[seminar] 09.06.2017. Jerzy Cioslowski: Wigner Crystallization in Central Potentials

[Damir Pajic]

Dear colleagues,
just a reminder about our seminar today:





petak/Friday  09.06.2017. u 15:15 h
room F201 (floor II)

Wigner Crystallization in Central Potentials

Prof. dr. Jerzy Cioslowski

http://www.fiz.univ.szczecin.pl/index.php/en/people/29.html?showall=1

Institute of Physics, University of Szczecin, Poland
and
Max-Planck-Institut für Physik komplexer Systeme, Dresden, Germany

In 1934, Eugene Wigner predicted spatial localization of electrons in a 
low-density homogeneous electron gas (HEG). This Wigner crystallization, 
which is triggered when the kinetic energy of HEG is sufficiently small 
relative to the sum of the electron-electron  repulsion energy and the 
energy of interaction of electrons with the uniform neutralizing 
background, is sudden i.e. it is associated with crossing of two energy 
levels. In 3D, HEG crystallizes at the  Wigner-Seitz radius r_s = 106 
(in atomic units), producing the  body-centered cubic lattice, whereas 
in 2D the Wigner crystallization takes place at r_s = 31, the resulting 
lattice being hexagonal (triangular).

In general, weak confinement is a prerequisite for formation of the 
Wigner crystals, which are simply classical systems perturbed by 
zero-point vibrations about equilibrium positions of the constituting 
particles. In ground states of fully Coulombic systems (i.e. atoms and 
molecules), autoionization precludes Wigner crystallization. However, 
systems with unbound confining potentials (e.g. harmonium atoms) 
crystallize gradually upon decrease of the confinement strength.

In this talk, several aspects of Wigner crystallization in central 
confining potentials are discussed. In particular, the following 
subjects are covered:
1. Harmonium atoms and their weak- and strong-correlation limits.
2. Robust interpolation between the weak- and strong-correlation limits.
3. Correlation in Coulomb crystals: the Madelung energy and its 
variational estimation.
4. Smooth, oscillatory, and fluctuating components of energies of 
Coulomb crystals.
5. The ground-and excited-state wavefunctions at the strong-correlation 
limit.
6. The corresponding 1-matrices, natural spinorbitals, and their 
occupancies.

Lijep pozdrav / Best regards
Damir Pajić