15.5.2013

Hysterezis Phenomena in Nonequilibrium Phase Transitions

Abstract:

Non-equilibrium phase transitions represent a topical problem of research in various fields of physics. As they appear in complex systems, an alternative approach of their understanding is that of the nonlinear dynamics.

Hysteresis is the property of an evolving complex system which emphasizes the dependence of its states on the previous ones, or, with other words, on the system’s history. Because the equilibrium thermodynamics properties of a system are completely determined by the state parameters, as pressure and temperature, and they are independent of the way the system reached that state, it follows that hysteresis is a characteristic of the system driven outside the thermodynamic equilibrium.

Complex systems are nonlinear and dissipative systems, the evolution of which can be described by an adequate evolution equation or system of equations, which relates the dependence of the order parameter(s) of the system on the control parameter(s) that can be externally modified as desired.

In the present talk two types of reaction functions are analyzed, together with the associated Lyapunov-like functionals. These functionals can describe two different types of Thom’s catastrophes, as well as the first-, respectively the second-order phase transitions.

Using the functional ascribed to the first-order phase transitions, the stationary structured states are found and their stability to perturbations is analyzed. The bifurcation types and the critical points are established. The sudden jumps, instabilities, the bistability range and the hysteresis phenomenon are also studied. Also, a quantitative discussion of the stability exchange in the bistability domain is done from the nonlinear dynamics point of view.

For the functional ascribed to the second-order phase transitions an analysis similar to that for the first-order ones is performed and the results showed that the entire bistability domain collapses to the critical point. In order to highlight the presence of hysteresis in the phase transitions governed by a functional specific to the second-order ones, a symmetry-breaking perturbation is used and the analytic results clearly mimic the experimental results reported in the literature, e.g., for the paraelectric-ferroelectric transitions.

In order to bring the results closer to an experimentalist perspective, all the results are illustrated for the transitions taking place in the nonlinear dielectrics.