理想费米气体在n维势阱中的空间分布与有效囚禁范围（英文）

在Thomas-Fermi半经典近似适用条件下,求得了理想费米气体在n维广义幂律势阱中的态密度,进而研究了粒子数密度的空间分布,内能,热容量的空间变化以及等效化学势的一级近似.定义了绝对零度下的特征长度,求出了理想费米气体在n维广义幂律势阱中的有效囚禁范围.利用两个例子,揭示了理想费米气体的有效囚禁范围与外势形式,粒子数,粒子质量以及势场圆频率的依赖关系.     

谐振子势阱囚禁玻色气体的玻色-爱因斯坦凝聚

基于Thomas-Fermi半经典近似研究了谐振子势阱约束下任意维理想玻色气体的玻色-爱因斯坦凝聚(BEC).导出了玻色气体的BEC转变温度、基态粒子占据比例、内能和热容量等物理量的解析表达式,讨论了空间维度和谐振子势阱的影响.以二维和三维玻色系统为例,数值计算了上述热力学量,并与解析结果进行了对比,二者获得了较好的吻合.     

囚禁弱相互作用玻色气体的势场优化准则

根据Thomas-Fermi近似,在基于最小动量态上玻色-爱因斯坦凝聚的前提下,研究了囚禁弱相互作用玻色气体势场的最优化问题.导出了指数吸引势阱中有效势场和粒子数极限判据,粒子数给定时,可由此判据求出所需势场强度;势场强度给定时,可由此判据求出粒子数极限.根据吸引相互作用系统的稳定性以及求出的排斥相互作用的最大粒子数极限,结合有效势场判据,分别给出了囚禁吸引和排斥相互作用玻色气体时,势场强度的最佳取值范围. 关键词： 玻色-爱因斯坦凝聚 弱相互作用 粒子数极限 势场强度     

谐振子势阱囚禁玻色气体的玻色-爱因斯坦凝聚

基于Thomas-Fermi半经典近似方法研究了谐振子势阱约束下任意维理想玻色气体的玻色-爱因斯坦凝聚(BEC)．导出了玻色气体的BEC转变温度、基态粒子占据比例、内能和热容量等物理量的解析表达式,讨论了空间维度和谐振子势阱的影响．以二维和三维玻色系统为例,数值计算了上述热力学量,并与解析结果进行了对比,二者获得了较好的吻合．     

势阱中二维理想玻色气体的磁性质

采用半经典近似方法,研究简谐势阱中二维理想带电玻色气体的磁性质.推导出了该体系的热力学势、相变温度、内能、比热、磁场强度和磁化率随外加磁场的变化关系,进而分析了约束势阱对理想带电玻色气体热力学性质的影响.     

玻色-爱因斯坦凝聚临界温度的估算

引进有效数密度的概念，对球谐势阱中理想玻色气体的临界温度作了简便的估算，并以此为例讨论应如何将玻色－爱因斯坦凝聚的研究引入教学，同时还阐述了这种引入的重要意义。     

玻色-费米超流混合体系中的相互作用调制隧穿动力学

研究了玻色-费米超流混合体系中的相互作用调制隧穿动力学特性,其中玻色子位于对称双势阱中,费米子位于对称双势阱中心的简谐势阱中.采用双模近似方法得到描述双势阱玻色-爱因斯坦凝聚的动力学特性方程组,并将其与简谐势阱中分子玻色-爱因斯坦凝聚的Gross-Pitaevskii方程进行耦合.通过对不同参数下玻色-费米混合体系中的隧穿现象进行数值研究,发现简谐势阱中费米子与双势阱中玻色子的相互作用使双势阱玻色-爱因斯坦凝聚的隧穿动力学特性更加丰富.不但驱使双势阱中玻色-爱因斯坦凝聚从类约瑟夫森振荡转变为宏观量子自囚禁,而且宏观量子自囚禁表现为三种不同的形式:相位与时间呈负相关并随时间单调减小的自囚禁、相位随时间演化有界的自囚禁以及相位与时间呈正相关并随时间单调增大的自囚禁.     

谐振势阱中旋转广义玻色系统的热力学性质

以非广延Tsallis统计理论为基础,导出了广义玻色-爱因斯坦统计分布表达式,并用其分别讨论了三维和二维谐振势阱约束的旋转广义玻色气体的热力学性质.结合系统粒子数、玻色-爱因斯坦凝聚(BEC)临界温度、基态粒子占据率和比热等物理量的解析表达式,分析了非广延参数和势阱旋转频率等因素对系统热力学性质的影响.     

非谐势阱中二维G-P方程的数值计算

通过能量泛函的方法得到描述囚禁在非谐势阱中玻色-爱因斯坦凝聚体的二维G-P方程数值解,讨论原子间相互作用和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.     

三维简谐势阱中玻色-爱因斯坦凝聚的边界效应

在定义特征长度的基础上,应用Euler–MacLaurin公式,研究了理想玻色气体在三维简谐势阱中玻色-爱因斯坦凝聚的边界效应.结果表明:粒子的凝聚分数由于有限尺度和有限粒子数效应而减小,修正的凝聚分数和凝聚温度由于边界效应存在一个极大值,选择优化的最佳势阱参数,可以有效提高凝聚分数和凝聚温度;热容量的跃变存在边界效应和粒子数效应,选择合理的势阱参数时,热容量的跃变存在一个极小值.导出了简谐势阱中有限理想玻色气体的状态方程,揭示了压强的各向异性(或各向同性)取决于简谐势频率的各向异性(或各向同性).     

Fermi气体在势阱中的最大囚禁范围与状态方程

在Thomas-Fermi近似条件下,研究了n维广义幂律势阱中Fermi原子气体的最大囚禁范围,给出了n维势阱中气体的实际囚禁体积,导出了状态方程.结果表明,最大囚禁范围和囚禁气体压强不仅与势阱性质有关,也与自由理想Fermi系统的化学势有关.对三维球对称简谐势阱进行了应用,表明在Thomas-Fermi近似有效的前提下,当系统满足条件((kT)/(hω))² ((16π²g)/ 关键词： Fermi气体 n维势阱')" href="#">n维势阱 最大囚禁范围 状态方程     

Renormalisation group approach to the ideal Bose gas ind dimensions

Critical behaviour of ad-dimensional ideal Bose gas is investigated from the point of view of the renormalisation-group approach. Rescaling of quantum-field amplitudes is avoided by introducing a scaling variable inversely proportional to the thermal momentum of the particles. The scaling properties of various thermodynamic quantities are seen to emerge as a consequence of the irrelevant nature of this variable. Critical behaviour is discussed at fixed particle density as well as at fixed pressure. Connection between susceptibility and correlation function of the order-parameter for a quantum system is elucidated.     

The universal sound velocity formula for the strongly interacting unitary Fermi gas

Due to the scale invariance,the thermodynamic laws of strongly interacting limit unitary Fermi gas can be similar to those of non-interacting ideal gas.For example,the virial theorem between pressure and energy density of the ideal gas P=2E/3V is still satisfied by the unitary Fermi gas.This paper analyses the sound velocity of unitary Fermi gases with the quasi-linear approximation.For comparison,the sound velocities for the ideal Boltzmann,Bose and Fermi gas are also given.Quite interestingly,the sound velocity formula for the ideal non-interacting gas is found to be satisfied by the unitary Fermi gas in different temperature regions.     

Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas

We study a system consisting of a heavy quantum particle, called the tracer particle, coupled to an ideal gas of light Bose particles, the ratio of masses of the tracer particle and a gas particle being proportional to the gas density. All particles have non-relativistic kinematics. The tracer particle is driven by an external potential and couples to the gas particles through a pair potential. We compare the quantum dynamics of this system to an effective dynamics given by a Newtonian equation of motion for the tracer particle coupled to a classical wave equation for the Bose gas. We quantify the closeness of these two dynamics as the mean-field limit is approached (gas density ${\to \infty}$ ). Our estimates allow us to interchange the thermodynamic with the mean-field limit.     

Free Energies of Dilute Bose Gases: Upper Bound

We derive an upper bound on the free energy of a Bose gas at density ϱ and temperature T. In combination with the lower bound derived previously by Seiringer (Commun. Math. Phys. 279(3): 595–636, 2008), our result proves that in the low density limit, i.e., when a ³ ϱ≪1, where a denotes the scattering length of the pair-interaction potential, the leading term of Δf, the free energy difference per volume between interacting and ideal Bose gases, is equal to 4pa(2r²-[r-r_c]²₊)4\pi a(2\varrho^{2}-[\varrho-\varrho_{c}]^{2}_{+}). Here, ϱ _c (T) denotes the critical density for Bose–Einstein condensation (for the ideal Bose gas), and [⋅]₊=max {⋅,0} denotes the positive part.     

Ground State Energy of Dilute Bose Gas in Small Negative Potential Case

It is well known that the ground state energy of a three dimensional dilute Bose gas in the thermodynamic limit is E=4π a ρ N when the particles interact via a non-negative, finite range, spherically symmetric, two-body potential. Here, N is the number of particles, ρ is the density of the gas, and a is the scattering length of the potential. In this paper, we prove the same result without the non-negativity condition on the potential, provided the negative part is small.     

Higher order solutions of Lieb-Liniger integral equation

We study higher order solutions of Lieb-Liniger integral equation for a one-dimensional δ-function Bose gas. By use of the power series expansion method, the integral equation is solved and the correction terms which improve the Bogoliubov theory are calculated analytically in the weak coupling regime. Physical quantities such as the ground state energy and the chemical potential are represented by a dimensionless parameter γ=c/ρ, where c is the interaction strength and ρ is the number density of particles while the quasi-momentum distribution function is expressed in terms of a dimensionless parameter λ=c/K, where K is the cut-off momentum.     

Oscillating Casimir force between two slabs in a Fermi sea

The Casimir effect for two parallel slabs immersed in an ideal Fermi sea is investigated at both zero and nonzero temperatures. It is found that the Casimir effect in a Fermi gas is distinctly different from that in an electromagnetic field or a massive Bose gas. In contrast to the familiar result that the Casimir force decreases monotonically with the increase of the separation L between two slabs in an electromagnetic field and a massive Bose gas, the Casimir force in a Fermi gas oscillates as a function of L. The Casimir force can be either attractive or repulsive, depending sensitively on the magnitude of L. In addition, it is found that the amplitude of the Casimir force in a Fermi gas decreases with the increase of the temperature, which also is contrary to the case in a Bose gas, since the bosonic Casimir force increases linearly with the increase of the temperature in the region T < T_c, where T_c is the critical temperature of the Bose-Einstein condensation.     

On the issue of zero point energy in Bose–Einstein condensates

Following on our earlier work in this area, here we examine in some detail the physical mechanism involved in the Bose–Einstein condensation process. In particular we emphasise the significance of the zero value of the chemical potential at and below the critical temperature. The molar zero-point energy (ZPE) for an ideal gas of He⁴ atoms in our new analysis is estimated and found to be very close to that calculated for an ideal Fermi gas of He³ atoms under the same conditions. This gives numerical support to our theory. We also show how the theory is consistent with the presence of a density maximum in liquid He⁴.     

Do Bosons Condense in a Homogeneous Magnetic Field?

It has been known since the paper⁽²⁶⁾ and then due to a rigorous result⁽³⁾ that the answer to the question in the title is negative for a three-dimensional “ideal gas of charged bosons”. The present paper adds a new rigorous result in this direction. We show that the answer to the question becomes positive, if this “ideal gas of charged bosons” is simultaneously embedded in an appropriate periodic external potential. We prove that it is true for the Perfect Bose Gas (PBG), as well as for the Imperfect Bose Gas with a Mean-Field repulsive particle interaction.