Simulations of Bose fields at finite temperature

Area of Science:

• Quantum mechanics
• Statistical physics
• Condensed matter physics

Background:

• Bose-Einstein condensation (BEC) describes a state of matter formed by cooling bosons to near absolute zero.
• Understanding the thermal behavior and equilibrium states of Bose gases is crucial for BEC research.
• Existing theories may have limitations in describing the nonperturbative dynamics of Bose gases.

Purpose of the Study:

• To introduce a time-dependent projected Gross-Pitaevskii equation for homogeneous Bose gases.
• To investigate the evolution of randomized initial wave functions towards equilibrium.
• To determine the validity range of a second-order theory for Bose-Einstein condensation by comparing it with numerical data.

Main Methods:

• Development of a time-dependent projected Gross-Pitaevskii equation.
• Numerical simulation of randomized initial wave functions.
• Comparison of numerical results with predictions from a gapless, second-order theory of Bose-Einstein condensation.

Main Results:

• The introduced equation successfully evolves randomized wave functions to equilibrium.
• A specific temperature range was identified where the second-order theory accurately describes the Bose gas behavior.
• The nonperturbative nature of the Gross-Pitaevskii equation suggests its applicability when relevant modes are highly occupied.

Conclusions:

• The time-dependent projected Gross-Pitaevskii equation provides a valuable tool for studying partially condensed Bose gases.
• The study establishes criteria for the validity of existing theoretical models in describing BEC.
• The developed method has potential applications for other boson field systems.