Critical temperature of Bose-Einstein condensation for weakly interacting bose gas in a potential trap

It has been a long history to study Bose-Einstein condensation (BEC) of weakly in-teracting Bose gas, and several theoretical models have been developed to research uni-form and weakly interacting Bose gas. Ref. [1] summarized all of these models and the corresponding results, which gave a derivation of critical temperature from ideal case 1/30Tc c n,?T = α (1) with a wide spread of parameter c from 0.7 to 2.33, where α is the scattering length of s wave and n is atom number density. Due…     

The condensation of ideal Bose gas in a gravitational field

Bose–Einstein condensation of two- and three-dimensional boson gases confined in the one-dimensional gravitational field is investigated. Using the semiclassical approximation method, the expressions for the BEC transition temperature, condensate fraction, heat capacity and the entropy of the system are obtained. The heat capacities of the systems with D  =1, 2, 3 (D$D$ is the dimension) at the critical temperature are discussed. We find that for the 1-D and 2-D boson systems, the heat capacities are continuous, but for the 3-D case there is a gap at the critical temperature T_c$T_c$. The entropies of the systems with D=1, 2, 3 are also studied in detail. It is found that the entropies increase with the increasing of the temperature T.     

Collective mode evidence of high-spin bosonization in a trapped one-dimensional atomic Fermi gas with tunable spin

We calculate the frequency of collective modes of a one-dimensional repulsively interacting Fermi gas with high-spin symmetry confined in harmonic traps at zero temperature. This is a system realizable with fermionic alkaline-earth-metal atoms such as ¹⁷³Yb, which displays an exact SU(κ$\kappa$) spin symmetry with κ?2$\kappa ?2$ and behaves like a spinless interacting Bose gas in the limit of infinite spin components κ→∞$\kappa \to \infty$, namely high-spin bosonization. We solve the homogeneous equation of state of the high-spin Fermi system by using Bethe ansatz technique and obtain the density distribution in harmonic traps based on local density approximation. The frequency of collective modes is calculated by exactly solving the zero-temperature hydrodynamic equation. In the limit of large number of spin-components, we show that the mode frequency of the system approaches that of a one-dimensional spinless interacting Bose gas, as a result of high-spin bosonization. Our prediction of collective modes is in excellent agreement with a very recent measurement for a Fermi gas of ¹⁷³Yb atoms with tunable spin confined in a two-dimensional tight optical lattice.     

Thermodynamic Limit and Proof of Condensation for Trapped Bosons

We study condensation of trapped bosons in the limit when the number of particles tends to infinity. For the noninteracting gas we prove that there is no phase transition in any dimension, but in any dimension, at any temperature the system is 100% condensated into the one-particle ground state. In the case of an interacting gas we show that for a family of suitably scaled pair interactions, the Gross–Pitaevskii scaling included, a less-than-100% condensation into a single-particle eigenstate, which may depend on the interaction strength, persists at all temperatures.     

Coherent state approach to the cross-collisional effects in the population dynamics of a two-mode Bose–Einstein condensate

We reanalyze the non-linear population dynamics of a Bose–Einstein condensate (BEC) in a double well trap considering a semiclassical approach based on a time dependent variational principle applied to coherent states associated to SU(2) group. Employing a two-mode local approximation and hard sphere type interaction, we show in the Schwinger’s pseudo-spin language the occurrence of a fixed point bifurcation that originates a separatrix of motion on a sphere. This separatrix corresponds to the borderline between two dynamical regimes of Josephson oscillations and mesoscopic self-trapping. We also consider the effects of interaction between particles in different wells, known as cross-collisions. Such terms are usually neglected for traps sufficiently far apart, but recently it has been shown that they contribute to the effective tunneling constant with a factor growing linearly with the particle number. This effect changes considerably the effective tunneling of the system for sufficiently large number of trapped atoms, in perfect accord with experimental data. Finally, we identify analytically the transition parameter associated to the bifurcation in the generalized phase space of the model with cross-collision terms, and show how the dynamical regime depends on the initial conditions of the system and the collisional parameters values.     

Manifestation of a gap due to the exchange energy in a spinor condensate

We investigate the dynamic response of population transfer between two components of a finite temperature spinor Bose condensed gas to a time-dependent coupling potential. Comparison between the results obtained in the Bogoliubov–Popov approximation (BPA) and in the generalized random phase approximation (GRPA) shows noticeable discrepancies. In particular, the inter-component current response function calculated in the GRPA displays a gapped spectrum due to the exchange interaction energy whereas the corresponding density response function is gapless. We verify that, contrary to the BPA, the GRPA preserves the SU(2) symmetry and the f-sum rule associated to the spinor gas. In order to validate the approximation, we propose an experimental setup that allows the observation of the predicted gap.     

The Bogoliubov model of weakly imperfect Bose gas

We present a systematic account of known rigorous results about the Bogoliubov model of weakly imperfect Bose gas (WIBG). This model is a basis of the celebrated Bogoliubov theory of superfluidity, although the physical phenomenon is, of course, more complicated than the model. The theory is based on two Bogoliubov's ansätze: the first truncates the full Hamiltonian of the interacting bosons to produce the WIBG, whereas the second substitutes some operators by c-numbers (the Bogoliubov approximation). After some historical remarks, and physical and mathematical motivations of this Bogoliubov treatment of the WIBG, we turn to revision of the Bogoliubov's ansätze from the point of view of rigorous quantum statistical mechanics. Since the exact calculation of the pressure and the behaviour of the Bose condensate in the WIBG are available, we review these results stressing the difference between them and the Bogliubov theory. One of the main features of the mathematical analysis of the WIBG is that it takes into account quantum fluctuations ignored by the second Bogoliubov ansatz. It is these fluctuations which are responsible for indirect attraction between bosons in the fundamental mode. The latter is the origin of a nonconventional Bose condensation in this mode, which has a dynamical nature. A (generalized) conventional Bose–Einstein condensation appears in the WIBG only in the second stage as a result of the standard mechanism of the total particle density saturation. It coexists with the nonconventional condensation. We give also a review of some models related to the WIBG and to the Bogoliubov theory, where a similar two-stage Bose condensation may take place. They indicate possibilities to go beyond the Bogoliubov theory and the Hamiltonian for the WIBG.     

Dephasing in the presence of a two-dimensional electron gas at high magnetic fields

By means of degenerate four-wave mixing (FWM), we investigate the quantum coherence of electron–hole pairs in the presence of a two-dimensional electron gas in modulation-doped GaAs–AlGaAs quantum wells in the regime of the integer quantum-Hall effect. We observe large jumps in the decay time of the FWM signal at even Landau level filling factors. The main features of the experimental observations can be qualitatively reproduced by a model which takes into account the number of unoccupied states within the highest partially occupied Landau level. Furthermore, we observe quantum beats between up to three different Landau level transitions.     

Thermodynamic properties of two-dimensional few-electrons quantum dot using the static fluctuation approximation (SFA)

The two-dimensional GaAs parabolic quantum dot (QD) is investigated in the static fluctuation approximation (SFA) where both the magnetic field and the electron-electron interaction are fully taken into account. The thermodynamic properties of the system are computed as functions of the temperature and magnetic field for different numbers of electrons (N). It is noted that the mean internal energy increases with increasing number of electrons and magnetic field. This increase is not smooth, and a sudden change in slope is observed at a certain value of magnetic field for N≥4. It is found that the magnetization has sharp jumps for N≥4; for N≤3 a smooth monotonic diamagnetism is exhibited. A sharp peak is observed in the specific heat when the magnetic field is increased. It is found that the lowest-state transitions occur at a critical value of magnetic field. These transitions appear in the mean internal energy and magnetization.     

Sensing domain wall pinning in the longitudinal magnetoresistance of a two-dimensional electron gas

We investigate the sensing of domain wall pinning in thin Co wires positioned on top of a two-dimensional electron gas (2DEG) heterostructure by measuring the longitudinal resistance of the 2DEG as the magnetic field is swept, in an analogy to the Barkhausen effect. For comparison, we also measure the magnetoresistance of the ferromagnetic film in the same device in a subsequent sweep. Compared to the Hall measurements, the longitudinal measurement has the advantage of sensing magnetic activity over longer lengths, while compared to the measurement of the magnetoresistance in the ferromagnetic wire, it offers complementary information related to the pinning and unpinning of the domain wall, due to its sensitivity only to the out-of-plane magnetic field component.     

A new rigorous upper bound for the inverse critical temperature of the two-dimensional Coulomb gas

In this paper we show how to improve the recent result _c 17.2 on the inverse critical temperature for the two-dimensional Coulomb gas at low density to get the following upper bound: _c 16.     

Oscillations of the magnetoresistance of a two-dimensional electron gas under microwave irradiation: Influence of the irradiation frequency

We present measurements of the magnetoresistance of a two-dimensional electron gas (2DEG) under continuous microwave as a function of the irradiation frequency. In a previous work by Simovič et al. [Phys. Rev. B 71 (2005) 233303], the magnetoresistance under microwave was shown to be modulated by oscillations of large amplitude that are periodic with magnetic field, their period and phase depending strongly on the electron density. Here we show that the phase and the amplitude of the microwave-induced oscillations also depend on the frequency of irradiation and the sign of the magnetic field.     

Effects of a finite number of particles on the thermodynamic properties of a harmonically trapped ideal charged Bose gas in a constant magnetic field

We investigate the thermodynamic properties of an ideal charged Bose gas confined in an anisotropic harmonic potential and a constant magnetic field. Using an accurate density of states, we calculate analytically the thermodynamic potential and consequently various intriguing thermodynamic properties, including the Bose–Einstein transition temperature, the specific heat, magnetization, and the corrections to these quantities due to the finite number of particles are also given explicitly. In contrast to the infinite number of particles scenarios, we show that those thermodynamic properties,particularly the Bose–Einstein transition temperature depends upon the strength of the magnetic field due to the finiteness of the particle numbers, and the collective effects of a finite number of particles become larger when the particle number decreases. Moreover, the magnetization varies with the temperature due to the finiteness of the particle number while it keeps invariant in the thermodynamic limit N →∞.     

Exchange-enhanced spin-splitting in a two-dimensional electron gas in the presence of the Rashba spin–orbit interaction

We present a theoretical study on how many-body effects can affect the spin-splitting of a two-dimensional electron gas in the presence of the Rashba spin–orbit interaction. The standard Hartree–Fock approximation and Green's function approach are employed to calculate the energy spectrum and density of states of a spin-split two-dimensional electron gas (2DEG). We find that the presence of the exchange interaction can enhance significantly the spin-splitting of a 2DEG on top of the Rashba effect. The physical reasons behind this important phenomenon are discussed.     

A Monte Carlo study of the classical two-dimensional one-component plasma

We present results from extensive Monte Carlo simulations of the fluid phase of the two-dimensional classical one-component plasma (OCP). The difficulties associated with the infinite range of the logarithmic Coulomb interaction are eliminated by confining the particles to the surface of a sphere. The results are compared to those obtained for a planar system with screened Coulomb interactions and periodic boundary conditions; in this case the infinite tail of the Coulomb interaction is treated as a perturbation. The exact simulation results are used to test various approximate theories, including a semiempirical modification of the hypernetted-chain (HNC) integral equation. The OCP freezing transition is located at a coupling= e²/k_BT–140.     

Alloy disorder scattering limited mobility of two-dimensional electron gas in the quaternary AlInGaN/GaN heterojunctions

Nitride heterojunction field effect transistors (HFETs) with quaternary AlInGaN barrier layers have achieved remarkable successes in recent years based on highly improved mobility of the two-dimensional electron gases (2DEGs) and greatly changed AlInGaN compositions. To investigate the influence of the AlInGaN composition on the 2DEG mobility, the quaternary alloy disorder (ADO) scattering to 2DEGs in AlInGaN/GaN heterojunctions is modeled using virtual crystal approximation. The calculated mobility as a function of AlInGaN alloy composition is shown to be a triangular-scarf-like curved surface for both cases of fixed thickness of AlInGaN layer and fixed 2DEG density. Though the two mobility surfaces are quite different in shape, both of them manifest the smooth transition of the strength of ADO scattering from quaternary AlInGaN to ternary AlGaN or AlInN. Some useful principles to estimate the mobility change with the Al(In,Ga)N composition in Al(In,Ga)N/GaN heterojunctions with a fixed 2DEG density are given. The comparison between some highest Hall mobility data reported for Al_xGa_1−xN/GaN heterojunctions (x=0.06~0.2) at very low temperature (0.3~13 K) and the calculated 2DEG mobility considering ADO scattering and interface roughness scattering verifies the influence of ADO scattering. Moreover, the room temperature Hall mobility data of Al(In,Ga)N/AlN/GaN heterojunctions with ADO scattering eliminated are summarized from literatures. The data show continuous dependence on Hall electron density but independence of the Al(In,Ga)N composition, which also supports our theoretical results. The feasibility of quaternary AlInGaN barrier layer in high conductivity nitride HFET structures is demonstrated.     

基于读出条读出的二维位置灵敏气体电子倍增器的研制

为研发能够满足北京同步辐射(BSRF)实验要求的二维探测器,研制了基于读出条读出的二维位置灵敏X射线气体电子倍增器(GEM).实验过程中通过改进读出条的周期,并基于中科院高能所实验物理中心电子学组研制的多路电荷放大器系统与VME存储-ADC系统,对软X射线源的位置分辨率进行了精密测量且得到了优异的二维位置分辨:X方向约为84μm,Y方向约为75μm.研究了三级GEM压差之和对位置分辨的影响,并测试了探测器的位置准确度与线性.对基于阳极读出的GEM用于模拟读出测试系统得到了一定的理论认识,侧重研究了GEM探测器基于模拟读出的系统特性,给出了相关的分析与讨论.     

A study of the ground-state energy of He with nucleon–nucleon potentials

Ground-state properties are evaluated for the finite nucleus ⁴He starting from realistic nucleon–nucleon interactions within the framework of the Green’s function approach. For the sake of comparison, the same calculations are performed using the Brueckner–Hartree–Fock approximation. For that purpose four high-quality modern nucleon–nucleon interactions represented in momentum space are employed: the Argonne V18, CD-Bonn, Bonn A and N³LO potentials. In these potentials, the effects of charge dependence are taken into account. Additional binding energy is obtained from the inclusion of the hole–hole scattering term within the framework of the Green function approach. It has been shown that the Green function results agree well with the results obtained by accurate methods for few-nucleon systems such as the Faddeev–Yakubovsky calculation. In this study, a comparison of the calculated ground-state energies, obtained by using the Green function approach and different nucleon–nucleon potentials, with experimental values is carried out. The results show good agreement between the calculated values and the experimental ones.     

Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas

Many two-dimensional spin models can be transformed into Coulomb-gas systems in which charges interact via logarithmic potentials. For some models, such as the eight-vertex model and the Ashkin-Teller model, the Coulomb-gas representation has added significantly to the insight in the phase transitions. For other models, notably theXY model and the clock models, the equivalence has been instrumental for almost our entire understanding of the critical behavior. Recently it was shown that theq-state Potts model and then-vector model are equivalent to a Coulomb gas with an asymmetry between positive and negative charges. Fieldlike operators in these spin models transform noninteger charges and magnetic monopoles. With the aid of exactly solved models the Coulombgas representation allows analytic calculation of some critical indices.     

A comparison of the transport properties of bilayer graphene,monolayer graphene,and two-dimensional electron gas

We studied and compared the transport properties of charge carriers in bilayer graphene, monolayer graphene, and the conventional semiconductors (the two-dimensional electron gas (2DEG)). It is elucidated that the normal incidence transmission in the bilayer graphene is identical to that in the 2DEG but totally different from that in the monolayer graphene. However, resonant peaks appear in the non-normal incidence transmission profile for a high barrier in the bilayer graphene, which do not occur in the 2DEG. Furthermore, there are tunneling and forbidden regions in the transmission spectrum for each material, and the division of the two regions has been given in the work. The tunneling region covers a wide range of the incident energy for the two graphene systems, but only exists under specific conditions for the 2DEG. The counterparts of the transmission in the conductance profile are also given for the three materials, which may be used as high-performance devices based on the bilayer graphene.