Real symmetry breaking

Real Symmetry Breaking - Jahn-Teller Effects in Singlet... 

This chapter is devoted to the behavior of double layers and inclusion-free membranes. Section II treats two simple models, the elastic dimer and the elastic capacitor. They help to demonstrate the origin of electroelastic instabilities. Section III considers electrochemical interfaces. We discuss theoretical predictions of negative capacitance and how they may be related to reality. For this purpose we introduce three sorts of electrical control and show that this anomaly is most likely to arise in models which assume that the charge density on the electrode is uniform and can be controlled. This real applications only the total charge or the applied voltage can be fixed. We then show that predictions of C < 0 under a-control may indicate that in reality the symmetry breaks. Such interfaces undergo a transition to a nonuniform state the initial uniformity assumption is erroneous. Most... 

The problem of symmetry breaking (SB) is well known and multiply discussed in literature. Briefly, we can formulate it as follows. The Hamiltonian of any system of particles forming the Universe is totally symmetric with respect to rotations and reflections in the isotropic space-time, as well as transmutations of identical and equivalent particles, whereas the real objects of the material world composed by these particles do not possess such symmetry. This is seen already from the examples that we live in a world of particles, not antiparticles, and in condensed matter, we have mostly low-symmetry structures. This circumstance can be expressed by the statement that the world is in a state of broken symmetry. An obvious explanation of the contradiction between the totally symmetric Hamiltonian and the broken symmetry of the real world is that the latter is not a solution of its Schrodinger equation. 

Originally, the Jahn-Teller (JT) theorem was formulated as a prediction of a symmetry break for any non-linear polyatomic molecule with an orbital degeneracy in its ground state. However, as we understand it now, the real meaning of the JT theorem is a non-zero slope of the adiabatic potential energy surface (APES) at the point of electron degeneracy. This does not necessarily result in a lowering of... 

E. R. Davidson and W. T. Borden, /. Phys. Chem., 87, 4783 (1983). Symmetry Breaking in Polyatomic Molecules Real and Artifactual. See also T. Bally and W. T. Borden, in Reviews in Computational Chemistry, K. B. Lipkowitz and D. B. Boyd, Eds., Wiley-VCH, New York, Vol. 13, pp. 1-97. Calculations on Open-Shell Molecules A Beginner s Guide. 

E. R. Davidson and W. T. Borden,/. Phys. Chem., 87, 4783 (1983). Symmetry Breaking in Polyatomic Molecules Real and Artifactual. 

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