Fermion Coherent State Studies of One-Dimensional Hubbard Model

We present a comparative study of the ground state of the one-dimensional Hubbard model. We first use a new fermion coherent state method in the framework of Fermi liquid theory by introducing a hole operator and considering the interactions of two pairs electrons and holes. We construct the ground state of the Hubbard model as ｜〉=[f＋∑^tφk1σ1hk2σ2ck3σ3hk4σ4 ∏exp（ρck1σ1 hk2σ2）]｜〉0,where φ and ρ are the coupling constants. Our results are then compared to those of varlational methods, density functional theory based on the exact solvable Bethe ansatz solutions, variational Monto-Carlo method （VMC） as well as to the exact result of the infinite system. We find satisfactory agreement between the fermion coherent state scheme and the VMC data, and provide a new picture to deal with the strongly correlated system.     

Deformation of Superoperator's Kraus Representation Derived by Weyl Correspondence and Entangled State Representation

By virtue of the Weyl correspondence and based on the the technique of integration within an ordered product of operators, we show under what condition the superoperator's Kraus representation ρ^ˊ=∑_μ A_μρA_μ^† can be deformed as ρ^ˊ=(1/π)∫d²αB(α)D(α)ρD^†(α), where D(α) is the displacement operator, B(α) is a probability density related to the classical Weyl correspondence of A_μ. An alternate discussion by using the entangled state representation and through a quantum teleportation process is also presented.     

A new two-mode thermo- and squeezing-mixed optical field

We propose a new two-mode thermo-and squeezing-mixed optical field, described by the new density operator ρ=1-e~f-|g|~2 e~(ga~+b~+)e~(fa~+a)|0〉 f_(bb) 〈0| e~(g*ab), where |0〉_(bb) 〈0| is the b-mode vacuum, e ~(fa~+a)represents the thermo-field, and e~(ga~+b~+) indicates squeezing. The photon statistics for ρ is studied by virtue of the method of integration within ordered product(IWOP) of operators. Such a field can be generated when a two-mode squeezed state passes through a one-mode dissipation channel.     

A New Approach to Elucidating Quantum-Mechanical SO(3) Rotation

In this letter, the logarithm of the three-dimensional Euclidean rotation matrix R is calculated, and its physical meaning is discussed. The new rotation operator identity D(R)≡ƒd³|Rr ><(r| = exp{a_i^†(lnR)_ija_j} (where a_i^†(a_i) are creation (annihilation) operators of a three-dimensional harmonic oscillator), which is deduced by the technique of integration within ordered product, motivates us to discuss In R. The present work, together with the previous one^[2], provides a new approach to elucidating quantum-mechanical rotation.     

The Three-Pion Decays of the a1(1260)

We investigate the decay of a₁⁺ (1260)→π⁺π⁺π^- with the assumption that the a₁(1260) is dynamically generated from the coupled channel ρπ and KK^* interactions. In addition to the tree level diagrams that proceed via a₁⁺ (1260)→ρ⁰π⁺→π⁺π⁺π^-, we take into account also the final state interactions of ππ→ππ and KK→ππ. We calculate the invariant π⁺π^- mass distribution and also the total decay width of a₁⁺ (1260)→π⁺π⁺π^- as a function of the mass of a₁(1260). The calculated total decay width of a₁(1260) is significantly different from other model calculations and tied to the dynamical nature of the a₁(1260) resonance. The future experimental observations could test of model calculations and would provide vary valuable information on the relevance of the ρπ component in the a₁(1260) wave function.     

Explicit Relations of Physical Potentials Through Generalized Hypervirial and Kramers' Recurrence Relations

Based on a Hamiltonian identity,we study one-dimensional generalized hypervirial theorem,Blanchardlike(non-diagonal case) and Kramers'(diagonal case) recurrence relations for arbitrary x~κ which is independent of the central potential V(x).Some significant results in diagonal case are obtained for special κ in x~κ(κ≥ 2).In particular,we find the orthogonal relation(n_1|n_2) = δ_(n_1n_2)(κ = 0),(n_1|V'(x)\n_2) =(E_(n_1)-E_(n_2))~2〈n_1x|n_2)(κ = 1),E_n =(n/V'(x)x/2|n) +(n|V(x)|n)(κ = 2) and-4E_n(n|x|n) +(n|V'(x)x~2\n〉 +4〈n|V(x)x|n〉 = 0(κ = 3).The latter two formulas can be used directly to calculate the energy levels.We present useful explicit relations for some well known physical potentials without requiring the energy spectra of quantum system.     

Pressure-Dependent Base-Wavefunction Admixture and Lifetime of R1 State of La3Lu2Ga3O12:Cr3+

As a key factor leading to the pressure-dependent R₁-line-shift reversal and R₁-state lifetime, at 10 K, the pressure-dependent variation of mixing-degree of |t₂²(³T₁)e⁴T₂〉 and |t₂³² E〉base-wavefunctions in the wavefunction of R₁ state of LLGG:Cr³⁺ has been calculated and analyzed. From this, the physical origin of the pressure-dependent R₁-line-shift reversal has been revealed. Furthermore, by using the pressure-dependent values of the sum of all square mixing-coefficients of |t₂²(³T₁)e⁴T₂〉in the wavefunction of R₁ state, the lifetimes of R₁ state of LLGG:Cr³⁺ at various pressures have been calculated, which are in good agreement with observed results. The quantum anticrossing effect between t₂³²E and t₂²(³T₁)e⁴T₂ levels due to both spin-orbital interaction and electron-phonon interaction is remarkable, which is related to the admixture of |t₂²(³T₁)e⁴T₂〉and |t₂³² E〉as well as the low-high crystal-field transition.     

Study of ion desorption induced by a resonant core-level excitation of condensed H2O using Auger electron photo-ion coincidence (AEPICO) spectroscopy combined with synchrotron radiation

Ion desorption induced by a resonant excitation of O 1s of condensed amorphous H₂O has been studied by total ion and total electron yield spectroscopy, nonderivative Auger electron spectroscopy (AES) and Auger electron photo-ion coincidence (AEPICO) spectroscopy. The spectrum of total ion yield divided by total electron yield exhibits a characteristic threshold peak at hν = 533.4 eV, which is assigned to the 4a₁ ← O 1s resonant transition. The AES at the 4a₁ ← O 1s resonance is interpreted as being composed of the spectator-AES of the surface H₂O, and the normal-AES of the bulk H₂O, where the 4a₁ electron is delocalized before Auger transitions. H⁺ is found to be the only ion species in AEPICO spectra measured at the 4a₁ ← O 1s resonance and at the O 1s ionization (hν = 560 eV). The electron kinetic energy dependence of the AEPICO yield (AEPICO yield spectrum) at the 4a₁ ← O 1s resonance is found to be greatly different from that at the O 1s ionization. The peak positions of the AEPICO yield spectrum at the 4a₁ ← O 1s resonance are found to correspond to those of the spectator-AES of the surface H₂O, which is extracted from the AES at the 4a₁ ← O 1s resonance. Furthermore, the AEPICO yield is greatly enhanced at the 4a₁ ← O 1s resonance as compared with that at the O 1s ionization. On the basis of these results, a spectator-Auger-stimulated ion desorption mechanism and/or ultra-fast ion desorption mechanism are concluded to be responsible for the H⁺ desorption at the 4a₁ ← O 1s resonance. The enhancement of the H⁺ yield is ascribed to the O---H anti-bonding character of the 4a₁ orbital.     

全局耦合网络上的两种类集团的聚集-湮没反应动力学

利用Monte-Carlo模拟研究了全局耦合网络上扩散限制的不可逆聚集-湮没过程的动力学行为. 在系统中, 同种类集团相遇, 将发生聚集反应; 不同种类的集团相遇, 则发生部分湮没反应. 模拟结果表明:1) 当两种粒子初始浓度相等时, 系统长时间演化后, 集团浓度c(t)和粒子浓度g(t)呈现幂律形式, c(t)～t^{- α}和g(t)～t^-β, 其中幂指数α 和β 满足α=2β 的关系, 且α=2/(2 + q); 集团大小分布随时间的演化满足标度律, a_kt)=k^-τt^-ω\varPhi (k/t^z), 其中τ≈-1.27q, ω≈(3 + 1.27q)/(2 + q), z=α/2=1/(2 + q); 2) 当两种粒子初始浓度不相等时, 系统经长时间演化后, 初始浓度较小的种类完全湮没, 而初始浓度较大的那个种类的集团浓度c_A(t)仍具有幂律形式, c_A(t)～t^-α, 其中α=1/(1+q), 其集团大小分布随时间的演化也满足标度律, 标度指数为τ≈-1.27q, ω≈(2 + 1.27q)/(1 + q)和z=α=1/(1 + q). 模拟结果与已报道的理论分析结果相符得很好.     

THE MEASURE OF CHAOTIC PARAMETER FOR ONE-DIMENSIONAL UNIMODAL MAPPING f(x)=1-a|x|Z

The asymptotic behavior of the accumulation point a_∞ for the one-dimensional unimodal mapping (x)=1-a|x|^Z is studied in the Limit Z→∞. We find that a_∞～2-lnZ/Z, as Z→∞. The measure of chaotic parameter for this mapping is also investigated. It decreases exponentially as the exponent z increases.     

Coordinate-Momentum Intermediate Representation and Marginal Distributions of Quantum Mechanical Bivariate Normal Distribution

We introduce bivariate normal distribution operator for state vector [ψ） and find that its marginal distribution leads to one-dimensional normal distribution corresponding to the measurement probability ｜λ,v〈x｜.ψ〉｜^2, where ｜x〉λ,v is the coordinate-momentum intermediate representation. As a by-product, the one-dimensional normal distribution in statistics can be explained as a Radon transform of two-dimensional Gaussian function.     

Energy Spectrum of La3Lu2Ga3O12：Cr^3＋ and Its Pressure-Induced R-Line-Shift Reversal

By means of both the theory for pressure-induced Shifts （PS） of energy spectra and the theory for shifts of energy spectra due to electron-phonon interaction （EPI）, the normal-pressure energy spectra of α and β centers of Cr^3＋ ions for LLGG：Cr^3＋ and the PS＇s of R1 lines and U band of these centers have been calculated at 10 K, respectively. The total calculated results are in very good agreement with the experimental data. For LLGG：Cr^3＋, the pressureinduced low-high crystal-field transition and the reversal of R1-line PS take place. The pressure-dependent variation of Rmix^ei （2E - 4T2） [mixing-degree of （t2^2 （^3T1）e^4T2） and （t2^3 E） base-wavefunctions in the wavefunction of R1 state without EPI] plays a key role for the reversal of R1-line PS. The behavior of the pure electronic PS of R1 line is quite different from that of the PS of R1 line due to EPI. It is the combined effect of them that gives rise to the total PS of R1 line. The comparison between R1-line PS＇s of GSGG：Cr^3＋ and LLGG：Cr^3＋ has been made. It is found that a peak of R1-line PS appears at Rmix^ei （^2E - ^4T2） ≈ 0.08.     

Study of ion desorption induced by a resonant core-level excitation of condensed NH3 using Auger-electron photo-ion coincidence (AEPICO) spectroscopy combined with synchrotron radiation

Photostimulated ion desorption at the 4a₁ ← N 1s resonant transition of condensed NH₃ was studied using electron emission spectroscopy and Auger-electron photoion coincidence (AEPICO) spectroscopy. The total ion yield divided by the Auger-electron yield exhibited a threshold peak at hν = 399 eV which is ascribed to the resonant transition from the N 1s to the N---H antibonding 4a₁ orbital. The electron emission spectrum at the 4a₁ ← N 1s resonance is decomposed into three components: a valence photoelectron emission spectrum, and normal- and resonant-Auger-electron emission spectra. We ascribe the resonant-Auger-electron emission spectrum mainly to spectator-Auger transitions on the basis of the peak assignment. A series of AEPICO spectra at the 4a₁ ← N 1s resonance was also measured as a function of the Auger-electron kinetic energy. The electron kinetic energy dependence of the H⁺ AEPICO yield displays a shape approximately similar to that of the mixed spectrum of normal- and spectator-Auger-electron emission spectra. Based on this result the H⁺ desorption at the 4a₁ ← N 1s resonance is concluded to originate from the spectator-Auger transitions and from the normal-Auger transitions following the delocalization of the excited electron.     

Improved Ligand-Field Theoretical Calculation of R-Line Pressure-Induced Shift of MgO:V2+

By means of an improved ligand-field theory, the “pure electronic” PS and the PS due to EPI of R line of MgO:V²⁺ have been calculated, respectively. The calculated results are in very good agreement with the experimental data. The behaviors of the pure electronic PS of R line of MgO:V²⁺ and the PS of its R line due to EPI are different. It is the combined effect of them that gives rise to the total PS of R line, which has satisfactorily explained the experimental results. The mixing-degree of |t₂²(³T₁)e⁴T₂〉and |t₂^{3 2}E〉 in the wavefunction of R level and its variation with pressure have been calculated and analyzed. The comparison between the feature of R-line PS of MgO:V²⁺ and that of MgO:Cr³⁺ has been made.     

Pressure-Induced Shifts of R, R', and B Line-Groups and Ground-State Zero-Field-Splitting of Ruby

By means of improved ligand-field theory, the “pure electronic” presure-induced shifts (PS's) and the PS's due to electron-phonon interaction (EPI) of the R₁, R₂, B₁, B₂, B₃, and R'₃ lines and the ground-state zero-field-splitting of ruby have been uniformly calculated. The calculation results are in very good agreement with all the experimental data. At normal pressure, ruby is a crystal with very strong crystal field. Thus, the admixture of |t₂²(³T₁)e⁴T₂〉and |t³₂²E〉bases in the wavefunction of R₁ level of ruby is small at normal pressure, and it gradually decreases with increasing pressure, which causes the R₁-line PS of ruby to monotonously red shift with approximate linearity. The combined effect of the pure electronic PS of R₁ line and the PS of R₁ line due to EPI gives rise to the total PS of R₁ line. The analyses and comparisons among the features of R₁-line PS's of three laser crystals (ruby, GSGG:Cr³⁺ and GGG:Cr³⁺) have been made, and the origin of their difference has been revealed.     

A Possible Generalization of Jaynes-Cummings Model with Degenerate Spectrum

We propose a generalized Jaynes-Cummings model (JCM) for three two-level atoms and three-mode radiation field with the interaction being H₁=λ(a₁⁺a₂⁺σ_1-σ_2-+a₂⁺a₃⁺σ_2-σ_3-+a₁⁺a₃⁺σ_1-σ_3-+H.C.). This model is characteristic of possessing partly degenerate spectrum. Some transition process of this system is calculated.     

用Na2O2-DMSO体系产生O2·的ESR研究

提出了Na₂O₂的二甲基亚砜(DMsO)/H₂O溶液中产生超氧阴离子自由基(O₂^·)的新方法,用电子自旋共振仪(ESR)可直接检测到很强的O₂^·信号,研究了反应的条件及其O₂^·信号的特性,并用该法考察了茶多酚等清除剂对于超氧阴离子自由基的清除作用。结果表明本体系是产生O₂^·的有效方法,可用于超氧阴离子自由基清除剂的研究。     

以新型原子距边矢量ν估计和预测烷烃核磁共振碳谱(13C NMR)化学位移(CSC)

系统研究了核磁共振碳谱与化学位移和规律,以及分子拓扑指数在定量[结]构[波]谱关系（QSSR）中的应用. 本文基于分子路径长度矢量p=（P₁, P₂, P, …, P_m）与分子中原子相互作用, 提出了一种新型原子距边矢量并发现它与烷烃¹³C NMR 化学位移有良好线性相关性, 回归方程及其统计参数为: CSC=aν+ap₃=∑^m_j=0a_jν_j+a₁₀p₃=a₀(ν₀₌₁)+a₁ν₁+a₂ν₂+a₃ν₃+a₄ν₄+bP₃, R>0.990, EV=94.5%, RMS<0.772, F=49.069-3513.18, 结果良好.     

The Role of a1(1260) in π-p→a1-(1260)p and π-p→π-ρ0p Reactions Near Threshold

We report on a theoretical study of the π^-p→a₁^-(1260) p and π^-p→π^-ρ⁰p reactions near threshold within an effective Lagrangian approach. The production process is described by t-channel ρ⁰ meson exchange. For the π^-p→π^-ρ⁰p reaction, the final π^-ρ⁰ results from the decay of the a₁(1260) resonance, which is assumed as a dynamically generated state from the K^*K and ρπ coupled channel interactions. We calculate the total cross section of the π^-p→a₁^-(1260)p reaction. It is shown that, with the coupling constant of the a₁(1260) to ρπ channel obtained from the chiral unitary theory and a cut off parameter Λρ~1.5 GeV in the form factors, the experimental measurement can be reproduced. Furthermore, the total and differential cross sections of π^-p→a₁^-(1260)p→π^-ρ⁰p reaction are evaluated, and it is expected that our model calculations can be tested by future experiments. These reactions are important for the study of the a₁(1260) resonance and would provide further constraints on the properties of the a₁(1260) state.