Pierfrancesco Buonsante - Università di Parma #
Dynamical bifurcation as a semiclassical counterpart of a 
quantum phase transition #
We illustrate how  dynamical transitions in nonlinear 
semiclassical models can be recognized as phase transitions in 
the corresponding -- inherently linear -- quantum model, where,  
in a Statistical Mechanics framework, the thermodynamic limit is 
realized  by letting the particle population go to infinity at 
fixed size. We focus on lattice bosons described by the  
Bose-Hubbard (BH) model and Discrete Self-Trapping (DST) 
equations at the quantum and semiclassical level, respectively.
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After showing  that  the gaussianity of the quantum ground 
states is broken at the phase transition, we work out the exact 
value of the critical exponents and provide numerical evidence 
confirming the relevant scaling hypothesis. Our analytical 
results rely on a general scheme obtained from a 
large-population expansion of the eigenvalue equation of the BH 
model. In this approach the DST equations resurface as solutions 
of the zeroth-order problem.