关于左手性介质几何光学的研究(一)

根据几何光学中的费马原理和完善成像原理研究了光线经过正负折射率界面时的传播特性,推导了单负折射率完善成像的曲面方程,讨论了单块负折射率透镜成像特性的一些缺陷及改进方案,依此指出了最短时间原理的适用范围的局限性和利用左手性介质制作光学器件的优越性,为进一步研究左手性介质的光学特性和相关光学器件设计提供了理论基础.     

Time optimal control of two-level quantum systems

The objective of time-optimal control that helps to minimize relaxation losses, is the evolution of a quantum state from a given initial mixed state to a final target mixed state in minimum time. In this paper, we study a time-optimal control problem of the dynamic of a pure two-level system with unbounded control using Pontryagin's minimum principle and obtain the minimal time for some initial and final states. The results will apply to basically all qubit systems that one can consider such as NMR spectroscopy, trapped ions, superconducting qubits, etc. We also show that these results hold for pure states, and only the direction $\hat{n}$ is important in the evolution of a quantum state. In this work, the problem of computing minimum time to produce any unitary transformation $U_f\in SU(2)$ is reduced to finding the minimum time to steer the system from an initial to a final state.     

A dynamic equivalence principle for systematic longevity risk management

This paper addresses systematic longevity risk in long-term insurance business. We analyze the consequences of working under unknown survival probabilities on the efficiency of the Law of Large Numbers and point out the need for appropriate and feasible risk management techniques. We propose a setting for risk sharing schemes between the insurer and policyholders via a dynamic equivalence principle. We focus on a pure endowment contract and derive conditions for a viable risk sharing scheme which enhances the solvency situation of the insurer while being more favorably priced for the policyholders.     

The Phragemén‐Lindelöf principle of harmonic functions and conditions for nevanlinna class in the half space

In this article, we firstly discuss a kind of Phragemén‐Lindelöf Principle of harmonic functions by using the Nevanlinna's representation in the high dimensional space. Secondly, we derive the sufficient conditions for subharmonic functions being in the Nevanlinna class as well. These results are main tools to study the Hilbert space of harmonic functions with analytic approaches and generalizations of some classic results.     

The physics of helical electron beam in a uniform magnetic field as a testing ground of gauge principle

According to Bliokh et al., allowing free propagation along the direction of a uniform magnetic field, the familiar Landau electron state can be regarded as a non-diffracting version of the helical electron beam propagating along the magnetic field. Based on this observation, they argued that, while propagating along the magnetic field, the Landau electrons receive characteristic rotation with three different angular velocities, depending on the eigen-value m of the canonical OAM operator, which is generally gauge-variant, and this splitting was in fact experimentally confirmed. Through complete analyses of highly mysterious m-dependent rotational dynamics of the quantum Landau states, we try to make clear how and why their observation does not contradict the widely-believed gauge principle.     

Modulation of electronic structure properties of C/B/Al-doped armchair GaN nanoribbons

ABSTRACT

The electronic structures of C/B/Al-doped armchair GaN nanoribbons (aGaNNRs) are systematically studied by using density functional theory. We find that the original aGaNNRs are direct band gap semiconductors and that the gaps monotonically decrease with increasing widths. Interestingly, the B- or Al-doped aGaNNRs are also direct-band gap semiconductors with a slightly larger gap than their undoped aGaNNRs, while the C-doped aGaNNRs display metallic characteristics with an impurity state across the Fermi level in band structures. The semiconducting or metallic behaviours of C/B/Al-doped aGaNNRs can be explained by the orbital coupling between the extrinsic atom and primary Ga, N in their partial density of states. Our results show a useful way to modulate the band gaps of aGaNNRs.

Using the density-functional theory, we performed a theoretical research to study the electronic structures of C/B/Al-doped armchair gallium nitride nanoribbons. The calculated band structures show that the perfect and original aGaNNRs are direct semiconductors regardless of ribbon widths, and gaps monotonically decrease with increasing the widths. The B/Al-doped aGaNNRs are semiconductors with a slightly larger gap, while metallic behavior presents in C-doped aGaNNRs with an impurity band across the EF. The results show a useful way to modulate the band gaps of aGaNNRs.