Coherent States in a Degenerate Electron Gas

Leon N. Cooper

Rolf Schumann

Abstract The Hubbard model extended by both nearest‐neighbour (nn) Coulomb correlation and nearest‐neighbour Heisenberg exchange is solved rigorously for a triangle and tetrahedron. All eigenvalues and eigenvectors are given as functions of the model parameters in a closed analytical form. For fixed electron numbers we found a multitude of level crossings, both in the ground state and in the excited states in dependence on the various model parameters. By coupling an ensemble of clusters to an electron bath we get the cluster gas model or the cluster gas approximation, if an extended array of weak‐interacting clusters is considered. The grand‐canonical potential Ω (μ, T , h ) and the electron occupation N (μ, T , h ) of the related cluster gases were calculated for arbitrary values (attractive and repulsive) of the three interaction constants. For the cluster gases without the additional interactions we found various steps in N (μ, T = 0, h = 0) higher than one. The reason is the degeneration of ground states differing in their electron occupation by more than one electron. For the triangular cluster gas we have one such degeneration point. For the tetrahedral cluster gas two. As a consequence, we do not find areas with one electron in the μ‐ U ground‐state phase diagram of the triangular cluster gas or with one, two and five electrons in the case of the tetrahedral cluster gas. The degeneration point of the triangular cluster gas can not be destroyed by an applied magnetic field. This holds also for the lower degeneration point of the tetrahedral cluster gas. Otherwise, the upper degeneration point breaks down at a critical magnetic field h c . The dependence of h c on U shows a maximum for strong on‐site correlation. The influence of nn‐exchange and nn‐Coulomb correlation on the ground‐state phase diagrams is calculated. Whereas antiferromagnetic nn‐exchange breaks the degeneration points of the tetrahedral cluster gas partially only, a repulsive nn‐Coulomb correlation lifts the underlying degeneracies completely. Otherwise both ferromagnetic nn‐exchange and attractive nn‐Coulomb interaction stabilise the degeneration points. The consequences of the cluster gas results for extended cluster arrays are discussed.

Evaldo M. F. Curado, M. A. Rego-Monteiro, Ligia M. C. S. Rodrigues +1 more

Yi Zhou, Hui Zhai, Lü, Rong +2 more

Macroscopic quantum coherence of Bose gas in a double-well potential is studied based on SU(2)-coherent-state path-integral. The ground state and fluctuations around it can be obtained by this method. In this picture, one can obtain macroscopic quantum superposition states for attractive Bose gas. The coherent gap of degenerate ground states is obtained with the instanton technique. The phenomenon of macroscopic quantum self-trapping is also discussed.

Tom Banks, Bingnan Zhang

Vasilka Steflekova, Dimo Zhechev

The degenerate Zeeman sublevels were found to contribute to the ionization in a gas discharge in accordance with their coherent state. The voltage across the discharge was monitored while the same ensemble of excited atoms was alternately self-aligned ↔ nonaligned or oriented ↔ aligned. In the latter case, the coherence was optically induced; the corresponding opto-galvanic signals, i.e. amplitude- and time-resolved ones, were compared. Each state of the ensemble of degenerate Zeeman sublevels, i.e. (self-) aligned, oriented or disordered was characterized by its own rate of ionization. Various hollow cathode discharge (HCD) media were studied, namely, Ne/As, Ne/Cu, Ne/Ni, Ne/Cd, Ne/Li and Ne/Si in the corresponding commercial HCD spectral lamps.