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behavior. Phys Rev A 49:2421–2431. doi:10.1103/PhysRevA.49.2421, http://link.aps.org/
doi/10.1103/PhysRevA.49.2421
55. Ammosov MV, Delone NB, Krainov VP (1986) Tunnel ionization of complex atoms and
atomic ions in a varying electromagnetic-field. Zh E ´ ksp Teor Fiz 91:2008–2013
56. Parker SD, McCurdy C (1989) Propagation of wave packets using the complex basis
function method. Chem Phys Lett 156(5):483–488. doi:10.1016/S0009-2614(89)87316-6,
http://www.sciencedirect.com/science/article/pii/S0009261489873166
57. Bengtsson J, Lindroth E, Selstø S (2008) Solution of the time-dependent Schr€ odinger
equation using uniform complex scaling. Phys Rev A 78:032502. doi:10.1103/PhysRevA.
78.032502, http://link.aps.org/doi/10.1103/PhysRevA.78.032502
58. Bengtsson J, Lindroth E, Selstø S (2012) Wave functions associated with time-dependent,
complex-scaled Hamiltonians evaluated on a complex time grid. Phys Rev A 85:013419.
doi:10.1103/PhysRevA.85.013419, http://link.aps.org/doi/10.1103/PhysRevA.85.013419
59. Gilary I, Fleischer A, Moiseyev N (2005) Calculations of time-dependent observables in
non-Hermitian quantum mechanics: the problem and a possible solution. Phys Rev A 72:
012,117. doi:10.1103/PhysRevA.72.012117, http://link.aps.org/doi/10.1103/PhysRevA.72.012117
60. Garcı ´a-Moliner F, Flores F (2009) Introduction to the theory of solid surfaces.
Cambridge University Press, Cambridge
61. Kudrnovsky ´ J, Drchal V, Turek I, Weinberger P (1994) Magnetic coupling of interfaces: a
surface-Green’s-function approach. Phys Rev B 50:16105–16108. doi:10.1103/PhysRevB.
50.16105, http://link.aps.org/doi/10.1103/PhysRevB.50.16105
62. Boucke K, Schmitz H, Kull HJ (1997) Radiation conditions for the time-dependent
Schr€ odinger equation: application to strong-field photoionization. Phys Rev A 56(1):763–771
63. Ermolaev A, Puzynin I, Selin A, Vinitsky S (1999) Integral boundary conditions for the timedependent Schr€ odinger equation: atom in a laser field. Phys Rev A 60(6):4831–4845
64. Hellums J, Frensley W (1994) Non-Markovian open-system boundary conditions for the
time-dependent Schr€ odinger equation. Phys Rev B 49(4):2904–2906
65. Kurth S, Stefanucci G, Almbladh CO, Rubio A, Gross EKU (2005) Time-dependent quantum
transport: a practical scheme using density functional theory. Phys Rev B 72(3):035308
66. Inglesfield JE (2001) Embedding at surfaces. Comput Phys Commun 137(1):89–107
67. Inglesfield JE (2011) A time-dependent embedding calculation of surface electron emission.
J Phys Condens Matter 23(30):305004
68. Antoine X, Arnold A, Besse C, Ehrhardt M, Scha ¨dle A (2008) A review of transparent and
artificial boundary conditions techniques for linear and nonlinear Schr€ odinger equations.
Commun Comput Phys 4:729–796
69. Inglesfield JE (1981) A method of embedding. J Phys C Solid State 14(26):3795–3806
70. Inglesfield J (2008) Time-dependent embedding. J Phys Condens Matter 20:095215
71. Ehrhardt M (1999) Discrete transparent boundary conditions for general Schr€ odinger-type
equations. VLSI Des 9(4):325–338
72. Szmytkowski R, Bielski S (2004) Dirichlet-to-Neumann and Neumann-to-Dirichlet embedding methods for bound states of the Schr€ odinger equation. Phys Rev A 70(4):042103
73. Frensley W (1990) Boundary conditions for open quantum systems driven far from equilibrium. Rev Mod Phys 62(3):745–791
74. De Giovannini U, Larsen AH, Rubio A (2015) Modeling electron dynamics coupled to
continuum states in finite volumes. Eur Phys J B 88(3):56. doi:10.1140/epjb/e2015-50808-0
75. Neuhauser D, Baer M (1989) The application of wave packets to reactive atom–diatom
systems: a new approach. J Chem Phys 91(8):4651–4657
76. Neuhauser D, Baer M (1989) The time-dependent Schr€ odinger equation: application of
absorbing boundary conditions. J Chem Phys 90(8):4351
77. Berenger JP (1994) A perfectly matched layer for the absorption of electromagnetic waves.
J Comput Phys 114(2):185–200
Dynamical Processes in Open Quantum Systems from a TDDFT Perspective:. . .
269
behavior. Phys Rev A 49:2421–2431. doi:10.1103/PhysRevA.49.2421, http://link.aps.org/
doi/10.1103/PhysRevA.49.2421
55. Ammosov MV, Delone NB, Krainov VP (1986) Tunnel ionization of complex atoms and
atomic ions in a varying electromagnetic-field. Zh E ´ ksp Teor Fiz 91:2008–2013
56. Parker SD, McCurdy C (1989) Propagation of wave packets using the complex basis
function method. Chem Phys Lett 156(5):483–488. doi:10.1016/S0009-2614(89)87316-6,
http://www.sciencedirect.com/science/article/pii/S0009261489873166
57. Bengtsson J, Lindroth E, Selstø S (2008) Solution of the time-dependent Schr€ odinger
equation using uniform complex scaling. Phys Rev A 78:032502. doi:10.1103/PhysRevA.
78.032502, http://link.aps.org/doi/10.1103/PhysRevA.78.032502
58. Bengtsson J, Lindroth E, Selstø S (2012) Wave functions associated with time-dependent,
complex-scaled Hamiltonians evaluated on a complex time grid. Phys Rev A 85:013419.
doi:10.1103/PhysRevA.85.013419, http://link.aps.org/doi/10.1103/PhysRevA.85.013419
59. Gilary I, Fleischer A, Moiseyev N (2005) Calculations of time-dependent observables in
non-Hermitian quantum mechanics: the problem and a possible solution. Phys Rev A 72:
012,117. doi:10.1103/PhysRevA.72.012117, http://link.aps.org/doi/10.1103/PhysRevA.72.012117
60. Garcı ´a-Moliner F, Flores F (2009) Introduction to the theory of solid surfaces.
Cambridge University Press, Cambridge
61. Kudrnovsky ´ J, Drchal V, Turek I, Weinberger P (1994) Magnetic coupling of interfaces: a
surface-Green’s-function approach. Phys Rev B 50:16105–16108. doi:10.1103/PhysRevB.
50.16105, http://link.aps.org/doi/10.1103/PhysRevB.50.16105
62. Boucke K, Schmitz H, Kull HJ (1997) Radiation conditions for the time-dependent
Schr€ odinger equation: application to strong-field photoionization. Phys Rev A 56(1):763–771
63. Ermolaev A, Puzynin I, Selin A, Vinitsky S (1999) Integral boundary conditions for the timedependent Schr€ odinger equation: atom in a laser field. Phys Rev A 60(6):4831–4845
64. Hellums J, Frensley W (1994) Non-Markovian open-system boundary conditions for the
time-dependent Schr€ odinger equation. Phys Rev B 49(4):2904–2906
65. Kurth S, Stefanucci G, Almbladh CO, Rubio A, Gross EKU (2005) Time-dependent quantum
transport: a practical scheme using density functional theory. Phys Rev B 72(3):035308
66. Inglesfield JE (2001) Embedding at surfaces. Comput Phys Commun 137(1):89–107
67. Inglesfield JE (2011) A time-dependent embedding calculation of surface electron emission.
J Phys Condens Matter 23(30):305004
68. Antoine X, Arnold A, Besse C, Ehrhardt M, Scha ¨dle A (2008) A review of transparent and
artificial boundary conditions techniques for linear and nonlinear Schr€ odinger equations.
Commun Comput Phys 4:729–796
69. Inglesfield JE (1981) A method of embedding. J Phys C Solid State 14(26):3795–3806
70. Inglesfield J (2008) Time-dependent embedding. J Phys Condens Matter 20:095215
71. Ehrhardt M (1999) Discrete transparent boundary conditions for general Schr€ odinger-type
equations. VLSI Des 9(4):325–338
72. Szmytkowski R, Bielski S (2004) Dirichlet-to-Neumann and Neumann-to-Dirichlet embedding methods for bound states of the Schr€ odinger equation. Phys Rev A 70(4):042103
73. Frensley W (1990) Boundary conditions for open quantum systems driven far from equilibrium. Rev Mod Phys 62(3):745–791
74. De Giovannini U, Larsen AH, Rubio A (2015) Modeling electron dynamics coupled to
continuum states in finite volumes. Eur Phys J B 88(3):56. doi:10.1140/epjb/e2015-50808-0
75. Neuhauser D, Baer M (1989) The application of wave packets to reactive atom–diatom
systems: a new approach. J Chem Phys 91(8):4651–4657
76. Neuhauser D, Baer M (1989) The time-dependent Schr€ odinger equation: application of
absorbing boundary conditions. J Chem Phys 90(8):4351
77. Berenger JP (1994) A perfectly matched layer for the absorption of electromagnetic waves.
J Comput Phys 114(2):185–200
Dynamical Processes in Open Quantum Systems from a TDDFT Perspective:. . .
269