Physics – Condensed Matter
Scientific paper
1995-10-18
Physics
Condensed Matter
latex, 9 uuencoded figures appended
Scientific paper
10.1103/PhysRevE.53.6504
We used methods of Bayesian statistical inference and the principle of maximum entropy to analytically continue imaginary-time Green's function generated in quantum Monte Carlo simulations to obtain the real-time Green's functions. For test problems, we considered chains of harmonic and anharmonic oscillators whose properties we simulated by a hybrid path-integral quantum Monte Carlo method. From the imaginary-time displacement-displacement Green's function, we first obtained its spectral density. For harmonic oscillators, we demonstrated the peaks of this function were in the correct position and their area satisfied a sum rule. Additionally, as a function of wavenumber, the peak positions followed the correct dispersion relation. For a double-well oscillator, we demonstrated the peak location correctly predicted the tunnel splitting. Transforming the spectral densities to real-time Green's functions, we conclude that we can predict the real-time dynamics for length of times corresponding to 5 to 10 times the natural period of the model. The length of time was limited by an overbroadening of the peaks in the spectral density caused by the simulation algorithm.
Bonča Janez
Gubernatis James E.
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