7 research outputs found
General criteria for the stability of uniaxially ordered states of Incommensurate-Commensurate Systems
Reconsidering the variational procedure for uniaxial systems modeled by
continuous free energy functionals, we derive new general conditions for
thermodynamic extrema. The utility of these conditions is briefly illustrated
on the models for the classes I and II of incommensurate-commensurate systems.Comment: 5 pages, to be published in Phys. Rev. Let
Domain patterns in incommensurate systems with the uniaxial real order parameter
The basic Landau model for the incommensurate-commensurate transition to the uniform or dimerized uniaxial ordering is critically reexamined. The previous analyses identified only sinusoidal and homogeneous solutions as thermodynamically stable and proposed a simple phase diagram with the first-order phase transition between these configurations. By performing the numerical analysis of the free-energy and the Euler-Lagrange equation we show that the phase diagram is more complex. It also contains a set of metastable solutions present in the range of coexistence of homogeneous and sinusoidal solutions. These new configurations are periodic patterns of homogeneous domains connected by sinusoidal segments. They are Lyapunov unstable, very probably due to the nonintegrability of the free-energy functional. We also discuss some other mathematical aspects of the model and compare it with the essentially simpler sine-Gordon model for the transitions to the states with higher commensurabilities. We argue that the present results might be a basis for the explanation of phenomena such as thermal hystereses, cascades of phase transitions, and memory effects
Akustična kolektivna pobuđenja i statički dielektrični odziv u nesumjerljivim kristalima s realnim parametrom uređenja
Starting from the basic Landau model for the incommensurate-commensurate materials of the class I I, we derive the spectrum of collective modes for all (meta)stable states from the corresponding phase diagram. It is shown that all incommensurate states posses Goldstone modes with acoustic dispersions. The representation in terms of collective modes is also used in the calculation and discussion of static dielectric response for systems with the commensurate wave number in the center of the Brillouin zone.Polazeći od temeljnog Landauovog modela za nesumjerljive materijale II klase, izveli smo spektar kolektivnih grana za sva (meta)stabilna stanja iz odgovarajućeg faznog dijagrama. Pokazali smo da sva nesumjerljiva stanja posjeduju Goldstonove grane s akustičkim disperzijama. Reprezentaciju kolektivnih grana primijenili smo također u proračunu i raspravi statičkog dielektričnog odziva sustava sa sumjerljivim valnim brojem u središtu Brillouinove zone
Landau model for uniaxial systems with complex order parameter
We study the Landau model for uniaxial incommensurate-commensurate systems of
the I class by keeping Umklapp terms of third and fourth order in the expansion
of the free energy. It applies to systems in which the soft mode minimum lies
between the corresponding commensurate wave numbers. The minimization of the
Landau functional leads to the sine-Gordon equation with two nonlinear terms,
equivalent to the equation of motion for the well-known classical mechanical
problem of two mixing resonances. We calculate the average free energies for
periodic, quasiperiodic and chaotic solutions of this equation, and show that
in the regime of finite strengths of Umklapp terms only periodic solutions are
absolute minima of the free energy, so that the phase diagram contains only
commensurate configurations. The phase transitions between neighboring
configurations are of the first order, and the wave number of ordering goes
through harmless staircase with a finite number of steps. These results are the
basis for the interpretation of phase diagrams for some materials from the I
class of incommensurate-commensurate systems, in particular of those for
ABX and BCCD compounds. Also, we argue that chaotic barriers which
separate metastable periodic solutions represent an intrinsic mechanism for
observed memory effects and thermal hystereses.Comment: 12 pages, 14 figures, LaTeX, to be published in Phys. Rev.
Covariant and Heavy Quark Symmetric Quark Models
There exist relativistic quark models (potential or MIT-bag) which satisfy
the heavy quark symmetry (HQS) relations among meson decay constants and form
factors. Covariant construction of the momentum eigenstates, developed here,
can correct for spurious center-of-mass motion contributions.Proton form factor
and M1 transitions in quarkonia are calculated. Explicit expression for the
Isgur-Wise function is found and model determined deviations from HQS are
studied. All results depend on the model parameters only. No additional ad hoc
assumptions are needed.Comment: 34 pages (2 figures not included but avaliable upon request), LATEX,
(to be published in Phys.Rev.D