Mode-coupling theory of lattice dynamics for classical and quantum crystals

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Materials science

Background:

• Phonon quasiparticles are key to understanding nuclear dynamics in condensed matter.
• The harmonic approximation is limited; anharmonicity is crucial for accurate predictions of thermal properties.
• Highly anharmonic systems require non-perturbative approaches for lattice dynamics.

Purpose of the Study:

• To derive an exact generalized Langevin equation for quantum nuclear dynamics in crystals.
• To develop a formulation of vibrational spectra that fully incorporates anharmonicity.
• To establish a method for calculating quasiparticle lineshapes in anharmonic systems.

Main Methods:

• Application of the Mori-Zwanzig projector formalism.
• Projection onto reciprocal space quasiparticles and use of linear response theory.
• Mode-coupling approach for systematic perturbative expansion and self-consistent equations.

Main Results:

• An exact generalized Langevin equation for quantum nuclear dynamics was derived.
• A formulation for vibrational spectra accounting for anharmonicity was obtained.
• Self-consistent equations for quasiparticle lineshapes were derived, requiring only static Kubo correlation functions.

Conclusions:

• The developed theory accurately describes vibrational spectra and quasiparticle lineshapes in anharmonic systems.
• The method's inputs can be obtained from path-integral or ab initio molecular dynamics.
• The theory was successfully illustrated on face-centered cubic 4He, a strongly anharmonic quantum crystal.