Thursday, June 15, 2017

vacuum - What is the difference between quantum fluctuations and thermal fluctuations?


Start with a simple scalar field Lagrangian L(ϕ) at zero temperature T=0, which has a hidden symmetry and spontaneously break it. By the standard procedure a field ϕ is redefined


ϕϕ+ϕ,


where ϕ is a quantum fluctuation around some constant value ϕ. The constant value ϕ is called a condensate (or vacuum expectation value) of the field ϕ. (For example, in the case of pions and sigma mesons (L is a linear sigma model Lagrangian) fluctuations ϕ are physical pions and sigma mesons, with pion condensate equal to zero, and sigma meson condensate equal to σ=fπ.)


The spontaneus symmetry breaking looks the same for T0 scalar field theory. Again, we redefine the field ϕϕ+ϕ and obtain physical particles ϕ as a fluctuations around the condensate, which is now temperature dependent variable; and it can serve as an order parameter of the theory. (For example, in the case of sigma mesons and pions, the condensate σ will vanish at the chiral temperature point, displaying the existance of the chiral phase transition.)


So my question is, are the quantum fluctuations ϕ (i.e. the physical particles) the same in T=0 and T0 field theory? Or are they somehow 'mixed', so they are both thermal and quantum fluctuations? In addition, the diagram here http://upload.wikimedia.org/wikipedia/commons/0/06/QuantumPhaseTransition.png basically says that quantum and classical (critical) behaviour is the same thing, which adds up to my confusion.


Of course, if I completely missed the point, I hope that someone can explain in a better way what is the concept of the symmetry breaking and emergence of a condensate (and physical particles).





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