GENERAL |
|
|
|
|
Nonsensitive Nonlinear Homotopy Approach |
GAO Yuan1, TANG Xiao-Yan1, LOU Sen-Yue1,2,3 |
1Department of Physics, Shanghai Jiao Tong University, Shanghai 2002402Faculty of Science, Ningbo University, Ningbo 3152113School of Mathematics, Fudan University, Shanghai 200433 |
|
Cite this article: |
GAO Yuan, TANG Xiao-Yan, LOU Sen-Yue 2009 Chin. Phys. Lett. 26 110201 |
|
|
Abstract Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. We construct a new theory that combines perturbation and nonperturbation. An artificial nonlinear homotopy parameter plays the role of a perturbation parameter, while other artificial nonlinear parameters, which are independent of the original problems, introduced in the nonlinear homotopy models are nonperturbatively determined by means of the principle of minimal sensitivity. The method is demonstrated through several quantum anharmonic oscillators and a non-hermitian parity-time symmetric Hamiltonian system. In fact, the framework of the theory is rather general and can be applied to a broad range of natural phenomena. Possible applications to condensed matter physics, matter wave systems, and nonlinear optics are briefly discussed.
|
Keywords:
02.60.-x
03.65.-w
02.90.+p
|
|
Received: 16 March 2009
Published: 30 October 2009
|
|
PACS: |
02.60.-x
|
(Numerical approximation and analysis)
|
|
03.65.-w
|
(Quantum mechanics)
|
|
02.90.+p
|
(Other topics in mathematical methods in physics)
|
|
|
|
|
[1] Yang J K 2003 Phys. Rev. Lett. 91 143903 [2] Hoefer M A et al 2005 Phys. Rev. Lett. 95267206 [3] Klaiman S et al 2008 Phys. Rev. Lett. 101080402 [4] Wilson R M et al 2008 Phys. Rev. Lett. 100245302 [5] Gangadharaiah S et al 2005 Phys. Rev. Lett. 94156407 [6] Bravyi S et al 2008 Phys. Rev. Lett. 101070503 DuanL M, Demler E and Lukin M D 2003 Phys. Rev. Lett. 91 090402 [7] Wolf M M 2008 Nature Phys. 4 834 [8] Stevenson P M 1981 Phys. Rev. D 23 2916 [9] Halliday I G and Suranyi P 1980 Phys. Rev. D 21 1529 [10] Okopi\'nska A 1987 Phys. Rev. D 35 1835 [11] Lou S Y and Ni G J 1990 Sci. Sin. 33 1024 (inChinese) Lou S Y and Ni G J 1991 Sci. Sin. 34 68 (inChinese) [12] Lu W F et al 2001 Phys. Rev. D 64 025006 Lu W F, Kim C K and Nahm K 2002 Phys. Lett. B 546 177 [13] Lou S Y and Ni G J 1988 Phys. Rev. D 37 3770 Cai W and Lou S Y 2005 Commun. Theor. Phys. 43 1075 [14] Buckley I R C, Duncan A and Jones H F 1993 Phys.Rev. D 47 2554 Duncan A and Jones H F 1993 Phys. Rev. D 47 2560 [15] Guida R, Konishi K and Suzuki H 1995 Ann. Phys. 241 152 [16] Kowalski K et al 1998 Phys. Rev. Lett. 811195 [17] Liao S and Cheung K F 2003 J. Engng Math. 45105 Liao S 2004 Appl. Math. Comput. 147 499 [18] Bender C M and Wu T T 1969 Phys. Rev. 1841231 Bender C M and Wu T T 1971 Phys. Rev. Lett. 27461 Bender C M and Wu T T 1973 Phys. Rev. D 7 1620 [19] Mei{\ssner H and Steinborn E O 1997 Phys. Rev. A 56 1189 [20] Heng T H et al 2008 Chin. Phys. Lett. 25 3535 Heng T H et al 2007 Chin. Phys. Lett. 24 592 [21] Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243 [22] Bender C M and Gunne D V 1999 J. Math. Phys. 40 4616 [23] Musslimani Z H et al 2008 Phys. Rev. Lett. 100 030402 |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|