condensates. Communications in Mathematical Sciences, 2005, 3(1): 57-88 doi: 10.4310/CMS.2005.v3.n1.a5
[9]	Bose. Plancks gesetz und lichtquantenhypothese. Zeitschrift fur Physik, 1924, 26: 178-181 doi: 10.1007/BF01327326
[10]	Bradley C C, Sackett C A, Tollett J J, Hulet R G. Evidence of Bose-Einstein condensation in an atomic gas with attractive interaction. Physical Review Letters, 1995, 75: 1687-1690
[11]	Cai Y, Liu W. Efficient and accurate gradient flow methods for computing ground states of spinor Bose-Einstein condensates. Journal of Computational Physics, 2021, 433: 110183 doi: 10.1016/j.jcp.2021.110183
[12]	Davis K B, Mewes M O, Andrews M R, et al. Bose-Einstein condensation in a gas of sodium atoms. Physical Review Letters, 1995, 75: 3969-3973 pmid: 10059782
[13]	Einstein A. Quantentheorie des einatomigen idealen gases. Sitzungsberichte der Preussischen Akademie der Wissenschaften, 1924, 22: 261-267
[14]	Einstein A. Quantentheorie des einatomigen idealen gases, zweite abhandlung. Sitzungsberichte der Preussischen Akademie der Wissenschaften, 1925, 1: 3-14
[15]	Ho T L. Spinor Bose condensates in optical traps. Physical Review Letters, 1998, 81: 742-745 doi: 10.1103/PhysRevLett.81.742
[16]	Kawaguchi Y, Ueda M. Spinor Bose-Einstein condensates. Physics Reports, 2012, 520: 253-381 doi: 10.1016/j.physrep.2012.07.005
[17]	Liu W, Cai Y. Normalized gradient flow with Lagrange multiplier for computing ground states of Bose-Einstein condensates. SIAM Journal on Scientific Computing, 2021, 43(1): B219-B242 doi: 10.1137/20M1328002
[18]	Lin Y J, Compton R L, Jimenez-Garcia K, et al. Synthetic magmetic fields for ultracold neutral stoms. Nature, 2009, 462: 628-632 doi: 10.1038/nature08609
[19]	Lin Y J, Compton R L, Perry A R, et al. Bose-Einstein condensates in a uniform light-induced vector potential. Physical Review Letters, 2009, 102: 130401 doi: 10.1103/PhysRevLett.102.130401
[20]	Lin Y J, Jimenez-Garcia K, Spielman I B. A spin-orbit-coupled Bose-Einstein condensates. Nature, 2011, 471: 83-86 doi: 10.1038/nature09887
[21]	Stamper-Kurn D M, Andrews M R, Chikkatur A P, et al. Optical confinement of a Bose-Einstein condensate. Physical Review Letters, 1998, 80: 2027-2030 doi: 10.1103/PhysRevLett.80.2027
[22]	Stamper-Kurn D M, Ueda M. Spinor Bose gases: Symmetries, magnetism, and quantum dynamics. Review of Modern Physics, 2013, 85: 1191-1244 doi: 10.1103/RevModPhys.85.1191
[23]	Yuan Y, Xu Z, Tang Q, Wang H. The numerical study of the ground states of spin-1 Bose-Einstein condensates with spin-orbit-coupling. East Asian Journal on Applied Mathematics, 2018, 8(3): 598-610 doi: 10.4208/eajam

A Normalized Gradient Flow with Lagrange Multipliers for Computing Ground States of Spin-Orbit Coupled Spin-2 Bose-Einstein Condensates

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