Perfect absorption in Schrödinger-like problems using non-equidistant complex grids

Two non-equidistant grid implementations of infinite range exterior complex scaling are introduced that allow for perfect absorption in the time dependent Schr\"odinger equation. Finite element discrete variables grid discretizations provide as efficient absorption as the corresponding finite elements basis set discretizations. This finding is at variance with results reported in literature [L. Tao et al., Phys. Rev. A 48, 063419 (2009)]. For finite differences, a new class of generalized $Q$-point schemes for non-equidistant grids is derived. Convergence of absorption is exponential $\sim \Delta x^{Q-1}$ and numerically robust. Local relative errors $\sim10^{-9}$ are achieved in a standard problem of strong-field ionization.

[1]  Christophe Besse,et al.  A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrödinger Equations , 2008 .

[2]  J. G. Muga,et al.  Complex absorbing potentials , 2004 .

[3]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[4]  A. Scrinzi,et al.  Dynamic Exchange in the Strong Field Ionization of Molecules. , 2015, Physical Review Letters.

[5]  A. Scrinzi,et al.  Photoionization of few electron systems: a hybrid coupled channels approach , 2014, 1412.3666.

[6]  Norbert J. Mauser,et al.  On the non-equivalence of perfectly matched layers and exterior complex scaling , 2013, J. Comput. Phys..

[7]  Dexter Kozen,et al.  New , 2020, MFPS.

[8]  Angel Rubio,et al.  Modeling electron dynamics coupled to continuum states in finite volumes with absorbing boundaries , 2014 .

[9]  J. Combes,et al.  A class of analytic perturbations for one-body Schrödinger Hamiltonians , 1971 .

[10]  André D. Bandrauk,et al.  Electron-nuclear dynamics of multiphoton H + 2 dissociative ionization in intense laser fields , 1998 .

[11]  Schafer,et al.  High-order harmonic generation from atoms and ions in the high intensity regime. , 1992, Physical review letters.

[12]  Thomas N. Rescigno,et al.  TOPICAL REVIEW: Solving the three-body Coulomb breakup problem using exterior complex scaling , 2004 .

[13]  C. William McCurdy,et al.  Implementation of exterior complex scaling in B-splines to solve atomic and molecular collision problems , 2004 .

[14]  L. Tao.  Long-time solution of the time-dependent Schroedinger equation for an atom in an electromagnetic field using complex coordinate contours , 2009 .

[15]  Hiroyuki Kamada.  Communications in Mathematical Physics Compact Scalar-flat Indefinite Kähler Surfaces with Hamiltonian S 1-Symmetry , .

[16]  Ursula Keller,et al.  Interpreting electron-momentum distributions and nonadiabaticity in strong-field ionization , 2014 .

[17]  Stroud,et al.  Solving the time-dependent Schrödinger equation using complex-coordinate contours. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[18]  C. Hernández-García,et al.  Targeting multiple rescatterings through VUV-controlled high-order-harmonic generation , 2014 .

[19]  The shape resonance , 1987 .

[20]  P. Schlagheck,et al.  A study of one-dimensional transport of Bose–Einstein condensates using exterior complex scaling , 2013, 1310.3669.

[21]  H. Muller,et al.  Interpreting attoclock measurements of tunnelling times , 2014, Nature Physics.

[22]  A. Scrinzi,et al.  Infinite-range exterior complex scaling as a perfect absorber in time-dependent problems , 2010, 1002.2520.

[23]  S. Chu,et al.  Exterior complex scaling method in time-dependent density-functional theory: Multiphoton ionization and high-order-harmonic generation of Ar atoms , 2013 .

[24]  N. Moiseyev,et al.  Tunneling rates in bound systems using smooth exterior complex scaling within the framework of the finite basis set approximation , 1990 .

[25]  A. Scrinzi,et al.  A finite element implementation of exterior complex scaling for the accurate determination of resonance energies , 1993 .

[26]  David E. Manolopoulos,et al.  Quantum scattering via the log derivative version of the Kohn variational principle , 1988 .

[27]  A. Scrinzi,et al.  Double photo-electron momentum spectra of Helium at infrared wavelength , 2015, 1511.06655.