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We discuss the origin of topological defects in phase transitions and analyze their role as a diagnostic tool in the study of the non-equilibrium dynamics of symmetry breaking. Homogeneous second order phase transitions are the focus of our attention, but the same paradigm is applied to the cross-over and inhomogeneous transitions. The discrepancy between the experimental results in 3He and 4He is discussed in the light of recent numerical studies. The possible role of the Ginzburg regime in determining the vortex line density for the case of a quench in 4He is raised and tentatively dismissed. The difference in the anticipated origin of the dominant signal in the two (3He and 4He) cases is pointed out and the resulting consequences for the subsequent decay of vorticity are noted. The possibility of a significant discrepancy between the effective field theory and (quantum) kinetic theory descriptions of the order parameter is briefly touched upon, using atomic Bose-Einstein condensates as an example.
The equation of state of a system at equilibrium may be derived from the canonical or the grand canonical partition function. The former is a function of temperature T, while the latter also depends on the chemical potential mu for diffusive equilibr
The physics of highly excited Rydberg atoms is governed by blockade or exclusion interactions that hinder the excitation of atoms in the proximity of a previously excited one. This leads to cooperative effects and a relaxation dynamics displaying spa
Dark states are stationary states of a dissipative, Lindblad-type time evolution with zero von Neumann entropy, therefore representing examples of pure, steady quantum states. Non-equilibrium dynamics featuring a dark state recently gained a lot of a
We unveil the universal (model-independent) symmetry satisfied by Schwinger-Keldysh quantum field theories whenever they describe equilibrium dynamics. This is made possible by a generalization of the Schwinger-Keldysh path-integral formalism in whic
We consider 1D integrable systems supporting ballistic propagation of quasiparticles, perturbed by a localised defect that breaks most conservation laws and induces chaotic dynamics. We study an out-of-equilibrium protocol engineered activating the d