Semiclassical calculation of the vibrational echo

The infrared echo measurement probes the time scales of the molecular motions that couple to a vibrational transition. Computation of the echo observable within rigorous quantum mechanics is problematic for systems with many degrees of freedom, motivating the development of semiclassical approximations to the nonlinear optical response. We present a semiclassical approximation to the echo observable, based on the Herman-Kluk propagator. This calculation requires averaging over a quantity generated by two pairs of classical trajectories and associated stability matrices, connected by a pair of phase-space jumps. Quantum, classical, and semiclassical echo calculations are compared for a thermal ensemble of noninteracting anharmonic oscillators. The semiclassical approach uses input from classical mechanics to reproduce the significant features of a complete, quantum mechanical calculation of the nonlinear response

Sushi in the United States, 1945-1970

Sushi first achieved widespread popularity in the United States in the mid-1960s. Many accounts of sushi’s US establishment foreground the role of a small number of key actors, yet underplay the role of a complex web of large-scale factors that provided the context in which sushi was able to flourish. This article critically reviews existing literature, arguing that sushi’s US popularity arose from contingent, long-term, and gradual processes. It examines US newspaper accounts of sushi during 1945–1970, which suggest the discursive context for US acceptance of sushi was considerably more propitious than generally acknowledged. Using California as a case study, the analysis also explains conducive social and material factors, and directs attention to the interplay of supply- and demand-side forces in the favorable positioning of this “new” food. The article argues that the US establishment of sushi can be understood as part of broader public acceptance of Japanese cuisine

INTERFERENCE AND QUANTIZATION IN SEMICLASSICAL VIBRATIONAL RESPONSE FUNCTIONS

W. Noid, G. Ezra, and R. Loring, J. Chem. Phys. 119, 1003 (2003).S. Gruenbaum and R. Loring, J. Chem. Phys. 128, in press (2008).Author Institution: Department of Chemistry and Chemical Biology, Baker Laboratory; Cornell University, Ithaca, New York 14853The calculation of an optical response function is a direct way to predict the results of a wide range of linear and nonlinear spectroscopic measurements. As quantum response theory is impratical for large systems and as classical response functions can be qualitativly incorrect, there is a need for a method to calculate spectroscopic response functions semiclassically. The semiclassical Herman-Kluk propagator has previously been applied to both linear and third--order vibrational response functions. In this approach, spectroscopic response functions are expressed as multiple phase-space integrals over pairs of classical trajectories and their associated stability matrices. For anharmonic oscillators this procedure has demonstrated quantitative agreement with quantum response functions; however, the calculations were computationally challenging even for small systems}. Here we determine how the Herman-Kluk linear response function reproduces the quantum result using only classical dynamical information. This analysis identifies the pairs of trajectories that are most important on different time scales as well as suggests a simplifying procedure wherein the interference between pairs of classical trajectories is treated approximately, resulting in an integral over a single average trajectory, as in a purely classical calculation}. The extension of this procedure to nonlinear response functions is also considered