Small Amplitude Perturbation Theory (Linear Response)

  • Wilhelm Brenig


The basic equations (2.24, 28) are, of course, far from a solution of the problem of nonequilibrium statistical physics. The evaluation of the expression (2.25) for the susceptibility is difficult. In fact it is impossible in the general nonlinear case. The situation is improved a great deal for sufficiently small amplitudes of the external forces f e(t) or the Lagrange parameters f(0). Then a linear approximation for the response Q(t) can be adopted in which the statistical operator ϱ d(t) is replaced by the operator ϱ of total equilibrium. Furthermore, the initial deviation Q k (0) occurring in (2.28) can be expressed in terms of the f k (0) by means of the isothermal susceptibility X T in thermal equilibrium as
$$\Delta {Q_k}\left( 0 \right) = \mathop \sum \limits_l \chi _{kl}^Tfl\left( 0 \right).$$


External Force Classical Limit Heat Bath Relaxation Function Subtraction Term 
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  1. 3.1
    Brenig, W.: Statistische Theorie der Wärme I. 2nd ed. ( Springer, Berlin, Heidelberg 1983 )Google Scholar
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Additional Reading

  1. Kadanoff, LJP., Martin, P.C.: Ann. Phys. 24, 419 (1963) Martin, P.C., Schwinger, J.: Phys. Rev. 115, 1342 (1959)Google Scholar
  2. Martin, P.C., Schwinger, J.: Phys. Rev. 115, 1342 (1959)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Wilhelm Brenig
    • 1
  1. 1.Physik-DepartmentTechnische Universität MünchenGarchingFed. Rep. of Germany

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