The Husimi distribution is proposed for a phase-space analysis of quantum phase transitions in the Dicke model of spin-boson interactions. We show that the inverse participation ratio and Wehrl entropy of the Husimi distribution give sharp signatures of the quantum phase transition. The analysis is done using two frameworks: a numerical treatment and an analytical variational approximation. Additionally, we propose a characterization of the Dicke model quantum phase transition by means of the zeros of the Husimi distribution in the variational approach. DOI: http://dx.doi.org/10.1103/PhysRevA.85.053831 ©2012 American Physical Society

The Husimi distribution is proposed for a phase-space analysis of quantum phase transitions in the two-dimensional U(3) vibron model for $N$-size molecules. We show that the inverse participation ratio and Wehrl's entropy of the Husimi distribution give sharp signatures of the quantum (shape) phase transition from linear to bent. Numerical results are complemented with a variational approach using parity-symmetry-adapted U(3) coherent states, which reach the minimum Wehrl entropy $\frac{N(3+2N)}{(N+1)(N+2)}$, in the rigidly linear phase, according to a generalized Wehrl-Lieb conjecture. We also propose a characterization of the vibron-model quantum phase transition by means of the zeros of the Husimi distribution. DOI: http://dx.doi.org/10.1103/PhysRevA.86.032508 ©2012 American Physical Society

Rényi uncertainty relations are shown to have significant importance in quantum phase transitions. They detect the quantum phase transition in the Dicke model. The Rényi entropy sum is more appropriate for describing quantum fluctuations than the standard variance products. DOI: http://dx.doi.org/10.1103/PhysRevA.85.053813 ©2012 American Physical Society