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Symmetry breaking in the periodic Thomas-Fermi-Dirac-von Weizsäcker model. (English) Zbl 1420.35376
The paper addresses a density-functional theory for the electron gas interacting with a spatially periodic ionic lattice. It is proved that, if strength \(c\) of the term which accounts for the exchange-correlation energy in the system’s Hamiltonian exceeds a certain critical value, the ground state changes the periodicity of its electron density undergoes doubling, in comparison with the period of the ionic lattice. In that case, an effective nonlinear Schrödinger equation for the real stationary electron wave function takes the following form: \[ -\Delta Q+ Q^{7/3} - cQ^{5/3} = \mu Q, \] where \(\mu\) is the chemical potential.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
35Q40 PDEs in connection with quantum mechanics
81V55 Molecular physics
Software:
PROFESS
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