Rank one HCIZ at high temperature: interpolating between classical and free convolutions

Interpolating Between Quantum and Classical Complexity Classes

We reveal a natural algebraic problem whose complexity appears to interpolate between the well-known complexity classes BQP and NP: ⋆ Decide whether a univariate polynomial with exactly m monomial terms has a p-adic rational root. In particular, we show that while (⋆) is doable in quantum randomized polynomial time when m=2 (and no classical randomized polynomial time algorithm is known), (⋆) i...

Harmonic Functions on Classical Rank One Balls

Free energy of QCD at high temperature.

Effective-field-theory methods are used to separate the free energy for a nonabelian gauge theory at high temperature T into the contributions from the momentum scales T , gT , and g2T , where g is the coupling constant at the scale 2πT . The effects of the scale T enter through the coefficients in the effective lagrangian for the 3-dimensional effective theory obtained by dimensional reduction...

On a Surprising Relation between Rectangular and Square Free Convolutions

Debbah and Ryan have recently [DR07] proved a result about the limit empirical singular distribution of the sum of two rectangular random matrices whose dimensions tend to infinity. In this paper, we reformulate it in terms of the rectangular free convolution introduced in [BG07b] and then we give a new, shorter, proof of this result under weaker hypothesis: we do not suppose the probability me...

Classical Limit for Scalar Fields at High Temperature

We study real-time correlation functions in scalar quantum field theories at temperature T = 1/β. We show that the behaviour of soft, long wave length modes is determined by classical statistical field theory. The loss of quantum coherence is due to interactions with the soft modes of the thermal bath. The soft modes are separated from the hard modes by an infrared cutoff Λ ≪ 1/(¯ hβ). Integrat...