Transport in low-dimensional interacting systems
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One-dimensional quantum many-body systems have been an interesting area of theoretical research since last 90 years. However, advances in fabrication technologies has led to influx of real materials and devices that are one-dimensional or quasi one-dimensional. These devices have brought back a renewed interest in understating the physics of such systems. However, the established Luttinger liquid theory has some limitations due to absence of scattering processes at finite temperatures. Further, any arbitrarily weak interaction potential between Luttinger liquid bosons leads to divergences already in the first order calculation. We adopt the low energy one-dimensional Wigner crystal as the strongly interacting regime of Luttinger liquid. We show that the violation of the Wiedemann-Franz law can be demonstrated by calculating correction to thermal conductance of a non-linear interacting Wigner crystal.