We study the energy level crossings of the states and thermal fidelity for a two-qubit system in the presence of a transverse and inhomogeneous magnetic field. It is shown clearly the effects of the anisotropic factor of the magnetic field through the contour figures of energy level crossing in two subspaces, the isotropy subspace and anisotropy subspace. We calculate the quantum fidelity between the ground state and the state of the system at temperature $T$, and the results show the strong effect of the anisotropic factor again. In addition, by making use of the transition of Yangian generators in the tensor product space, we study the evolution of the thermal fidelity after the transition. The potential applications of Yangian algebra, as a switch to turn on or off the fidelity, are proposed.
We study thermal entanglement in a two-superconducting-qubit system in two cases, either identical or distinct. By calculating the concurrence of system, we find that the entangled degree of the system is greatly enhanced in the case of very low temperature and Josephson energies for the identical superconducting qubits, and our result is in a good agreement with the experimental data.
The unipolar and bipolar macroscopic quantum models derived recently for instance in the area of charge transport are considered in spatial one-dimensional whole space in the present paper. These models consist of nonlinear fourth-order parabolic equation for unipolar case or coupled nonlinear fourth-order parabolic system for bipolar case. We show for the first time the self-similarity property of the macroscopic quantum models in large time. Namely, we show that there exists a unique global strong solution with strictly positive density to the initial value problem of the macroscopic quantum models which tends to a self-similar wave (which is not the exact solution of the models) in large time at an algebraic time-decay rate.
An important instance of Rota-Baxter algebras from their quantum field theory application is the ring of Laurent series with a suitable projection. We view the ring of Laurent series as a special case of generalized power series rings with exponents in an ordered monoid. We study when a generalized power series ring has a Rota-Baxter operator and how this is related to the ordered monoid.
