Unified properties of a weakly interacting Fermi gas in a weak magnetic field

When the orbital motion and the spin motion of particles were considered simultaneously, the thermodynamic potential function of a weakly interacting Fermi gas in a weak magnetic field was derived using the thermodynamics method. Based on the derived expression, the analytical expressions of energy, heat capacity, chemical potential, susceptibility and stability conditions of the system were given, and the effects of the interparticle interactions as well as the magnetic field on the properties of the system were analyzed. It was shown that the magnetic field always causes energy and stability to decrease, while the chemical potential of the system to increase. The repulsive (attractive) interactions always increase (decrease) energy and stability, but decrease (increase) the chemical potential and paramagnetism. The repulsive (attractive) interactions decrease (increase) heat capacity of the system at high temperatures but increase (decrease) it at low temperatures.     

强磁场中弱相互作用费米气体的热力学性质

基于赝势法和局域密度近似研究了强磁场中弱相互作用费米气体的热力学性质,得出化学势、总能和热容量的解析式,同时分析了磁场及相互作用对系统热力学性质的影响.研究表明,无论是高温情况还是低温情况下,磁场都能调节相互作用的影响.低温下,与无磁场的系统相比,磁场降低系统的化学势、总能和热容量;与无相互作用系统相比,排斥作用增加化学势而降低总能及热容量.高温下,磁场和排斥作用均可降低系统的总能而增加热容量,强磁场可以改变相互作用对总能及热容量的影响. 关键词： 强磁场 弱相互作用 费米气体 热力学性质     

弱磁场中弱相互作用费米气体的有限粒子数效应(英文)

由弱磁场中弱相互作用费米气体的配分函数,导出有限粒子数条件下系统的配分函数G(β,N ).在此基础上,运用统计平均方法求解有限粒子数弱相互作用费米气体热力学量的解析表达式,给出各种温度条件下的热力学性质.研究结果表明,有限粒子数效应使各个热力学量都产生了一个修正项,除温度趋于0外,粒子数对化学势的修正项有直接影响,对内能和热容量的修正项并不产生直接影响.并且有限粒子数效应总是降低化学势,从而使化学势的0点向低温漂移,粒子数增大,会削弱这种效应,粒子间的相互排斥会加强这种效应.     

Relativistic thermodynamic properties of a weakly interacting Fermi gas in a weak magnetic field

This paper derives the analytical expression of free energy for a weakly interacting Fermi gas in a weak magnetic field, by using the methods of quantum statistics as well as considering the relativistic effect. Based on the derived expression, the thermodynamic properties of the system at both high and low temperatures are given and the relativistic effect on the properties of the system is discussed. It shows that, in comparison with a nonrelativistic situation, the relativistic effect changes the influence of temperature on the thermodynamic properties of the system at high temperatures, and changes the influence of particle-number density on them at extremely low temperature. But the relativistic effect does not change the influence of the magnetic field and inter-particle interactions on the thermodynamic properties of the system at both high and extremely low temperatures.     

Stable, strongly attractive, two-state mixture of lithium fermions in an optical trap

We use an all-optical trap to confine a strongly attractive two-state mixture of lithium fermions. By measuring the rate of evaporation from the trap, we determine the effective elastic scattering cross section 4pia(2) to show that the magnitude of the scattering length |a| is very large, in agreement with predictions. We show that the mixture is stable against inelastic decay provided that a small bias magnetic field is applied. For this system, the s-wave interaction is widely tunable at low magnetic field, and can be turned on and off rapidly via a Raman pi pulse. Hence, this mixture is well suited for fundamental studies of an interacting Fermi gas.     

弱相互作用费米气体的不稳定性判据

根据由赝势法得到的弱相互作用费米气体的自由能，利用热力学方法研究了无外场时弱相互作用费米气体的稳定性.结果表明，无外场情况下理想费米气体与存在弱排斥相互作用的费米气体是稳定的；而具有弱吸引相互作用的费米气体在一定条件下可出现不稳定性.给出了不稳定性的粒子数密度判据和温度判据，就不同逸度情况下临界粒子数密度的具体表达结果以及温度、粒子质量和吸引相互作用对临界粒子数密度的影响进行了讨论. 关键词： 费米气体 相互作用 不稳定性判据     

Phase behaviors of strongly correlated Fermi gases in one-dimensional confinements

We report on the ground state of models for strongly correlated one-dimensional Fermi systems by means of theoretical studies of two-component atomic Fermi gases in highly anisotropic harmonic traps. In this context, we consider (i) the Gaudin-Yang model for a Luttinger liquid with repulsive interactions, including an analysis of the emergence of Wigner molecules in the 2k _F → 4k _F crossover, and (ii) the lattice Hubbard model yielding Luttinger liquid and Mott insulator or band-insulator phases for repulsive interactions and the Luther-Emery phase for attractive interactions, including in the former case an analysis of the role of disorder. Our calculations use novel versions of density and spin-density functional theory and a density-matrix renormalization-group technique. We also discuss preliminary results and future perspectives in the study of nonsymmetric two-component Fermi gases.     

Controlling optical responses through local dielectric resonance in nanometre metallic clusters

Optical responses in dilute composites are controlled through the local dielectric resonance of metallic clusters. We consider two located metallic clusters close to each other with admittances \varepsilon₁ and \varepsilon₂. Through varying the difference admittance ratio \eta [ = (\varepsilon₂- \varepsilon ₀) / (\varepsilon₁- \varepsilon₀)], we find that their optical responses are determined by the local resonance. There is a blueshift of absorption peaks with the increase of \eta. Simultaneously, it is known that the absorption peaks will be redshifted by enlarging the cluster size. By adjusting the nano-metallic cluster geometry, size and admittances, we can control the positions and intensities of absorption peaks effectively. We have also deduced the effective linear optical responses of three-component composites \varepsilon_e= \varepsilon₀ \bigl(1 + \sum_n=1^{n_s} [(\gamma_n2+ \eta \gamma_n2)/({\varepsilon₀(s - s_n))]} \bigr), and the sum rule of cross sections: \sum_n=1^{n_s} {(\gamma_n2+ \eta \gamma_n2 ) = N_h1+ N_h2, where N_h1and N_h2 are the numbers of \varepsilon₁ and \varepsilon₂ bonds along the electric field, respectively. These results may be beneficial to the study of surface plasmon resonances on a nanometre scale.     

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     

弱磁场中弱相互作用费米气体的热力学性质

根据赝势法和系综理论导出弱磁场中弱相互作用费米气体的内能、化学势和热容量的小参数r的解析式.在此基础上给出高温和低温两种情况下弱磁场中弱相互作用费米气体的热力学性质,探讨磁场及粒子间相互作用对热力学性质的影响,分析磁场与三维谐振势两种约束对系统性质影响的不同及其原因. 关键词： 赝势法 费米气体 相互作用 热力学性质     

Nature and properties of a repulsive Fermi gas in the upper branch of the energy spectrum

We generalize the Noziéres-Schmitt-Rink method to study the repulsive Fermi gas in the absence of molecule formation, i.e., in the so-called "upper branch." We find that the system remains stable except close to resonance at sufficiently low temperatures. With increasing scattering length, the energy density of the system attains a maximum at a positive scattering length before resonance. This is shown to arise from Pauli blocking which causes the bound states of fermion pairs of different momenta to disappear at different scattering lengths. At the point of maximum energy, the compressibility of the system is substantially reduced, leading to a sizable uniform density core in a trapped gas. The change in spin susceptibility with increasing scattering length is moderate and does not indicate any magnetic instability. These features should also manifest in Fermi gases with unequal masses and/or spin populations.     

Singularities in the Vertex Function in Two-Dimensional Tight-Binding Fermi Systems

The singularities in the vertex function are studied within the ladder approximation for a non-half-filled two-dimensional tight- binding Fermi system. The location of all the possible poles of the vertex function has been clarified for both repulsive and attractive interacting cases.. The scattering phase shift is examined and found not always zero at Fermi energy. The Kohn-lut tinger-like singularity is also briefly discussed.     

Polaron, molecule and pairing in one-dimensional spin-1/2 Fermi gas with an attractive Delta-function interaction

Using solutions of the discrete Bethe ansatz equations, we study in detail the quantum impurity problem of a spin-down fermion immersed into a fully ploarized spin-up Fermi sea with weak attraction. We prove that this impurity fermion in the one-dimensional (1D) fermionic medium behaves like a polaron for weak attraction. However, as the attraction grows, the spin-down fermion binds with one spin-up fermion from the fully-polarized medium to form a tightly bound molecule. Thus it is seen that the system undergos a crossover from a mean field polaron-like nature into a mixture of excess fermions and a bosonic molecule as the attraction changes from weak attraction into strong attraction. This polaron-molecule crossover is universal in 1D many-body systems of interacting fermions. In a thermodynamic limit, we further study the relationship between the Fredholm equations for the 1D spin-1/2 Fermi gas with weakly repulsive and attractive delta-function interactions.     

Interaction induced Raman light scattering as a probe of the local density structure of binary supercritical solutions

Interaction induced Raman light scattering is presented as a unique tool for the understanding of solvation processes from the solute's point of view in weakly interacting solute-solvent systems. A review of pertinent literature shows that this technique should be useful at least in single-phase binary mixtures such as supercritical solutions. Methane is used here as a probe molecule at 10mol% concentration (as the solute) and 90mol% CO and CO₂ are the solvents. The light scattering results, i.e., the dependence of the anisotropic intensities divided by density (I/d) on the density, are interpreted by use of the Duh-Haymet-Henderson closure (bridge) function of the Ornstein-Zernike integral equation. These data, together, are examined in the context of known supercritical solution thermodynamics and statistical mechanical results. It is shown that the light scattering I/d data versus density yield maxima in both attractive and repulsive solute-solvent systems. The local number density maxima were found near these same densities by the integral equation calculations for both methane + carbon monoxide or carbon dioxide using only Lennard-Jones single-centre parameters as input. The methane + carbon monoxide system is identified as weakly attractive (augmenting), whereas the methane + carbon dioxide system is identified as repulsive (avoidance).     

Effect of flux-dependent Friedel oscillations upon the effective transmission of an interacting nano-system

We consider a nano-system connected to measurement probes via non interacting leads. When the electrons interact inside the nano-system, the coefficient |t_s(E_F)|² describing its effective transmission at the Fermi energy E_F ceases to be local. This effect of electron-electron interactions upon |t_s(E_F)|² is studied using a one dimensional model of spinless fermions and the Hartree-Fock approximation. The non locality of |t_s(E_F)|² is due to the coupling between the Hartree and Fock corrections inside the nano-system and the scatterers outside the nano-system via long range Friedel oscillations. Using this phenomenon, one can vary |t_s(E_F)|² by an Aharonov-Bohm flux threading a ring which is attached to one lead at a distance L_c from the nano-system. For small distances L_c, the variation of the quantum conductance induced by this non local effect can exceed 0.1 (e²/h).     

Instability of a trapped ultracold Fermi gas with attractive interactions: quantum effects

We consider the possible mechanical instability of an ultracold Fermi gas due to the attractive interactions between fermions of different species. We investigate how the instability, predicted by a mean field calculation, is modified when the gas is trapped in a harmonic potential and quantum effects are included.Received: 19 July 2004, Published online: 6 December 2004PACS: 03.75.Ss Degenerate Fermi gases - 03.75.Kk Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow     

Conductance of nano-systems with interactions coupled via conduction electrons: effect of indirect exchange interactions

A nano-system in which electrons interact and in contact with Fermi leads gives rise to an effective one-body scattering which depends on the presence of other scatterers in the attached leads. This non local effect is a pure many-body effect that one neglects when one takes non interacting models for describing quantum transport. This enhances the non-local character of the quantum conductance by exchange interactions of a type similar to the RKKY-interaction between local magnetic moments. A theoretical study of this effect is given assuming the Hartree-Fock approximation for spinless fermions of Fermi momentum k_F in an infinite chain embedding two scatterers separated by a segment of length L_c. The fermions interact only inside the two scatterers. The dependence of one scatterer onto the other exhibits oscillations of period π/k_F which decay as 1/L_c and which are suppressed when L_c exceeds the thermal length L_T. The analytical results given by the Hartree-Fock approximation are compared with exact numerical results obtained with the embedding method and the DMRG algorithm.     

Thermodynamic stability of a weakly interactingFermi gas trapped in a harmonic potential

Based on the theoretical results derived from pseudopotential method and local approximation, this paper studies the thermodynamic stability of a weakly interacting Fermi gas trapped in a harmonic potential by using analytical method of thermodynamics. The effects of the interparticle interactions as well as external potential on the thermodynamic stability of the system are discussed. It is shown that the system is stable as for the complete average, but as for local parts, the system is unstable anywhere. This instability shows that the stability conditions of mechanics cannot be satisfied anywhere, and the stability conditions of thermostatics cannot be satisfied somewhere. In addition, the interactions and external potential have direct effects on the local stability of the system.     

Boson-fermion Demixing and collapse in low dimensions

We evaluate in a mean-field model the equilibrium stability conditions of a gaseous mixture of bosonic and spin-polarized fermionic atoms inside a pancake-shaped or a cigar-shaped harmonic trap, under conditions such that the trap thickness approaches the magnitude of the s-wave scattering lengths but the atoms still experience collisions in three dimensions. With decreasing dimensionality, the Fermi pressure plays an increasingly dominant role. Full demixing in the case of repulsive boson-fermion interactions can be induced by squeezing the thickness of the clouds in a pancake-shaped trap or by lowering the number of trapped fermions in a cigar-shaped trap. Collapse under attractive interspecies interaction in quasi-one-dimensional confinement is inhibited within the range of validity of a mean-field model.