Frequency-Dependent Diffusion Constant of Quantum Fluids from Path Integral Monte Carlo and Tikhonov's Regularizing...

Area of Science:

• Quantum physics
• Condensed matter physics
• Computational physics

Background:

• Studying quantum liquids' transport properties at finite temperatures is crucial.
• Analytic continuation of the velocity autocorrelation function (VACF) is a key method.
• Inverting Fredholm integral equations in VACF analysis is mathematically challenging.

Purpose of the Study:

• To present a novel implementation for analytic continuation of the VACF method.
• To accurately study quantum liquid transport properties at finite temperatures.
• To improve the inversion of ill-posed linear Fredholm integral equations.

Main Methods:

• Combining Tikhonov's first-order regularizing functional with automatic regularization parameter selection methods.
• Utilizing L-curve and quasi-optimality criterion for regularization parameter selection.
• Reconstructing the real-time frequency-dependent diffusion power spectrum from limited Trotter slices.

Main Results:

• The frequency-dependent diffusion power spectrum of normal liquid (4)He exhibits a single asymmetric peak.
• The self-diffusion coefficient of (4)He was predicted to be 0.57-0.58 Å(2)/ps, matching prior studies.
• Successful reconstruction of the diffusion power spectrum was achieved without covariance matrix knowledge.

Conclusions:

• The novel method enables successful reconstruction of quantum liquid dynamics from path integral Monte Carlo simulations.
• Recommended regularization parameter selection methods (L-curve, quasi-optimality) enhance accuracy.
• Small regularization parameters suggest efficient extraction of quantum dynamics information.