Characteristics of strong-coupling bipolaron qubit in two-dimensional quantum dot in electric field

Based on Lee-Low-Pines(LLP) unitary transformation, this article adopts the variational method of the Pekar type and gets the energy and wave functions of the ground state and the first excited state of strong-coupling bipolaron in two-dimensional quantum dot in electric field, thus constructs a bipolaron qubit. The numerical results represent that the time oscillation period T0 of probability density of the two electrons in qubit decreases with the increasing electric field intensity F and dielectric constant ratio of the medium η; the probability density Q of the two electrons in qubit oscillates periodically with the increasing time t; the probability of electron appearing near the center of the quantum dot is larger, while that appearing away from the center of the quantum dot is much smaller.

Geometric sigma model of the Universe

The purpose of this work is to demonstrate how an arbitrarily chosen background of the Universe can be made a solution of a simple geometric sigma model.Geometric sigma models are purely geometric theories in which spacetime coordinates are seen as scalar fields coupled to gravity.Although they look like ordinary sigma models,they have the peculiarity that their complete matter content can be gauged away.The remaining geometric theory possesses a background solution that is predefined in the process of constructing the theory.The fact that background configuration is specified in advance is another peculiarity of geometric sigma models.In this paper,I construct geometric sigma models based on different background geometries of the Universe.Whatever background geometry is chosen,the dynamics of its small perturbations is shown to have a generic classical stability.This way,any freely chosen background metric is made a stable solution of a simple model.Three particular models of the Universe are considered as examples of how this is done in practice.