Virial Relations for Electrons Coupled to Quantum Field Modes

Area of Science:

• Quantum chemistry
• Theoretical physics
• Computational chemistry

Background:

• Growing interest in the Pauli-Fierz Hamiltonian for describing molecular systems strongly coupled to photonic modes.
• Understanding modifications to chemical properties in cavity quantum electrodynamics compared to free space.

Purpose of the Study:

• To present a set of virial relations for many-electron systems coupled to classical and quantum fields.
• To demonstrate the relevance of these relations for mass renormalization and energy calculations.
• To provide an exact method for obtaining total energies from potentials within quantum electrodynamical density functional theory.

Main Methods:

• Utilizing the Pauli-Fierz Hamiltonian in dipole approximation and length gauge.
• Developing and applying novel virial relations.
• Connecting virial relations to mass renormalization and energy calculations.

Main Results:

• A set of exact virial relations for the described systems.
• Demonstrated connection between virial relations and mass renormalization.
• An exact method for calculating total energies from potentials.

Conclusions:

• The presented virial relations are a significant advancement for studying quantum-field-coupled electron systems.
• These relations provide a powerful tool for quantum electrodynamical density functional theory.
• The findings facilitate a deeper understanding of modified chemical properties in cavity environments.