A new quantum statistical evaluation method for time correlation functions

D. N. Zubarev, Yu. G. Rudoi

D. N. Zubarev, Yu. G. Rudoi

Dave Thirumalai, B. J. Berne

Patrick Huang, Alexandra Viel, K. Birgitta Whaley

We describe and systematically analyze new implementations of the Projection Operator Imaginary Time Spectral Evolution (POITSE) method for the Monte Carlo evaluation of excited state energies. The POITSE method involves the computation of a correlation function in imaginary time. Decay of this function contains information about excitation energies, which can be extracted by a spectral transform. By incorporating branching processes in the Monte Carlo propagation, we compute these correlation functions with significantly reduced statistical noise. Our approach allows for the stable evaluation of small energy differences in situations where the previous POITSE implementation was limited by this noise.

Philipp Stegmann, Satyendra Nath Gupta, Gilad Haran +1 more

Among the best known quantities obtainable from photon correlation measurements are the g ( m ) correlation functions. Here, we introduce a new procedure to evaluate these correlation functions based on higher-order factorial cumulants C F, m that integrate over the time dependence of the correlation functions, that is, summarize the available information at different time spans. In a systematic manner, the information content of higher-order correlation functions as well as the distribution of photon waiting times is taken into account. Our procedure greatly enhances the sensitivity for probing correlations and, moreover, is robust against a limited counting efficiency and time resolution in experiment. It can be applied even in case g ( m ) is not accessible at short time spans. We use the new evaluation scheme to analyze the photon emission of a plasmonic cavity coupled to a single quantum dot. We derive criteria that must hold if the system can be described by a generic Jaynes–Cummings model. A violation of the criteria can be explained by the presence of an additional excited quantum dot state.

Vladimir S. Filinov

A new numerical approach to time correlation functions in the Wigner representation of quantum statistical mechanics has been developed. The time correlation functions have been presented in the form of the integral of the Weil symbol of operators and the Fourier transform of the product of matrix elements of the dynamic propagators. For the last function the integral Wigner-Liouville type equation has been derived. The initial condition for this equation has been obtained in the form of the Fourier transform of the Wiener path integral representation of the matrix elements of the propagators at initial time. The numerical procedure for solving this equation combining both molecular dynamics and Monte Carlo methods has been developed.