一维简谐势阱中超冷费米气体的孤子解及其稳定性

利用虚时演化算法研究了准一维简谐势阱中的超冷费米气体,发现在超冷费米气体的不同超流态上孤子空间分布存在明显的差异.在BCS端,随着弱吸引相互作用逐渐增大,孤子的峰值不断增大,宽度不断变小;在分子BEC端,随着弱排斥相互作用逐渐增大,孤子的峰值不断减小,宽度不断增大;并且在BCS端的孤子峰值大于分子BEC端孤子的峰值,而...     

非线性弹性杆波动方程的显式精确解北大核心CSCD

应用sine-cosine方法对非线性弹性杆波动方程进行了求解,得到了该方程的一些新的周期波解和孤波解(材料常数n为不等于1的常数).对部分结果通过数学软件得到了解的图像,获得的结果有助于非线性弹性杆中孤波存在性问题的进一步研究.     

相对论长脉冲激光在非均匀等离子体中的传播特性

通过解析和数值方法研究了相对论长脉冲激光在非均匀等离子体中的传播.首先,得到了激光脉冲在均匀等离子体中传播的解析解,并通过数值模拟进行了验证.结果表明,长脉冲激光在均匀等离子体中传播时,脉冲宽度的变化不影响激光强度空间分布的变化;然而,激光脉冲的强度和电子密度的空间分布可以通过调制等离子体频率来调节.在具有高斯型密度分...     

超流Fermi气体在非简谐势阱中的集体激发

研究了非谐振势中超流Fermi气体的集体激发. 基于一维超流流体动力学模型, 采用变分法获得了体系从分子Bose-Einstein凝聚端渡越到Cooper对凝聚端时系统的两个低能激发模, 即偶极模和呼吸模. 分析发现: 在整个跨越区偶极模和呼吸模都发生了频移现象, 且在BCS端频移更加显著. 进一步研究发现在不同驱动振幅激发下超流Fermi气体质量中心和宽度变化呈现出了复杂动力学特性, 由于非谐振势的贡献,超流Fermi气体两低能模发生耦合, 使宽度变化产生量子拍频现象, 且拍频频率随着驱动振幅的增加而增大. 这种非线性耦合对外部驱动的响应在幺正区尤其显著. 关键词： 超流Fermi气体 非谐振势 集体激发     

一维光晶格中超流Fermi气体基态性质的研究

研究了一维光晶格中超流Fermi气体基态解的性质.在平均场理论框架下,利用超流Fermi体系中原子间相互作用能与晶格势能相互平衡的条件,得到了一维光晶格中超流Fermi气体在整个BEC-BCS跨越区的一组基态解,给出了基态的原子数密度空间分布、总原子数和能量.进一步对系统从BEC端转变到BCS端时的基态解性质进行了深入分析和对比.结果表明,一维光晶格中超流Fermi气体基态分布具有一些特殊的性质,由于Fermi压力,相比而言超流Fermi气体在BCS端的基态原子数密度空间分布较为扩展,平均能量明显偏高.     

因式分解法求解非线性电报方程

应用科尔内霍-佩雷斯和罗苏提出的一种因式分解法获得了非线性电报方程的几类精确解.结果表明,因式分解法是一种简便、直接的方法,并且可用于求解其它非线性数学物理方程.     

Generation of high quality ion beams through the stable radiation pressure acceleration of the near critical density target

In order to generate high quality ion beams through the stable radiation pressure acceleration(RPA) of the near critical density(NCD) target, we propose a new type of target where an ultra-thin high density(HD) layer is attached to the front surface of an NCD target, which has a preferable self-supporting property in the RPA experiments than the ultra-thin foil target. It is found that in one-dimensional particle-in-cell(PIC) simulation, by the block of the HD layer in the new target,there emerges the hole-boring process rather than propagation in the NCD layer when the intense laser pulse impinges on this target. As a result, a typical RPA structure that the compressed electron layer overlaps the ion layer as a whole is formed and a high quality ion beam is obtained, e.g., a circularly polarized laser pulse with normalized amplitude a_0= 120 impinges on this new target and a 1.2 GeV monoenergetic ion beam is generated through the RPA of the NCD layer. Similar results are also found in the two-dimensional PIC simulation.     

利用部分非线性项替代精确同步连续时间混沌系统

讨论了连续时间混沌系统的精确同步问题.将系统线性项与非线性项分离,并将响应系统的部分非线性项由驱动系统替代来实现同步.由于可供替代的部分具有较大的灵活性,从而使该方法在具体操作中灵活性更大,实用性更强.以Lorenz系统为例的数值实验证实了该方法的有效性和鲁棒性.另外,在数值实验中考虑了噪声的影响,结果表明,该方法具有强的抗噪声能力.     

超强激光-纳米丝靶相互作用过程中纳米丝结构演化的研究

纳米丝靶的特殊结构对于超强激光与纳米丝靶相互作用产生高品质的超热电子和高能离子有非常重要的作用.文中利用粒子模拟(Particle-in-cell,PIC)方法研究了超强激光与碳纳米丝靶相互作用过程中纳米丝结构随时间的演化过程,理论分析了纳米丝内部自生电磁场的产生机制和离子在纳米丝靶内部的运动过程,研究结果表明,纳米丝靶内部会产生100 MG量级的自生磁场和1013V·m^-1量级的静电场.在激光和自生电磁场的作用下碳纳米丝靶结构能够保持完整性的时间大约为50～100 fs,100 fs后,纳米丝靶的结构会被逐渐破坏.该研究对超强激光与纳米丝靶相互作用的相关理论和实验有重要的参考价值.     

Propagation dynamics of relativistic electromagnetic solitary wave as well as modulational instability in plasmas

By one-dimensional particle-in-cell(PIC) simulations, the propagation and stability of relativistic electromagnetic(EM) solitary waves as well as modulational instability of plane EM waves are studied in uniform cold electron-ion plasmas.The investigation not only confirms the solitary wave motion characteristics and modulational instability theory, but more importantly, gives the following findings. For a simulation with the plasma density 10²³ m^-3 and the dimensionless vector potential amplitude 0.18, it is found that the EM solitary wave can stably propagate when the carrier wave frequency is smaller than 3.83 times of the plasma frequency. While for the carrier wave frequency larger than that, it can excite a very weak Langmuir oscillation, which is an order of magnitude smaller than the transverse electron momentum and may in turn modulate the EM solitary wave and cause the modulational instability, so that the solitary wave begins to deform after a long enough distance propagation. The stable propagation distance before an obvious observation of instability increases(decreases) with the increase of the carrier wave frequency(vector potential amplitude). The study on the plane EM wave shows that a modulational instability may occur and its wavenumber is approximately equal to the modulational wavenumber by Langmuir oscillation and is independent of the carrier wave frequency and the vector potential amplitude.This reveals the role of the Langmuir oscillation excitation in the inducement of modulational instability and also proves the modulational instability of EM solitary wave.