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SMAI-JCM
SMAI Journal of
Computational Mathematics
Erratum: Numerical Simulations on
Nonlinear Quantum Graphs with
the GraFiDi Library
Christophe Besse, Romain Duboscq & Stefan Le Coz
Volume 11 (2025), p. 37-38.
https://doi.org/10.5802/smai-jcm.118
© The authors, 2025.
The SMAI Journal of Computational Mathematics is a member
of the Centre Mersenne for Open Scientific Publishing
http://www.centre-mersenne.org/
Submissions at https://smai-jcm.centre-mersenne.org/ojs/submission
e-ISSN: 2426-8399
SMAI Journal of Computational Mathematics
Vol. 11, 37-38 (2025)
Erratum: Numerical Simulations on Nonlinear Quantum Graphs
with the GraFiDi Library
Christophe Besse 1
Romain Duboscq 2
Stefan Le Coz 3
1 Institut de Mathématiques de Toulouse ; UMR5219, Université de Toulouse ; CNRS, UPS
IMT, F-31062 Toulouse Cedex 9, France
E-mail address: Christophe.Besse@math.univ-toulouse.fr
2 Institut de Mathématiques de Toulouse ; UMR5219, Université de Toulouse ; CNRS, INSA
IMT, F-31077 Toulouse, France
E-mail address: Romain.Duboscq@math.univ-toulouse.fr
3 Institut de Mathématiques de Toulouse ; UMR5219, Université de Toulouse ; CNRS, UPS
IMT, F-31062 Toulouse Cedex 9, France
E-mail address: stefan.lecoz@math.cnrs.fr.
2020 Mathematics Subject Classification. 35R02, 65N06, 35Q55.
Keywords. Quantum Graphs; Python Library; Nonlinear Schrodinger equation; Finite Differences; Ground
states.
In the published version of our article [1], an error occurred in the presentation of Listing 8. Due to
an oversight during the production process, Listing 8 was inadvertently replaced by a copy of Listing 7.
The correct version of Listing 8 is provided below.
fun = {}
fun[(’D’, ’B’, ’0’)]=lambda x: np.exp(-10e-2*(x-20)**2)
fun[(’C’, ’A’, ’0’)]=lambda x: np.exp(-10e-2*(x-20)**2)
fun[(’A’, ’B’, ’0’)]=lambda x: 1-(x-10)*x/50
fun[(’B’, ’A’, ’0’)]=lambda x: 1+(x-5)*x/20
fun[(’B’, ’A’, ’1’)]=lambda x: 1+(x-10)*x/30
u = WF(fun,g)
rho = 1
u = rho*u/WF.norm(u,2)
def E(u):
return -0.5*WF.Lap(u).dot(u) - 0.25*WF.norm(u,4)**4
En0 = E(u)
delta_t = 10e-1
Epsilon = 10e-8
M_1 = g.Id - delta_t*g.Lap
This work was supported by the ANR LabEx CIMI (grant ANR-11-LABX-0040) within the French State Programme
Investissements d’Avenir.
https://doi.org/10.5802/smai-jcm.118
© The authors, 2025
37
C. Besse, R. Duboscq, et al.
for n in range(1000):
u_old = u
M = M_1 - delta_t*GR.Diag(g,abs(u)**2)
u = WF.Solve(M,u)
u = rho*WF.abs(u)/WF.norm(u,2)
En = E(u)
print(f"Energy evolution: {En-En0 : 12.8e}",end=’\r’)
En0 = En
Stop_crit = WF.norm(u-u_old,2)/WF.norm(u_old,2)<Epsilon
if Stop_crit:
break
_=WF.draw(u)
print()
Listing 8. Computation of a ground state using the CNGF method.
References
[1] Christophe Besse, Romain Duboscq, and Stefan Le Coz. Numerical simulations on nonlinear quantum graphs
with the GraFiDi library. SMAI J. Comput. Math., 8:1–47, 2022.
38


Erratum: Numerical Simulations on Nonlinear Quantum Graphs with the GraFiDi Library

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