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Transconducting Transition for a Dynamic Boundary Coupled to Several Luttinger Liquids
B Horovitz1, T Giamarchi2, P Le Doussal3
1Department of Physics, Ben Gurion University, Beer Sheva 84105, Israel.
Researchers found a quantum phase transition in coupled Tomonaga-Luttinger liquids (TLLs) for N≥2. This transition, occurring at K≥1/2, results in a nonzero transconductance and signals Josephson coupling onset for superconducting grains.
Area of Science:
- Condensed Matter Physics
- Quantum Many-Body Systems
Background:
- Tomonaga-Luttinger liquids (TLLs) describe one-dimensional interacting electron systems.
- Dynamic boundaries, such as mobile impurities or superconducting grains, introduce unique boundary conditions.
Purpose of the Study:
- Investigate quantum phase transitions in TLLs coupled to dynamic boundaries.
- Characterize the behavior of transconductance and Josephson coupling at these transitions.
Main Methods:
- Theoretical analysis of N independent TLLs coupled to a dynamic boundary.
- Examination of the interaction parameter K and the number of TLLs N.
Main Results:
- A quantum phase transition occurs for N≥2 at K≥1/2, where TLLs lock at the particle position.
- This transition yields a nonzero transconductance of e^{2}/Nh.
- For superconducting grains, the transition indicates the onset of relevant Josephson coupling.
Conclusions:
- Dynamic boundaries can induce quantum phase transitions in TLL systems.
- The transconductance and Josephson coupling are sensitive probes of these transitions.
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