engleski

Periodic Solutions and Role of Chaos in Structural Phase Transitions in Uniaxial Systems

We propose a model for uniaxial incommensurate-commensurate phase transitions based on the Landau phenomenological theory with two Umklapp terms in the expansion of the free energy functional. The corresponding Euler-Lagrange equation has a form of the sine-Gordon equation with two nonlinear terms, well known in the classical mechanics as the problem of two mixing resonances. We show that the solution of this equation which has the lowest averaged free energy is periodic for the whole relevant range of control parameters. The corresponding phase diagram has the form of harmless staircase with the first order transitions between neighboring subphases. This diagram is in accordance with recent experimental observations on some ferroelectric materials. We also discuss some points which are common to the equivalent classical and quantum mechanical problems.

incommensurate-commensurate systems; mixing resonances;harmless staircase

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