自旋相干态变换和自旋-玻色模型的基于变分法的基态解析解

提出一种基于自旋相干态变换求解自旋-玻色模型基态的变分法, 并将其用于单原子模型, 得到旋波近似和非旋波近似情形下的解析基态能量和波函数, 特别是在光场与原子的弱、强耦合区域都与数值对角化结果符合得很好. 另外, 该方法也可以直接用于求解任意原子数的Dicke模型基态和相应的量子相变研究, 而通常基于Holstein-Primakoff变换的变分法, 原则上只适用于原子数趋于无穷的热力学极限情形. 关键词： 自旋相干态 变分法 J-C模型     

spin-Peierls系统低能量激发谱的理论研究

用玻色化技术和量子自洽方法研究了spin-Peierls系统的低能量激发谱,计算了二聚化相的基态、单粒子激发态和双粒子束缚态的能量、阻挫对其低能量行为的影响及其各自的自旋-自旋关联函数.结果表明,随着阻挫的增大,spin-Peierls系统中的基态能会逐渐减小,单粒子激发态能隙和双粒子束缚态能隙却会增大.双粒子束缚态和基态的关联函数具有类似的短程关联,而单粒子激发态的关联函数具有长程关联.因此导出,单粒子激发态为自旋三重态,双粒子束缚态与基态类似为自旋单态,它存在于双粒子连续激发态的下边.该结果与Ain等 关键词： spin-Peierls系统 束缚态 关联函数     

三维非谐势阱中玻色－爱因斯坦凝聚的数值计算

本文从G－P平均势场理论出发,探讨了三维球对称非谐势阱中玻色－爱因斯坦凝聚(BEC)的G－P方程;用数值计算方法研究了三维球对称非谐势阱中原子间有相互作用的玻色－爱因斯坦凝聚气体的基态解;分析了非谐振势能项对玻色－爱因斯坦凝聚体的分布、能量和化学势的影响。     

用遗传算法研究一维光晶格中玻色凝聚气体基态波函数

以Gross-Pitaevskii（G-P）平均场能量泛函为目标函数,运用遗传算法研究一维光晶格系统中玻色凝聚气体的基态性质,提出了求解系统波函数的一种新方法.通过优化计算,对当前常用的托马斯-费米近似和高斯近似模型进行修正和讨论,并给出最优基态波函数. 关键词： 玻色凝聚气体 遗传算法 波函数     

简谐+四次势中自旋轨道耦合旋转玻色-爱因斯坦凝聚体的基态结构

研究了囚禁于简谐+四次势中具有自旋轨道耦合相互作用的旋转玻色-爱因斯坦凝聚体的基态结构; 考虑了自旋轨道耦合相互作用和旋转对基态结构的影响; 结果发现在自旋轨道耦合相互作用与旋转共同作用下, 系统呈现出丰富且新奇的基态结构, 如条形、双排和蛇皮花斑状等.     

环形势阱中自旋-轨道耦合旋转玻色-爱因斯坦凝聚体的基态

研究了在环形势阱中自旋-轨道耦合旋转玻色-爱因斯坦凝聚体的基态结构.探索了自旋-轨道耦合作用和旋转效应对基态的影响.结果发现,在环形势阱下,基态结构呈现环形分布的half-skyrmion链.调节自旋-轨道耦合强度,不仅可以改变体系内half-skyrmion数量,而且能够调控half-skyrmion环形排列的对称性.随着旋转频率增大,体系从平面波相转化为环形对称排列的half-skyrmion链相,最后过渡到三角格子的half-skyrmion相.讨论了自旋相互作用和势阱形状对基态的影响.自旋-轨道耦合强度和旋转频率作为体系的调控参数,可用于控制不同基态相间的转化.     

梯度磁场中自旋-轨道耦合旋转两分量玻色-爱因斯坦凝聚体的基态研究

利用准二维Gross-Pitaevskii方程,研究了在梯度磁场中具有自旋-轨道耦合的旋转两分量玻色-爱因斯坦凝聚体的基态结构.探索了自旋-轨道耦合作用和梯度磁场对基态的影响.结果发现,在梯度磁场下,随着自旋-轨道耦合强度增大,基态结构由skyrmion格子逐渐过渡为skyrmion列.对于弱自旋-轨道耦合和小旋转频率情况,增大磁场梯度强度可导致基态由平面波相转变为half-skyrmion;对于强自旋-轨道耦合和大旋转频率情况,梯度磁场可诱导hidden涡旋的产生.梯度磁场、自旋-轨道耦合和旋转作为体系的调控参数,可用于控制不同基态相间的转化.     

类氩体系基态能量的相对论修正

以相对论修正哈密顿(包括质量修正、单体和双体达尔文修正、自旋-自旋接触相互作用)的张量形式为基础,借助不可约张量理论导出了类氩体系基态能量的相对论修正的解析表达式.在斯莱特表象中完成了所有的角向积分和自旋求和计算,能量的相对论修正式用径向矩阵元的线性组合来表示.对类氩体系基态能量的相对论修正值进行了具体计算,修正后基态能量与实验值的相对误差小于0.0459%.     

光腔中两组分玻色-爱因斯坦凝聚体的受激辐射特性和量子相变

研究了单模光腔中两组分玻色-爱因斯坦凝聚的基态性质和相关的量子相变.通过利用自旋相干态变换将等效赝自旋哈密顿算符对角化并求得基态能量泛函.基态能量泛函对其经典场变量进行变分并取极小值,得到光子数解和相边界曲线.通过稳定性讨论发现系统除了出现正常相和超辐射相之外,还得到了多稳的宏观量子态;受激辐射来自于原子数反转的集体态,单组分的Dicke系统中并没有此现象;受激辐射只能从一组分的原子中产生,而另外的仍保持在普通超辐射状态.通过调整相关的原子-场耦合强度和频率失谐,超辐射和受激辐射态的顺序可以在原子的两个组分之间互换.     

周期莫尔晶格中里德伯缀饰玻色气体的基态结构

里德伯缀饰和自旋轨道耦合的实验实现极大地拓宽了冷原子作为量子模拟平台的研究视野.本文研究了莫尔晶格中里德伯缀饰自旋轨道耦合玻色气体的基态结构,探索了非局域里德伯相互作用和自旋轨道耦合强度对该系统基态的影响.研究发现,当出现非局域里德伯相互作用时,系统不再具有平移对称性,倾向于形成更多更规则的周期性结构;当存在自旋轨道耦合相互作用时,系统的基态在此周期性结构的基础上,将呈现出更加丰富的内部结构.     

Exact and approximate results for the Anderson impurity model

This paper provides exact and rigorous upper and lower bounds to the ground state energy of the Single Impurity Anderson Model in the limit of infiniteU. The upper bound approximates the ground state energy very well and the corresponding state may be used as a starting point for further investigations. The energy spectrum of the Single Impurity Anderson Model is calculated exactly for a special non-trivial model density of states describing the bare band electrons. All approaches introduced here are compared to this exact result and to other ground state energy calculations.     

Density modulation and superconductivity in a system of fermions

An antisymmetrized product of periodic density modulated one particle functions is investigated as a trial wave function for different local twobody forces. The model is compared with a BCS ground state. For some potentials a lower ground state energy has been found for the density modulated state. In lowest order cluster expansion forces with a hard core have been examined. A liquid-solid transition is indicated for³He at a density near the experimental value.     

Ground state properties of a Bose－Einstein condensate confined in an anharmonic external potential

In light of the interference experiment of Bose－Einstein condensates, we present an anharmonic external potential model to study ground state properties of Bose－Einstein condensates. The ground state energy and the chemical potential have been analytically obtained, which are lower than those in harmonic trap. Additionally, it is found that the anharmonic strength of the external potential has an important effect on density and velocity distributions of the ground state for the Thomas－Fermi model.     

Level density parameters for the back-shifted fermi gas model in the mass range 40 < A < 250

The parameters a and Δ for the Fermi gas model with fictive ground state are determined for about 220 nuclei from experimental level densities at low excitation energy and at the neutron binding energy. In. agreement with previous results it is found that for most nuclei the fictive ground state is back-shifted relative to the conventionally shifted ground state as determined by the pairing energy. Shell effects are evident at the mass numbers 90, 140 and 208 for both the level density parameter a and the back-shift. A comparison is given with previous results and different experimental data on level densities.     

二维电子体系在高密度下的稳定性

本文计算了高密度的二维电子体系的边缘能(将二维体系沿某一直线解离成两片时,形成单位长度新边缘所需要的能量)。结果发现,当r_ss^(c)(约0.415)时,边缘能变负,从而表明在高密度下,二维电子气的基态有可能发生不稳。我们分别讨论了二维非束缚的电子气和束缚的电子气基态的稳定性,并在一个简化的模型下给出了束缚的电子气基态稳定性的判据。 关键词：     

Ground-state and quenched-state properties of a one-dimensional interacting lattice gas in a random potential

We determine the zero-temperature properties of a one-dimensional lattice gas of particles that interact via a nearest neighbor exclusion potential and are subject to a random external field. The model is a special limiting case of the random field Ising chain. We calculate (1) the energy and density of the ground state as well as the local energy-density correlation and (2) the pair correlation function. The latter calculation gives access to all higher order correlations. The structure factor is shown to be a squared Lorentzian. We also compare the ground state to the quenched state obtained by sequentially filling the lowest available energy levels.     

Two-dimensional random walk on the ground state energy surface: The N-Z distributions from nuclear heavy-ion collisions

The nucleon transfer process in deep inelastic collision is formulated as a two-dimensional random walk process on the N-Z plane. The probability of each step is assumed to be proportional to the available final state density which is determined by the ground state energy surface of the colliding dinuclear system. Here a model problem is considered, where the long and narrow valley in the energy surface is replaced by a slot with a flat bottom. Even in this crude model, good agreement is obtained between the calculated widths of the N-Z distribution and the experimental values, indicating that the ground state energy surface plays an important role in the mass and charge transfer phenomena in deep inelastic processes.     

Gapless Excitation above a Domain Wall Ground State in a Flat-Band Hubbard Model

We construct a set of exact ground states with a localized ferromagnetic domain wall and with an extended spiral structure in a deformed flat-band Hubbard model in arbitrary dimensions. We show the uniqueness of the ground state for the half-filled lowest band in a fixed magnetization subspace. The ground states with these structures are degenerate with all-spin-up or all-spin-down states under the open boundary condition. We represent a spin one-point function in terms of local electron number density, and find the domain wall structure in our model. We show the existence of gapless excitations above a domain wall ground state in dimensions higher than one. On the other hand, under the periodic boundary condition, the ground state is the all-spin-up or all-spin-down state. We show that the spin-wave excitation above the all-spin-up or -down state has an energy gap because of the anisotropy     

Ground State and Band Gap of MX complex

Using the one-band model of halogen-bridged mixed-valence transition metal complex (MX complex), within mean field theory, we have proved for fixed electron-phonon coupling, the band gap reaches the minimum at the boundary of the charge density wave state and the spin density wave state in the phase diagram. The analytic form of the ground state energy and the band gap are also obtained.