In this paper, the finite difference time domain (FDTD) method is applied to solve the Gross-Pitaevskii (GP) equation. A simple procedure to include the non-linear term of the GP equation in the FDTD algorithm is given and discussed. For validation of the FDTD method, ground state, excited state wavefunctions and energies are computed for various trap potentials and compared to results from other numerical methods. The FDTD method is shown to be suitable and accurate for solving the GP equation.
REFERENCES
1.
C. J.
Pethick
and H.
Smith
, Bose-Einstein Condensation in Dilute Gases
(Cambridge University Press
, Cambridge
, 2004
), pp. 146
–164
.2.
E. P.
Gross
, Nuovo Cimento.
20
, 454
–457
(1961
).3.
L. P.
Pitaevskii
, Sov. Phys. -JETP.
13
, 451
–454
(1961
).4.
Z.
Marojević
, E.
Göklü
, and C.
Lämmerzahl
, Comput. Phys. Commun.
184
, pp. 1920
–1930
(2013
).5.
Z.
Marojević
, E.
Göklü
, and C.
Lämmerzahl
, Comput. Phys. Commun.
202
, pp. 216
–232
(2016
).6.
P.
Muruganandam
and S. K.
Adhikari
, J. Phys. B.
36
, pp. 2501
–2514
(2003
).7.
P.
Muruganandam
and S. K.
Adhikari
, Comput. Phys. Commun.
180
, 1888
–1912
(2009
).8.
D.
Vudragovic
, I.
Vidanović
, A.
Balaž
, P.
Muruganandam
, and S. K.
Adhikari
., Comput. Phys. Commun.
183
, pp. 2021
–2025
(2012
).9.
R. K.
Kumar
, L. E.
Young-S
, D.
Vudragović
, A.
Balaž
, P.
Muruganandam
, and S. K.
Adhikari
.,Comput. Phys. Commun.
195
, pp. 117
–128
(2015
)10.
L. E.
Young-S
, D.
Vudragović
, P.
Muruganandam
, S. K.
Adhikari
, and A.
Balaž.
, Comput. Phys. Commun.
204
, pp. 209
–213
(2016
).11.
X.
Antoine
, and R.
Duboscq
, Comput. Phys. Commun.
185
, pp. 2969
–2991
(2014
).12.
X.
Antoine
, and R.
Duboscq
, Comput. Phys. Commun.
193
, pp. 95
–117
(2015
).13.
I. W.
Sudiarta
and D. J. W.
Geldart
, J. Phys. A: Math. Theor.
40
, pp. 1885
–1896
(2007
).14.
I. W.
Sudiarta
and D. J. W.
Geldart
, Physics Letters A
372
, pp. 3145
–3148
(2008
).15.
I. W.
Sudiarta
and D. J. W.
Geldart
, J. Phys. A: Math. Theor.
42
, pp. 285002
(2009
).16.
I. W.
Sudiarta
and L. M.
Angraini
, AIP Conference Proceedings
2023
, pp. 020199
(2018
).17.
M.
Mitchell
, B.
Muftakhidinov
and T.
Winchen
, Engauge Digitizer Software
, http://markummitchell.github.io/engauge-digitizer© 2019 Author(s).
2019
Author(s)
