We study the energy deposition in a one dimensional interacting quantum system with a point like potential modulated in amplitude. The point like potential at position $x=0$ has a constant part and a small oscillation in time with a frequency $ω$. We use bosonization, renormalization group and linear response theory to calculate the corresponding energy deposition. It exhibits a power law behavior as a function of the frequency that reflects the Tomonaga-Luttinger liquid (TLL) nature of the system. Depending on the interactions in the system, characterized by the TLL parameter $K$ of the system, a crossover between week and strong coupling for the backscattering due to the potential is possible. We compute the frequency scale $ω_\ast$, at which such crossover exists. We find that the energy deposition due to the backscattering shows different exponent for $K>1$ and $K<1$. We discuss possible experimental consequences, in the context of cold atomic gases, of our theoretical results.
Thermodynamics and Tomonaga-Luttinger liquid behavior of the quantum 1D hard rod model
CPHT, CNRS, Ecole Polytechnique, IP Paris（法国国家科学研究中心，巴黎综合理工学院，巴黎理工学院）；Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）
Tomonaga-Luttinger liquid theory for one-dimensional attractive Fermi gases
Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences（中国科学院精密测量科学与技术创新院）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Physics and Astronomy, Rice University（莱斯大学物理与天文系）；Department of Quantum Matter Physics, University of Geneva（日内瓦大学量子物质物理系）；Hefei National Laboratory（合肥国家实验室）；Department of Fundamental and Theoretical Physics, Research School of Physics, Australian National University（澳大利亚国立大学物理研究学院基础与理论物理系）
