Second Sound in Systems of One-Dimensional Fermions

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems
• Low-Temperature Physics

Background:

• Understanding emergent phenomena in low-dimensional quantum systems is crucial.
• Sound propagation in interacting fermion systems reveals fundamental properties.
• Galilean invariance provides a theoretical framework for studying such systems.

Purpose of the Study:

• To investigate the nature of sound propagation in one-dimensional (1D) Galilean invariant fermion systems.
• To identify and characterize novel sound modes beyond simple density waves.
• To analyze the temperature and frequency dependence of sound damping and heat transport.

Main Methods:

• Theoretical analysis of one-dimensional fermion systems.
• Low-temperature and low-frequency regime analysis.
• Hydrodynamic theory to describe sound propagation and heat transport.

Main Results:

• Discovery of a second sound mode, distinct from density waves, at low temperatures.
• This second sound corresponds to the ballistic propagation of heat.
• Weak damping of the second sound is observed at high frequencies, dependent on an exponentially small relaxation rate.

Conclusions:

• A second sound mode exists in 1D Galilean invariant fermion systems at low temperatures.
• This mode facilitates ballistic heat transport, with damping becoming significant only at lower frequencies.
• The findings offer insights into heat transport mechanisms in quantum many-body systems.