Rainbow Nambu-Goldstone Modes under a Shear Flow

Area of Science:

• Theoretical physics
• Condensed matter physics
• Quantum field theory

Background:

• Spontaneous symmetry breaking (SSB) in physical systems leads to emergent phenomena.
• Nambu-Goldstone modes are characteristic excitations in systems with SSB.
• Understanding non-equilibrium dynamics is crucial for modern physics.

Purpose of the Study:

• To investigate the behavior of Nambu-Goldstone modes in an O(N) scalar model subjected to shear flow.
• To characterize the novel gapless modes arising from spontaneous symmetry breaking under non-equilibrium conditions.
• To explore the unique dispersion relations of these modes.

Main Methods:

• Analysis of an O(N) scalar model.
• Application of shear flow to the model.
• Identification and characterization of Nambu-Goldstone modes and their transformations.
• Derivation of the dispersion relation for the emergent modes.

Main Results:

• The single Nambu-Goldstone mode associated with O(N)→O(N-1) symmetry breaking splits into an infinite number of gapless modes.
• These novel modes are termed
• rainbow Nambu-Goldstone modes.
• The rainbow Nambu-Goldstone modes exhibit distinct group velocities.
• A fractional dispersion relation of ω∼k_{1}^{2/3} was identified, where k_{1} is the wave number along the flow.

Conclusions:

• Shear flow in an O(N) scalar model induces unique non-equilibrium phenomena.
• The emergent rainbow Nambu-Goldstone modes possess properties not observed in equilibrium systems.
• This study reveals new insights into symmetry breaking and excitation dynamics in driven systems.