(viii) Measurable quantities (applications to condensed matter physics)

Due to the general motivation of the entire area, many of the aforementioned results are of a rather formal mathematical nature and very often lack a direct link to physical application. Nonetheless, lately the experimental techniques have advanced to such an extent that one can realistically hope to be able to use the entire arsenal of non-perturbative techniques for the computation of physical quantities which are directly accessible to experiments. We can imagine that our IQFT describes a one dimensional quantum wire, possibly finite such that the boundaries capture the effects from the constrictions or with some impurities. Then one quantity which can be measured very easy without disturbing the system too much is the conductance (conductivity). In [26 ,27 ] we considered impurity systems and addressed the question to which extend one can use the above mentioned techniques to compute the conductance in the framework of a Landauer semi-classical transport theory [ 98 ] or the Kubo formula [97 ] which is the outcome of a dynamical linear-response theory. In the first description one requires the density distributions which are accessible through a TBA analysis (see (iii)) and in the second, the key quantity needed is the current-current correlation function which can be computed along the lines described above. We adopted the techniques to this set up and could demonstrate that both methods lead to the same results. In [ 25 ] we compared the conductance of a quantum wire described by a theory which included unstable particles with the one obtained from a double defect system and showed that they are qualitatively the same. Surprisingly, when computing the conductance of a quantum wire described by ATFT [ 30 ], we obtained in some cases rational values for the filling fractions which resemble those of the famous Jain [90 ] sequence occurring in the context of the quantum Hall effect. The other application we studied was concerned with the question whether it is possible to generate harmonic spectra when a three dimensional laser field is coupled to a one dimensional quantum wire [ 32 ]. High harmonic generation is the non-linear response of a medium (a crystal, an atom, a gas, ...) to a laser field. The importance of harmonic generation is related to the fact that it allows to convert infrared input radiation of frequency $%% \omega$ into light in the extreme ultraviolet regime whose frequencies are multiples of $\omega$ (nowadays even up to the order $\sim 1000$ ). In gases, composed of atoms or small molecules, this phenomenon is well understood. In more complex systems, however, for instance solid state materials, or larger molecules, high-harmonic generation is still an open problem. This is due to the fact that, until a few years ago, such systems were expected not to survive the strong laser fields one needs to produce such effects. However, nowadays, with the advent of ultrashort pulses, there exist solid-state materials whose damage threshold is beyond the required intensities of $10^{14}{\rm W/cm}^{2}$ [100 ]. As a direct consequence, there is an increasing interest in such materials as potential sources for high-harmonics. In fact, several groups are currently investigating this phenomenon in systems such as thin crystals [ 1 ,87 ], carbon nanotubes [2 ], or organic molecules [91 ,4 ]. Therefore our prediction [32 ] that high harmonics can be generated from solid state material is very important. Here one still has to explore a huge territory, as essentially all measurable quantities can be expressed in some way in terms of correlation functions. With regard to the conductance there is of course the need to consider more types of models, refine the techniques and especially important is to include temperature on the side of the Kubo formula description. Concerning the filling fractions the interesting question of a possible deeper relation to the fractional quantum Hall effect needs to be answered.