Recently, I've been selected for an ICTP program named Physics of Complex Systems. But, I have a keen interest in Particle Physics & Quantum networks. As statistical mechanics involved in Complex systems. One of my professors said that statistical mechanics could be a helpful tool for particle physics.
From the point of view of statistical mechanics, particle physics is a special case of the formalism: In statistical mechanics one is interested in the probability distribution of certain degrees of freedom and in studying their properties by computing the identities satisfied by the correlation functions of the probability distribution. Particle physics focuses on a special case of this approach, where the degrees of freedom are the fields whose one-particle excitations are the particles-for the Standard Model these are the quarks, leptons, the Higgs and the gauge bosons. And in particle physics one is interested in the special case of invariance under global Lorentz transformations and of particular gauge transformations of the fields, which impose additional constraints on the correlation functions. So one is interested in probability distributions of infinitely many degrees of freedom, with the special properties implied by invariance under global Lorentz transformations and particular gauge transformations.
Statistical mechanics isn't just a ``helpful tool'' for particle physics; it's the other way around! Particle physics is a particular example of statistical mechanics, where the probability distributions of the physical quantities are peaked about their average values and these do represent the typical values.
Quantum networks don't have anything, directly, to do with particle physics. It does appear, however, that they can provide a way for computing certain quantities that are relevant for particle physics and that can't be computed efficiently using the known methods. These pertain to ``real time'' evolution, since, in statistical mechanics in general and in particle physics, in particular, the quantities that are computed refer to equilibrium situations.
However, for the moment, the models to which quantum networks can be applied and have proved useful are in models in less than 3+1 dimensions and without the symmetries of the Standard Model. Of course experiments in particle physics, where real time evolution is of relevance are, also, not common, either (typically, in special circumstances, in heavy ion collisions).
They do appear to be more relevant to describing the transport properties of low-dimensional condensed matter systems, rather than those encountered, for the moment, in particle physics.
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