Linear Response Theory of Composite System

Abstract

Kubo’s linear response theory is a general theory on the susceptibility or magnetization of the medium and various transport phenomena in the equilibrium region. It is based on the first-order perturbation theory and has been extended from single system to composite system in recent years. They most care about the response of the whole system but barely explore for the subsystem’s response of the composite system. In this paper, we develop a linear response theory for composite system to gain the subsystem’s information. We formulate this theory in terms of general susceptibility, after which we apply it to the derivation of a time-independent composite system composed of two coupled subsystems. That is calculating the response of subsystem 2 caused by the subsystem 1 subjected to perturbation. For a better explanation, we examine the susceptibility’s (imaginary part) images with various parameters. We point out the imaginary part of the susceptibility can be represented by Dirac δ function and change with temperature and the coupling strength. Our results provide a promising platform for the coherent manipulation of the linear response in composite system, which has potential applications for quantum information processing and statistical physics.

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Zhao, M.Y., Zhang, Y.N. Linear Response Theory of Composite System. Int J Theor Phys 59, 1788–1797 (2020). https://doi.org/10.1007/s10773-020-04445-w

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Keywords

  • Linear response
  • Composite system
  • Susceptibility