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Phonon-mediated Casimir interaction between mobile impurities in one-dimensional quantum liquids
Michael Schecter1, Alex Kamenev2
1School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA.
Physical Review Letters
|May 3, 2014
Summary
Virtual phonons mediate a long-range interaction between impurities in quantum liquids. This interaction
Area of Science:
- Condensed matter physics
- Quantum mechanics
- Low-dimensional systems
Background:
- Quantum liquids exhibit complex interactions mediated by emergent quasiparticles.
- Impurities in one-dimensional systems can significantly alter their properties.
- The Casimir effect demonstrates long-range forces arising from quantum fluctuations.
Purpose of the Study:
- To investigate the nature and characteristics of interactions induced by virtual phonons scattering off impurities in a one-dimensional quantum liquid.
- To explore the potential for tuning the attractive or repulsive nature of this interaction.
Main Methods:
- Theoretical analysis of virtual phonon scattering off impurities in a 1D quantum liquid.
- Calculation of the induced interaction potential and its dependence on impurity separation.
- Investigation of impurity-phonon scattering amplitudes and their relation to integrability.
Main Results:
- Virtual phonons induce a long-range interaction decaying as 1/r^3, slower than van der Waals forces.
- The interaction's sign (attractive/repulsive) is determined by impurity-phonon scattering amplitudes.
- A universal form for scattering amplitudes is identified, vanishing in integrable models.
Conclusions:
- The phonon-mediated interaction offers a novel mechanism for long-range forces in 1D quantum systems.
- Tunable interactions can be achieved by manipulating impurity parameters around integrable points.
- This provides a pathway to control emergent quantum phenomena through impurity engineering.
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