Dynamics of Symmetry Breaking: Phase Coherence in Finite and Random Systems
Purely relaxational dynamics for an n-component vectorial order parameter has been extensively used to study critical dynamics of Heisenberg magnetic systems (1) and statistical properties of transient laser radiation (2). The dynamical model we are referring to is the TDGL (time-dependent Ginzburg-Landau) model, i.e., non linear Langevin equation describing the evolution of the order parameter associated with the system. Non linearity is usually associated with a coupling between the degrees of freedom typical of the system. Only in the laser case it is possible to select a single degree of freedom (the unimode operation). In such a limit phase coherence phenomenon appears as a consequence of an instability of the system. In the opposite limit of an infinite number of degrees of freedom we have the thermodynamic limit in which the same instability can give rise to a phase transition.
KeywordsCritical Temperature Correlation Length Linear Relaxation Spherical Limit Random Magnetic Field
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