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Title: Monte Carlo Study of Real Time Dynamics on the Lattice

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Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 117; Journal Issue: 8; Related Information: CHORUS Timestamp: 2017-06-24 16:54:18; Journal ID: ISSN 0031-9007
American Physical Society
Country of Publication:
United States

Citation Formats

Alexandru, Andrei, Başar, Gökçe, Bedaque, Paulo F., Vartak, Sohan, and Warrington, Neill C.. Monte Carlo Study of Real Time Dynamics on the Lattice. United States: N. p., 2016. Web. doi:10.1103/PhysRevLett.117.081602.
Alexandru, Andrei, Başar, Gökçe, Bedaque, Paulo F., Vartak, Sohan, & Warrington, Neill C.. Monte Carlo Study of Real Time Dynamics on the Lattice. United States. doi:10.1103/PhysRevLett.117.081602.
Alexandru, Andrei, Başar, Gökçe, Bedaque, Paulo F., Vartak, Sohan, and Warrington, Neill C.. 2016. "Monte Carlo Study of Real Time Dynamics on the Lattice". United States. doi:10.1103/PhysRevLett.117.081602.
title = {Monte Carlo Study of Real Time Dynamics on the Lattice},
author = {Alexandru, Andrei and Başar, Gökçe and Bedaque, Paulo F. and Vartak, Sohan and Warrington, Neill C.},
abstractNote = {},
doi = {10.1103/PhysRevLett.117.081602},
journal = {Physical Review Letters},
number = 8,
volume = 117,
place = {United States},
year = 2016,
month = 8

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevLett.117.081602

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Cited by: 8works
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  • We used methods of Bayesian statistical inference and the principle of maximum entropy to analytically continue imaginary-time Green{close_quote}s functions generated in quantum Monte Carlo simulations to obtain the real-time Green{close_quote}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{close_quote}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 areas satisfied a sum rule. Additionally, as a function of wave number, the peak positions followed themore » correct dispersion relation. For a double-well oscillator, we demonstrated that the peak location correctly predicted the tunnel splitting. Transforming the spectral densities to real-time Green{close_quote}s functions, we conclude that we can predict the real-time dynamics for length of times corresponding to five to ten 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. {copyright} {ital 1996 The American Physical Society.}« less
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  • In this paper the authors report the initial steps in the development of a Monte Carlo method for evaluation of real-time Feynman path integrals for many-particle dynamics. The approach leads to Gaussian factors. These Gaussian factors result from the use of a generalization of their new discrete distributed approximating functions (DDAFs) to continuous distributed approximating functions (CDAFs) so as to replace the exact coordinate representation free-particle propagator by a {open_quotes}CDAF-class, free-particle propagator{close_quotes} which is highly banded. The envelope of the CDAF-class free propagator is the product of a {open_quotes}bare Gaussian{close_quotes}, exp[{minus}(x{prime} {minus} x){sup 2}{sigma}{sup 2}(0)/(2{sigma}{sup 4}(0) + {h_bar}{sup 2}{tau}{sup 2}/m{supmore » 2})], with a {open_quotes}shape polynomial{close_quotes} in (x{prime}{minus}x){sup 2}, where {sigma}(0) is a width parameter at zero time (associated with the description of the wavepacket in terms of Hermite functions), {tau} is the time step ({tau} = t/N, where t is the total propagation time), and x and x{prime} are any two configurations of the system. The bare Gaussians are used for Monte Carlo integration of a path integral for the survival probability of a Gaussian wavepacket in a Morse potential. The approach appears promising for real-time quantum Monte Carlo studies based on the time-dependent Schroedinger equation, the time-dependent von Neumann equation, and related equations. 38 refs., 3 figs., 3 tabs.« less
  • The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables is termed the 'weight', and its magnitude is related to the importance of the stochastic trajectory. We investigate the use of Monte Carlo algorithms to improve the sampling of the weighted trajectories and thus reduce sampling error in a simulation of quantum dynamics. The method can be applied to calculations in real time, as well as imaginary time for which Monte Carlo algorithms are more-commonly used. The Monte-Carlo algorithmsmore » are applicable when the weight is guaranteed to be real, and we demonstrate how to ensure this is the case. Examples are given for the anharmonic oscillator, where large improvements over stochastic sampling are observed.« less
  • Purpose: In-treatment tumor localization is critical for the management of tumor motion in lung cancer radiotherapy. Conventional tumor-tracking methods using a kV or MV x-ray projection has limited contrast. To facilitate real-time, marker-less and low-dose in-treatment image tumor tracking, we propose a novel scheme using Compton scatter imaging. This study reports Monte Carlo (MC) simulations on this scheme for the purpose of proof-of-principle. Methods: A slit x-ray beam along the patient superior-inferior (SI) direction is directed to the patient, intersecting the patient lung at a 2D plane containing majority part of the tumor motion trajectory. X-ray photons are scattered duemore » to Compton effect from this plane, which are spatially collimated by, e.g., a pinhole, on one side of the plane and then captured by a detector behind it. The captured image, after correcting for x-ray attenuation and scatter angle variation, reflects the electron density, which allows visualization of the instantaneous anatomy on this plane. We performed MC studies on a phantom and a patient case for the initial test of this proposed method. Results: In the phantom case, the contrast-resolution calculated using tumor/lung as foreground/background for kV fluoroscopy, cone-beam CT, and scattering image were 0.0625, 0.6993, and 0.5290, respectively. In the patient case, tumor motion can be clearly observed in the scatter images. Compared to fluoroscopy, scattering imaging also significantly reduced imaging dose because of its narrower beam design. Conclusion: MC simulation studies demonstrated the potential of the proposed scheme in terms of capturing the instantaneous anatomy of a patient on a 2D plane. Clear visualization of the tumor will probably facilitate ‘marker-less’ and ‘real-time’ tumor tracking with low imaging dose. NIH (1R01CA154747-01, 1R21CA178787-01A1 and 1R21EB017978-01A1)« less