Van der Waals interactions: evaluations by use of a statistical mechanical method

Area of Science:

• Quantum mechanics
• Statistical mechanics
• Atomic and molecular physics

Background:

• Van der Waals interactions are crucial for molecular behavior.
• Standard quantum mechanics (Schrödinger equation) describes these interactions but has limitations.
• Casimir-Polder interactions, important at larger separations, are typically derived from field theory.

Purpose of the Study:

• To explore the induced van der Waals interaction between neutral atoms/molecules.
• To demonstrate the equivalence between Casimir-Polder and van der Waals interactions.
• To validate the use of Casimir energy as a correction in molecular energy calculations.

Main Methods:

• Utilizing a statistical mechanical method with path integral representation.
• Applying standard quantum mechanical perturbation theory to second order.
• Comparing results from statistical mechanics with those from field theory.

Main Results:

• Explicitly showed the equivalence of Casimir-Polder and van der Waals interactions using the statistical mechanical method.
• Established this equivalence to leading order for short separations where retardation is negligible.
• Provided numerical estimates for Casimir energy, including analysis for uniform electron gas.

Conclusions:

• The equivalence validates the use of Casimir-Polder interaction calculations within a statistical mechanical framework.
• This equivalence suggests that incorporating Casimir energy corrections enhances the accuracy of molecular energy computations.
• The findings have implications for improving theoretical models in atomic and molecular physics.