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Center for Nonlinear Studies |
Response theory describes all experimental measurements and is the basis for computing linear and non-linear spectra. Yet, the simple classical limit of quantum response functions, often used in MD simulations of large systems, leads to divergence. I will discuss the origin and general features of this divergence. Using a simple perturbative expansion, we can improve the accuracy of classical response functions within a finite time range. To develop a non-perturbative treatment, we explore the classical-quantum correspondence of quantum transitions of anharmonic systems. Using the Morse oscillator as an example, we determine its exact quantum response function from classical dynamics by quantizing classical phase space and identifying the classical correspondence for the dipole operator. I will discuss the algebraic basis of this analysis and the common structures of the potentials that can be solved exactly or almost exactly using classical dynamics. For quasi-periodic systems, we establish a one-to-one correspondence between quantum transitions and classical trajectories by means of reconstruction and quantization of classical phase space. Our approach recovers the spectral analysis technique for the special case of linear response functions and builds on the concept of interference among multiple classical trajectories for non-linear response functions. Finally, I will discuss the implications for MD simulations of condensed phase spectra. References: [1] Wu and Cao, JCP 115, 5381 (2001) [2] Maksym and Cao, JCP 122, 024109 (2005) [3] Maksym and Cao, PRL 95, 1804005 (2005) [4] Maksym and Cao, PRL 96, 030403 (2006)
Host: Andrei Piryatinski