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Updated: Jul 2, 2026
08:01
The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Transport in a dissipative Luttinger liquid
Zoran Ristivojevic1, Thomas Nattermann
1Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, 50937 Köln, Germany.
Physical Review Letters
|September 4, 2008
Summary
We theoretically investigated transport through a single impurity in a Luttinger liquid with dissipation. Dissipation strongly suppresses transport, altering the current-voltage relationship and linear conductance at different temperatures.
Area of Science:
- Condensed matter physics
- Quantum transport phenomena
Background:
- Luttinger liquid theory describes interacting one-dimensional electron systems.
- Single impurities act as scattering centers, affecting electronic transport.
- Dissipative environments (Ohmic baths) introduce energy loss mechanisms.
Purpose of the Study:
- To theoretically analyze the impact of a single impurity on transport in a one-channel Luttinger liquid.
- To investigate the role of Ohmic dissipation in modifying transport properties.
- To determine the temperature dependence of conductance and the behavior of Friedel oscillations.
Main Methods:
- Theoretical modeling of quantum transport.
- Analysis of a single impurity in a Luttinger liquid model.
- Calculations for zero and nonzero temperatures.
Main Results:
- Nonzero dissipation makes the impurity a relevant perturbation, strongly suppressing transport.
- At zero temperature, current-voltage relation follows I ~ exp(-E0/eV).
- At nonzero temperature, linear conductance is proportional to exp(-sqrt(CE0/kBT)).
- Friedel oscillation decay saturates beyond a characteristic length scale.
Conclusions:
- Ohmic dissipation fundamentally alters transport through a single impurity in a Luttinger liquid.
- The impurity's relevance and transport suppression are key consequences of dissipation.
- Temperature significantly affects the conductance, with distinct behaviors at zero and nonzero temperatures.
- Dissipation influences the spatial extent of Friedel oscillations.
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