Abstract
So far we have discussed bulk matter as a collection of material points which are always in thermodynamic equilibrium with neighboring material points. The parameters which determine the equilibrium state, such as temperature, pressure or chemical potentials, may vary from location to location and with time. They are, however, well defined for each material point.
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Notes
- 1.
We shall soon see why they are called so.
- 2.
The symbol P in this book is used heavily, for momentum, polarization, and so forth. We therefore denote the probability operator by W, an allusion to the German word Wahrscheinlichkeit for probability.
- 3.
Since the symbol W had to be assigned to the probability operator, we here denote work by \(\mathrm{d}A\) alluding to Arbeit, German for work.
- 4.
Governed by its own laws.
- 5.
It should be clear from the context whether we speak of the observable or its expectation value in the perturbed state W t .
- 6.
Only perturbations in the past contribute.
- 7.
Note that we look upon time within the framework of the Heisenberg picture.
- 8.
Note however that the dielectric susceptibility χ jk (ω, q) is defined by splitting off a factor 1 ∕ ε0 because of \(\mathbf{\mathit{D}} = \mathbf{\mathit{P}} + {\epsilon }_{0}\mathbf{\mathit{E}}\), in usual notation.
- 9.
Photons, deuterium or helium nuclei are bosons, neutrinos, protons and electrons behave as fermions.
- 10.
Magnetic moment per unit volume.
- 11.
Super-conductivity or super-fluidity do not fit into this framework.
- 12.
Every system has an environment. There are actions of the environment on the system such that the re-action of the system on the environment can be neglected. A parameter describing such a one-sided action of the environment on a system is called external. Just think of a static electric field \(\mbox{ $\mathcal{E}$}\) produced by a plate capacitor the voltage of which is kept constant.
- 13.
The heat current density J { u} is nothing else but the conduction part of the internal energy current density.
- 14.
The square matrix L must not be singular.
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Hertel, P. (2012). Linear Response Theory. In: Continuum Physics. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29500-3_3
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