On Dijkgraaf-Witten-type invariants

We explicitly construct a series of lattice models based upon the gauge group Z _p which have the property of subdivision invariance, when the coupling parameter is quantized and the field configurations are restricted to satisfy a type of mod-p flatness condition. The simplest model of this type yields the Dijkgraaf-Witten invariant of a 3-manifold and is based upon a single link, or 1-simplex, field. Depending upon the manifold's dimension, other models may have more than one species of field variable, and these may be based on higher-dimensional simplices.Supported by Stichting voor Fundamenteel Onderzoek der Materie (FOM).     

The beryllium atom and beryllium positive ion in strong magnetic fields

The ground and a few excited states of the beryllium atom in external uniform magnetic fields are calculated by means of our 2D mesh Hartree-Fock method for field strengths ranging from zero up to 2.35×10⁹ T. With changing field strength the ground state of the Be atom undergoes three transitions involving four different electronic configurations which belong to three groups with different spin projections S _z = 0, - 1, - 2. For weak fields the ground state configuration arises from the 1s ²2s ², S _z = 0 configuration. With increasing field strength the ground state evolves into the two S _z = - 1 configurations 1s ²2s2p _-1 and 1s ²2p _-13d _-2, followed by the fully spin polarised S _z = - 2 configuration 1s2p _-13d _-24f _-3. The latter configuration forms the ground state of the beryllium atom in the high field regime γ > 4.567. The analogous calculations for the Be ⁺ ion provide the sequence of the three following ground state configurations: 1s^22s and 1s ²2p _-1 (S _z = - 1/2) and 1s2p _-13d _-2 (S _z = - 3/2). Received 2 October 2000 and Received in final form 8 January 2001     

基于p1-p2与a1+a2共同本征态的相干纠缠态表象的构建及性质

利用有序算符乘积内的积分技术（IWOP）,建立了一种称之为相干纠缠态的两粒子体系的新表象,研究了这种新表象的性质,从理论上探讨了这种相干纠缠态的产生方法.结果表明：本文建立的这种p₁-p₂与a₁+a₂的共同本征态|p,β〉,既具有相干态的特性,又体现了纠缠态的特征,具有超完备性,完全可以作为一个表象使用. 物理上可以用光分束器来实现|< 关键词： IWOP技术 相干纠缠态表象 分束器     

Coherent population trapping involving Rydberg states in xenon probed by ionization suppression

We report the observation of pronounced coherent population trapping and dark resonances in Rydberg states of xenon. A weak two-photon coupling with radiation of = 250 nm is induced between the 5p^{6 1} S ₀ ground state of xenon and state 5p ⁵6p[1/2]₀, leading to (2+1) resonantly enhanced three-photon ionization. The state 5p ⁵6p[1/2]₀ is strongly coupled by radiation with ≃ 600 nm to 5p ⁵ ns[J _C]₁ or 5p ⁵ nd[J _C]₁ Rydberg states with principal quantum numbers n in the range 18 ?n? 23 and with the rotational quantum number of the ionic core J _C = 1/2 or J _C = 3/2. The ionization is monitored through observation of the photoelectrons with an energy resolution ΔE = 150 meV which is sufficient to distinguish the ionization processes into the two ionization continua. Pronounced and robust dark resonances are observed in the ionization rate whenever is tuned to resonance with one of the ns- or nd-Rydberg states. The dark resonances are due to efficient population trapping in the atomic ground state 5p^{6 1} S ₀ through the suppression of excitation of the intermediate state 5p ⁵6p[1/2]₀. The resolution is sufficient to resolve the hyperfine structure of the ns-Rydberg levels for odd xenon isotopes. The hyperfine splitting does not vary significantly with n in the given range. Results from model calculations taking the natural isotope abundance into account are in good agreement with the observed spectral structures. Pronounced dark resonances are also observed when the dressing radiation field with is generated from a laser with poor coherence properties. The maximum reduction of the ionization signal clearly exceeds 50%, a value which is expected to be the maximum, when the dip is caused by saturation of the transition rate between the intermediate and the Rydberg state due to incoherent radiation. This work demonstrates the potential of dark resonance spectroscopy of high lying electronic states of rare gas atoms. Received 7 May 2000 and Received in final form 25 June 2001     

A Derivative Formula for the Free Energy Function

We consider bond percolation on the Z ^d lattice. Let M _n be the number of open clusters in B(n)=[−n,n] ^d . It is well known that E _p M _n /(2n+1) ^d converges to the free energy function κ(p) at the zero field. In this paper, we show that s²_p(M_n)/(2n+1)^d\sigma^{2}_{p}(M_{n})/(2n+1)^{d} converges to −p(1−p)κ′(p).     

Asymptotic Heat Kernel Expansion in the Semi-Classical Limit

Let H_(^h/2p) = (^h/_2p)²L +V{H_\hbar = \hbar^{2}L +V}, where L is a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold and V is a symmetric endomorphism field. We derive an asymptotic expansion for the heat kernel of H_(^h/2p){H_\hbar} as (^h/_2p) \searrow 0{\hbar \searrow 0}. As a consequence we get an asymptotic expansion for the quantum partition function and we see that it is asymptotic to the classical partition function. Moreover, we show how to bound the quantum partition function for positive (^h/_2p){\hbar} by the classical partition function.     

Singlet—triplet oscillations of spin-correlated radical pairs due to the Larmor precession in low magnetic fields

Singlet—triplet oscillations in spin-correlated radical pairs have been studied at magnetic field strengths low for one radical and high for the other. Oscillations with frequencies close to the Larmor frequency ω₀ of electron spin precession have been predicted under these conditions. Both numerical and exact analytical solutions in arbitrary magnetic fields are presented for three cases of hyperfine couplings in wide-spectrum radical. For the case of unresolved spectrum, singlet—triplet evolution was found to contain a single oscillating term with frequency ω₀. In the case of one spin-I magnetic nucleus, there are two low frequency oscillating terms with frequencies ω_? = ω₀ ? ω₀/(2I + 1) and ω₊ = ω₀ + ω₀/(2I + 1), the amplitude of the first term being larger than that of the second. The case of a number of equivalent protons also has been analysed as a superposition of one-nucleus oscillations. The predicted oscillations were observed in a time resolved magnetic field effect for several radical ion pairs produced by X-ray irradiation of alkane solutions with charge acceptors. For pairs (p-terphenyl-d ₁₄)^?./(isooctane)^+. and (p-terphenyl-d ₁₄)^?./(2,4-dimethylpentane)^+. the oscillation frequency in a field B ₀ of 0.5–4mT is about 20% lower than ω₀. Oscillations were observed also in pairs with equivalent nuclei: (p-terphenyl-d ₁₄)^+./(C₆F₆)^?. and (p-terphenyl-d ₁₄)^?./(hexamethylethane)^+.     

The argon nuclear quadrupole moments

New standard values -116(2) mb and 76(3) mb are suggested for the nuclear quadrupole moments (Q) of the ³⁹Ar and ³⁷Ar nuclei, respectively. The Q values were obtained by combining optical measurements of the quadrupole coupling constant (B or eqQ/h) of the 3s²3p⁵4s[3/2]₂ (³P^o) and 3s²3p⁵4p[5/2]₃ (³D^e) states of argon with large scale numerical complete active space self-consistent field and restricted active space self-consistent field calculations of the electric field gradient at the nucleus (q) using the LUCAS code, which is a finite-element based multiconfiguration Hartree–Fock program for atomic structure calculations.     

Dielectronic recombination of lithium-like gold: Towards QED tests

Dielectronic recombination (DR) and radiative recombination (RR) of lithium-like gold in the energy range of 0 to 225 eV have been studied at the Experimental Storage Ring (ESR) of the GSI in Darmstadt. Main objective of the measurements is the precise determination of the 2s_1/2−2p_1/2 energy splitting as an additional QED test. This novel method, developed at the ESR [1], is based on the extrapolation of a multitude of measured resonances Au⁷⁵⁺ (1s²2p_1/2 nl_j) up to the series limit (n = ∞). Furthermore experimental data for the Au⁷⁵⁺ (1s²2p_3/26l_j) resonance manifold are presented. This revised version was published online in July 2006 with corrections to the Cover Date.     

Electric dipole moment and charge transfer in alkali-C molecules

Electron excitation rate coefficients for 2p (2p₁, 2p₂, 2p₃, 2p₄, 2p₅, 2p₆) and 3p(3p₅, 3p₆, 3p₇, 3p₈, 3p₁₀) (in Paschen notation) levels of xenon atom have been measured by using electron drift tube technique. The absolute excitation coefficients were obtained from the optical signal at the anode in Townsend xenon discharges, after correction for detector quantum efficiency. The ionization coefficients were determined from the spatial emission profile. The measurement were made for the electric field to xenon atom number density ratios (E/N) from Vm² to Vm². The data were obtained between moderate E/N values where electrons are in equilibrium and very high E/N values where electrons may not be in equilibrium with the local field. It was found that at the highest values of E/N heavy particles do not contribute to the excitation under the present conditions. The absolute excitation coefficients for the studied levels of xenon are to our knowledge the only experimental data available in the literature. Received 17 March 1999 and Received in final form 9 August 1999     

Attosecond manipulation of ionization and efficient broadband supercontinuum generation in stretched molecules

<正>We theoretically investigate the high-order harmonic generation from stretched molecules in a linearly polarized intense field.By adopting an infrared pulse combined with an ultraviolet(UV) attosecond pulse,the ionization process can be controlled effectively.In this excitation scheme,the harmonic spectrum beyond I_p+3.17U_P is significantly enhanced by two orders,where I_p and U_p=e~2E_0~2/(4m_eω~2) are the ionization and ponderomotive potential,then smooth broadband supercontinuum with the bandwidth of about 120 eV is obtained,which leads to an isolated sub-60- as attosecond pulse with a high signal-noise ratio.Moreover,the bandwidth of the supercontinuum is weakly dependent on the location and pulse duration of the UV pulse.     

Low temperature electrical conductivity and magnetoconductivity of Fe39Ni39Mo4Si6B12 and Co58Ni10Fe5Si11B16 metallic glass alloys

A detailed study on the weak localization phenomenon vis-a-vis electron-electron interaction effects in magnetic metallic glasses has been carried out. We measured the electrical conductivity and magnetoconductivity within the temperature range 1.8≤T≤300K. A maximum on the conductivity versus temperature curve exists atT=T _m. The conductivity was observed to follow aT ^1/2 law forT<T _m andT ² law forT>T _m. Magnetoconductivity data of these alloys indicate the prominence of electron-electron interaction at low temperatures. The authors have determined the inelastic scattering field and spin-orbit scattering field from the magnetoconductivity data. The inelastic scattering field obeys aT ^p law (p=2) at low temperatures.     

A new theorem of information theory

Consider a random experiment whose possible outcomes arez ₁,z ₂,...,z _n. Let the prior probabilities be p₁ ⁰, ...,p_n ⁰, and let the posterior probabilities bep ₁,...,p _n. It is shown that, subject to certain prescribed and intuitively reasonable conditions, the expressionI =k p _i In (p _i/p _i ⁰), wherek is a positive constant, is the unique expression for the information contained in a message which alters the probabilities from thep _i ⁰ to thep _i.     

An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem

Let λ _d (p) be the p monomer-dimer entropy on the d-dimensional integer lattice ℤ ^d , where p∈[0,1] is the dimer density. We give upper and lower bounds for λ _d (p) in terms of expressions involving λ _d−1(q). The upper bound is based on a conjecture claiming that the p monomer-dimer entropy of an infinite subset of ℤ ^d is bounded above by λ _d (p). We compute the first three terms in the formal asymptotic expansion of λ _d (p) in powers of  \frac1d\frac{1}{d}. We prove that the lower asymptotic matching conjecture is satisfied for λ _d (p). Converted to a power series in p, our “formal” expansion shows remarkable validity in low dimensions, d=1,2,3, in which dimensions we give some numerical studies.     

Resonances in Muon Transfer from Muonic Hydrogen to Oxygen and Neon

The influence of resonances on the muon transfer processes from muonic hydrogen to oxygen and neon (pμ)_1s + O⁸⁺ → p + (μO)_nl⁷⁺ and (pμ)_1s + Ne¹⁰⁺ → p + (μNe)_nl⁹⁺ is considered using the Smith lifetime matrix formalism. It is shown that the existence of a long lived resonance in the case of Ne induces a stronger dependence on collision energy of the muon transfer cross-section for this system. Present address: Chemistry Department, Vancouver University, Vancouver, BC V6T 1Z3, Canada     

Magnetoresistivity and acoustoelectronic effects in a tilted magnetic field in <Emphasis Type="Italic">p</Emphasis>-Si/SiGe/Si structures with an anisotropic <Emphasis Type="Italic">g</Emphasis> factor

Magnetoresistivity ρ _xx and ρ _xy and the acoustoelectronic effects are measured in p-Si/SiGe/Si with an impurity concentration p = 1.99 × 10¹¹ cm⁻² in the temperature range 0.3–2.0 K and an tilted magnetic field up to 18 T. The dependence of the effective g factor on the angle of magnetic field tilt θ to the normal to the plane of a two-dimensional p-Si/SiGe/Si channel is determined. A first-order ferromagnet-paramagnet phase transition is observed in the magnetic fields corresponding to a filling factor ν = 2 at θ ≈ 59°–60°.     

第Ⅱ种强度不等的两态叠加多模叠加态光场的等阶N次方H压缩1腔模总数与压缩阶数两者之积取偶数的情形

利用多模压缩态理论研究了第种强度不等的非对称两态叠加多模叠加态光场|Ψ_Ⅱ^(ab)〉q的等阶N次方H压缩特性.结果发现:1)当腔模总数q与压缩阶数N的乘积取偶数,亦即qN=2p时,无论p=2m(m=1,2,3,…,…),还是p=2m+1(m=0,1,2,3,…,…),只要各模的初始相位差(φ_j^(a)-φ_j^(b))、态间的初始相位差(θ_nq^(aR)-θ_nq^(bR))及光子干涉项的幅度 1R_j^(a)R_j^(b)等分别满足一定的条件,则态|Ψ_||^(ab)〉q的第一和第二正交分量总可分别呈现出周期性变化的等阶N次方H压缩效应.2)当qN=2p且p=2m+1(m=0,1,2,3,…,…)时,若构成态|Ψ_Ⅱ^(ab)〉q的两个不同的量子光场态中各对应模的强度(即平均光子数)和初始相位相等,亦即R_j^(a)=R_j^(b)和φ_j^(a)=φ_j^(b)(j=1,2,3,…,q),则态|Ψ_Ⅱ^(ab)〉q可呈现出“等阶N次方H压缩简并”现象.     

Ba原子6pnd(J=1, 3)自电离光谱的实验研究

采用三台可调谐激光实施孤立实激发,分三步将处于基态的Ba原子激发到6p_1/2nd(J=1,3)和6p_3/2nd(J=1,3)自电离态上,获得了分别从6snd¹D₂(n=7—15)和6snd³D₂(n=7—12) 激发而得到的6p_1/2nd(J=1,3)和6p_3/2nd (J=1,3)自电离光谱,重点对主量子数n较低的自电离态进行了实验研究. 通过光谱的线形拟合得到了上述能级的位置和宽度等数据,进而获得了量子亏损和约化宽度等信息. 通过对不同系列的自电离光谱的分析和比较,详细讨论了这些自电离态的光谱特征及其复杂光谱结构的成因. 关键词： 孤立实激发 组态相互作用 自电离态     

Modulation-free pump-probe spectroscopy of strontium atoms

We have performed polarization spectroscopy on the 5s^{2 1}S₀ →5s5p¹P₁ transition of atomic strontium. The signal is generated by saturation effects, rather than optical pumping, as the ground state is non-degenerate. This technique generated a dispersion-type lineshape suitable for laser stabilization, without the need for frequency modulation. The dependence of the amplitude and gradient on intensity and magnetic field were also investigated, and compared to a related technique based on the circular dichroism induced by a magnetic field.     

Observation of the fast component in the fluorescence of gaseous SO2 excited to the A1A2 state in the presence of a magnetic field

Effects of an external magnetic field (B) on the SO₂ fluorescence have been examined under excitation of the ‘C’ band and the single rotational levels of the ‘B’ and ‘E’ bands of the A(¹A₂) ← X¹A₁ transition. For the ‘C’ band, the total SO₂ fluorescence was studied, while for excitation of the single rotational levels, fluorescence of the single rotational lines of (^rR₅(5) (31711 cm^-1), ^pP₇(7) (31662 cm^-1)) (‘E’ band) and of (^rR₈(8) (31000 cm^-1), ^pP₁₀(10) (30927 cm^-1)) (‘B’ band) was studied. Decay of the SO² fluorescence was studied with nanosecond time resolution in the 1?5–50 mTorr region. In the presence of a magnetic field, decay of the total SO₂ fluorescence and of the fluorescence belonging to the single rotational lines were fitted by the bi-exponential functions. In the case of the total SO₂ fluorescence, this function also includes the time independent term, which, however, is dependent on a magnetic field. The time independent term belongs to the long-living component, which can be approximated by a constant in the time-scale studied. Radiationless processes induced by an external field were directly observed. The magnetic field and pressure dependences of the processes induced by a field were studied under excitation of the SO₂ fluorescence by light of a different wavelength. The data obtained were explained by the direct mechanism.