[NCTS Lecture Series] Time-dependent variational principle of McLachlan in many-body quantum physics
Title: [NCTS Lecture Series] Time-dependent variational principle of McLachlan in many-body quantum physics
Speaker: Prof. Vladimir U. Nazarov (Hebrew University of Jerusalem)
Time: 2025/3/10 (Mon.) 10:20-11:20
Place: NCTS Physics Lecture Hall, 4F, Cosmology Hall, NTU
Abstract
Vladimir U. NazarovFritz Haber Research Center for Molecular Dynamics & Institute of Chemistry, Hebrew University of Jerusalem*
* vladimir.nazarov@mail.huji.ac.il
By minimizing, in the L2 norm, the difference between the left- and the right-hand sides of the many-body time-dependent Schrödinger equation, the variational principle of McLachlan [1] (McLVP) provides a powerful and systematic tool for the generation of equations of motion. I will compare the use of the McLVP with more familiar methods in quantum dynamics, claiming that the former either leads to the same results or outperforms the latter.
If the trial wave function is the Slater determinant, McLVP produces a temporally and spatially nonlocal exchange potential [2]. As an illustrating example, I will discuss the performance of the corresponding wave-vector and frequency-dependent exchange kernel f_x^h(q,ω) of the homogeneous electron liquid. While the McLVP-based f_x^h(q,ω) lacks correlations by construction, I will show that it accurately accounts for exchange, reproducing features in the quantum Monte Carlo data, which the known constraint-based kernels miss [3].
I will conclude by outlining the perspective of using the McLVP to handle electronic correlations.
[1]. A. McLachlan, Mol. Phys. 8, 39 (1964).
[2]. V. U. Nazarov, Phys. Rev. B 87, 165125 (2013).
[3]. V. U. Nazarov and V. M. Silkin, Phys. Rev. B 110, 104310 (2024).
