Monday, September 14, 2015

Quasihuman: the Fermi-liquid theory of society

Stoic returned from a strings conference in Hefei in good spirits. Olya remarked that he had fallen in love with China, to which he scowlingly snapped, why do you always tell people that. It is his way, to bristle when others speak his mind, no matter how true.

When I press him on his love of China, he admits to feeling like a celebrity. He cut an imposing presence, tall and blonde and biceps brimming. The children of Hefei, not accustomed to such sights, would whirl around him in delight, heads bobbing in excitement, running in circles and shouting, "Lao wai! Lao wai!" Foreigner! Foreigner!

This poignant scene evoked in me an analogy that has played on my mind, teasing me to probe its depths. Quasihuman, I exclaimed, to Fake's delight, but Olya's confusion. Stoic explained it as a condensed matter "thing" and she quieted.

This "thing" underlies the success of a single-particle description of metals, which is surprising given how strongly electrons interact through Couloumbic forces. This is the Fermi-liquid theory of metals, which I will henceforth summarize. A Fermi liquid is a many-body interacting state which is smoothly connected to a free-electron state; this smooth connection is very much a thought experiment - one must imagine being able to tune the strength of the Couloumb force from zero (a free-electron state) to its god-given value (a Fermi liquid). Throughout this tuning process, all measurable quantities do not exhibit any singular behavior that is indicative of a phase transition in matter.

Due to this continuity, a Fermi liquid has essentially a single-particle structure. That is, the many-body state is specified by the occupation numbers of single-particle fermionic states, each of which has a well-defined single-particle energy and momentum. We call this single-particle state a quasiparticle - it is an electron that becomes modified by its interactions with other electrons, but such modification is not so substantial and may be thought of as a dressing, such that under the dressing the electron retains its identity. Despite the single-particle structure, the Fermi liquid does not describe independent quasiparticles.

Despite the strength of the Coulomb interaction, its role in this theory is rather minor: (i) Interactions deform single-particle properties (such as mass, energy) from their free-electron values. (ii) Due to interactions, a quasiparticle is unstable and will eventually be scattered into a different quasiparticle state. However, for quasiparticles near the Fermi energy, energy conservation and the Pauli exclusion principle drastically reduce the phase space for scattering, resulting in long-lived quasiparticles.

Presently, I would discard scientific rigor for fanciful entertainment. I like to think of our genetic core as the bare electron, and our interactions with fellow human beings as our dressing, both in the sense of cloth and also of personality and ambition. The smooth connection between bare electron and quasihuman would be the gnarly process of growing up. At each intermediate stage, we are identifiably ourselves, but never exactly the same as before.

Our dressing, unique to ourselves, encourages us to adopt certain roles in society, be it a cook or a physicist. The finite number (N) of each role introduces a notion of exclusion - no role can be played by more than N quasihumans. For society to function with optimal efficiency, there is a unique set of roles that must be filled, comprising the Fermi sea. Society does not encourage quasihumans to rapidly change roles, lest nothing gets done. Indeed, it is quite rude to explain to somebody that they are wasting their lives in an under-appreciated role, unless said person is of a rare species undergoing a 'mid-life crisis' and is therefore receptive to honest criticism.

With the exception of our cloth dressing and language, the rest of our dressing is harder to pinpoint, and has to do with intangible skills that we pick up to navigate society. Once we have grown accustomed to society and society to us, these skills become formidable and, with near-constant repetition, they fade away from our consciousness and become invisible (Schrodinger: consciousness is the tutor of the living flesh). Indeed, once societal constraints (e.g., traffic rules) are completely internalized and therefore completely instinctive, every productive member of society believes themselves to be a free human, i.e., exhibiting free will that is both logical and contrary to common conception (Nietzsche).

The illusion of free will is dispelled once one ventures into a vastly different society. One becomes sharply aware that they dress differently from everybody around them, and attracts around themselves a cloud of honest appraisal. As Stoic found.

In condensed matter physics, another favourite thought experiment is to inject a bare electron into a strongly-interacting metal, and see to what extent it remains a bare electron over time. If the metal is a Fermi liquid, the answer is that this extent is less than unity but nonvanishing, and furthermore the injection excites an incoherent continuum of quasiparticles that we interpret as the dressing.




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