This talk is about the multi-configuration time-dependent Hartree (MCTDH) method for the approximation of multi-particle time-dependent Schr¨odinger equation. The MCTDH method approximates the multi-variate wave function by a linear combination of products of uni-variate functions and replaces the high-dimensional linear Schr¨odinger equation by a coupled system of ordinary differential equations and low-dimensional nonlinear partial differential equations. The main result yields an L2 error bound of the MCTDH approximation in terms of a best-approximation error bound in a stronger norm and of lower bounds of singular values of matrix unfoldings of the coefficient tensor. This result permits us to establish convergence of the MCTDH method to the exact wave function under appropriate conditions on the approximability of the wave function, and it points to reasons for possible failure in other cases. References [1] D. Conte and C. Lubich, An error analysis of the multi-configuration time-dependent Hartree method of quantum dynamics, Preprint, Math. Inst., Univ. Tuebingen, Jan. 2009. [2] H.-D. Meyer, F. Gatti, and G.A. Worth (eds.), Multidimensional Quantum Dynamics: MCTDH Theory and Applications, Wiley, New York, 2009.
On the multi-configuration time-dependent Hartree method of quantum dynamics
CONTE, Dajana;
2009-01-01
Abstract
This talk is about the multi-configuration time-dependent Hartree (MCTDH) method for the approximation of multi-particle time-dependent Schr¨odinger equation. The MCTDH method approximates the multi-variate wave function by a linear combination of products of uni-variate functions and replaces the high-dimensional linear Schr¨odinger equation by a coupled system of ordinary differential equations and low-dimensional nonlinear partial differential equations. The main result yields an L2 error bound of the MCTDH approximation in terms of a best-approximation error bound in a stronger norm and of lower bounds of singular values of matrix unfoldings of the coefficient tensor. This result permits us to establish convergence of the MCTDH method to the exact wave function under appropriate conditions on the approximability of the wave function, and it points to reasons for possible failure in other cases. References [1] D. Conte and C. Lubich, An error analysis of the multi-configuration time-dependent Hartree method of quantum dynamics, Preprint, Math. Inst., Univ. Tuebingen, Jan. 2009. [2] H.-D. Meyer, F. Gatti, and G.A. Worth (eds.), Multidimensional Quantum Dynamics: MCTDH Theory and Applications, Wiley, New York, 2009.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
