Showing papers by "P. C. Hohenberg published in 1990"

Pulses and fronts in the complex Ginzburg-Landau equation near a subcritical bifurcation.

Abstract: Uniformly translating solutions of the one-dimensional complex Ginzburg-Landau equation are studied near a subcritical bifurcation. Two classes of solutions are singled out since they are often produced starting from localized initial conditions: moving fronts and stationary pulses. A particular exact analytic front solution is found, which is conjectured to control the relative stability of pulses and fronts. Numerical solutions of the Ginzburg-Landau equation confirm the predictions based on this conjecture.

The Beginnings and Some Thoughts on the Future

Abstract: Publisher Summary This chapter discusses the density functional theory (DFT). It discusses two basic theorems expressing the ground state of a many-electron system in terms of the particle density distribution, and of the variational solution in terms of a single-particle Schrodinger equation. In conclusion, some challenges and directions for further progress in this field are indicated. Time-dependent density functional theory has been formally developed, but it has not yet found a practical incarnation of an ease and utility comparable to local density approximation for stationary ground and excited states and thermal ensembles. The practical implementations of DFT all take the uniform electron gas as their starting point for approximate representations of exchange-correlation effects. But in bounded systems the boundary region(s), where the density tends to zero and where the Kohn-Sham wave-functions evanesce rather than oscillate, are essentially different from a region of a uniform electron-gas, even if the density does not vary rapidly.