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Coherent State-Based Path Integral Methodology for Computing the Wigner Phase Space Distribution.

Amartya Bose¹, Nancy Makri¹

¹Department of Chemistry , University of Illinois , 505 S. Mathews Avenue , Urbana , Illinois 61801 , United States.

The Journal of Physical Chemistry. A

|April 16, 2019

Summary

This summary is machine-generated.

This study presents a novel path integral method for accurately calculating the Wigner phase space density in complex, multidimensional systems. This approach overcomes convergence issues in traditional methods, enabling precise quantum simulations.

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Area of Science:

Quantum Mechanics
Computational Chemistry
Statistical Physics

Background:

Accurate evaluation of Wigner phase space density for multidimensional systems is challenging.
Path integral Monte Carlo methods, while exact for Boltzmann density, suffer from poor convergence for Wigner distribution due to Fourier integrals.
The Monte Carlo sign problem limits applicability to systems with many degrees of freedom.

Purpose of the Study:

To develop a path integral method that mitigates the Monte Carlo sign problem for Wigner density calculation.
To enable accurate Wigner phase space density evaluation for systems with many degrees of freedom.
To provide an efficient and numerically exact approach for quantizing initial conditions in classical trajectory simulations.

Main Methods:

Utilizes a path integral representation of the coherent state density, avoiding Fourier integrals for rapid convergence.
Employs the relationship between coherent state and Wigner densities, using destructive phase cancellation to manage series truncation and avoid oscillatory regions.
Incorporates information-guided noise reduction (IGNoR) to enhance Monte Carlo statistics in difficult regimes.

Main Results:

The developed method successfully calculates the Wigner density for strongly anharmonic one-dimensional models, a system-bath Hamiltonian, and the formamide molecule.
Results show significant improvement in convergence and accuracy compared to approximate methods.
Demonstrates applicability to systems with many degrees of freedom, overcoming limitations of standard path integral Monte Carlo.

Conclusions:

The coherent state-based path integral method offers an efficient, numerically exact approach for Wigner phase space density construction.
This method is suitable for systems with numerous degrees of freedom, addressing a key challenge in quantum simulations.
The technique is valuable for quantizing initial conditions in classical trajectory-based simulations of dynamical properties.