三维QED中的几个重要问题（英文）

三维量子电动力学是一种看上去比较简单的Abel 类型的非微扰系统,其本身却有很多需要澄清的基本问题。从该系统是否具有密度依赖性,有限温下是否具有动力学自发对称破却以及规范玻色子可否具有质量这三方面出发,阐述了对三维量子电动力学一些基本问题的看法。Quantum electrodynamics in (2+1) dimensions (QED₃) is an important nonperturbative system. This seems relatively simple Abel system, there are several issues that need to be clarified: whether or not the partition function of the system depends on chemical potential; whether or not there exists dynamical chiral symmetric breaking; whether or not the boson can acquires nonzero mass. In this paper, we give an in sight of the traits of QED₃ from the dependence of density, temperature and massive boson to discuss those problems.     

Gauge-invariant dressed fermion propagator in massless QED3

The infrared behaviour of the gauge-invariant dressed fermion propagator in massless QED₃ is discussed for three choices of dressing. It is found that only the propagator with the isotropic (in three Euclidean dimensions) choice of dressing is acceptable as the physical fermion propagator. It is explained that the negative anomalous dimension of this physical fermion does not contradict any field-theoretical requirement.     

Dual fermion condensate and phase transition in QED3

In this paper,we investigate the behaviors of dual fermion condensate in QED 3 under variation of temperature.By means of Dyson-Schwinger equation for the fermion propagator,we extract the dual fermion condensate and compare its behavior with the ordinary chiral fermion condensate and the chiral susceptibility.It is found that the dual fermion condensate cannot be regarded as the order parameter for the confinement-deconfinement phase transition in QED 3.Furthermore,the change of the dual fermion condensate around the chiral phase transition point observed in the present work must therefore be interpreted as solely induced by the chiral transition.     

No parity anomaly in massless QED3: A BPHZL approach

In this Letter we call into question the perturbatively parity breakdown at 1-loop for the massless QED₃ frequently claimed in the literature. As long as perturbative quantum field theory is concerned, whether a parity anomaly owing to radiative corrections exists or not shall be definitely proved by using a renormalization method independent of any regularization scheme. Such a problem has been investigated in the framework of BPHZL renormalization method, by adopting the Lowenstein–Zimmermann subtraction scheme. The 1-loop parity-odd contribution to the vacuum-polarization tensor is explicitly computed in the framework of the BPHZL renormalization method. It is shown that a Chern–Simons term is generated at that order induced through the infrared subtractions — which violate parity. We show then that, what is called “parity anomaly”, is in fact a parity-odd counterterm needed for restauring parity.     

Continuum limit of QED2 on a lattice

A path integral is defined for the vacuum expectation values of Euclidean QED₂ on a periodic lattice. Wilson's expression is used for the coupling between fermion and gauge fields. The action for the gauge field by itself is assumed to be a quadratic in place of Wilson's periodic action. The integral over the fermion field is carried out explicitly to obtain a Matthews-Salam formula for vacuum expectation values. For a combination of gauge and fermion fields $\text{G}$ on a lattice with spacing proportional to N^?1, N?Z⁺, the Matthews-Salam formula for the vacuum expectation 〈G〉_N has the form ($\text{G}$)_N=∫d_nu;W_N($\text{G}$,f), where dμ is an N-independent measure on a random electromagnetic field ? and $\text{W}{}_{\mathrm{N}}\text{(G, ?)}$ is an N-dependent function of ? determined by $\text{G}$. For a class of $\text{G}$ we prove that as N → ∞, $\text{W}{}_{\mathrm{N}}\text{(C, ?)}$ has a limit $\text{W(G, ?)}$ except possibly for a set of ? of measure zero. In subsequent articles it will be shown that ∫d_nu;W_N($\text{G}$,f) exists and lim_N→∞∫d_nu;W_N($\text{G}$,f).     

The chiral phase transition of QED3 around the critical number of fermion flavors

At zero temperature and density, the nature of the chiral phase transition in QED₃ with N_f$N_f$ massless fermion flavors is investigated. To this end, in Landau gauge, we numerically solve the coupled Dyson–Schwinger equations for the fermion and boson propagator within the bare and simplified Ball–Chiu vertices separately. It is found that, in the bare vertex approximation, the system undergoes a high-order continuous phase transition from the Nambu–Goldstone phase into the Wigner phase when the number of fermion flavors N_f$N_f$ reaches the critical number N_f,c$N_{f,c}$, while the system exhibits a typical characteristic of second-order phase transition for the simplified Ball–Chiu vertex.     

Exact quantization of Einstein-Rosen waves coupled to massless scalar matter

We show in this Letter that gravity coupled to a massless scalar field with full cylindrical symmetry can be exactly quantized by an extension of the techniques used in the quantization of Einstein-Rosen waves. This system provides a useful test bed to discuss a number of issues in quantum general relativity, such as the emergence of the classical metric, microcausality, and large quantum gravity effects. It may also provide an appropriate framework to study gravitational critical phenomena from a quantum point of view, issues related to black hole evaporation, and the consistent definition of test fields and particles in quantum gravity.     

Portraits of the flux tube in QED3: A Monte Carlo simulation with external sources

We determine numerically, and display graphically, the electromagnetic energy distribution due to static sources in compact QED₃. Using the polymer formulation of the functional integral, Monte Carlo simulations are performed with external sources included in the lattice action. Both the Wilson and Villain forms of the action are studied, and the string tension is determined in a small range of weak couplings. For the Villain action, our values for the string tension σ are in agreement with Polyakov's formula. For the Wilson action, we are able to detect a string tension in a range of weak couplings 2.1 ? β ? 2.3 below the weak-to-strong coupling cross-over point. In the same range, standard Monte Carlo results for up to 8 × 8 Wilson loops are consistent with ordinary perturation theory (no confinement). A possible explanation of this discrepancy is discussed, and it is suggested that the standard (source-free) Monte Carlo might miss configurations which are important for flux-tube formation.     

CHF3双频电容耦合放电等离子体特性研究

研究了用于SiCOH 低介电常数薄膜刻蚀的CHF₃气体在1356 MHz/2 MHz,2712 MHz/2 MHz和60 MHz/2 MHz双频电容耦合放电时的等离子体性质.发现2 MHz低频源功率的增大主要导致F基团密度的增大;而高频频率从1356,2712增大到60 MHz,导致CF₂基团的密度增大和电极之间F基团密度的轴向空间不均匀性增加.根据电子温度的分布规律及离子能量随高频源频率的变化关系,提出CF₂基团的产生主要通过电子-中性气体碰撞,而F基团的产生是离子-中性气体碰撞的结果.     

有限温下三维QED中费米速度对费米子手征凝聚的影响（英文）

三维QED 具有两个和QCD类似的性质:动力学手征对称破缺和禁闭。为了研究动力学手征对称破缺,基于彩虹近似,在Dyson-Schwinger 方程框架下,通过迭代求解有限温下的费米子自能方程,讨论了不同的费米速度下费米子手征凝聚与费米子味数之间的关系。发现在有限温下,对于固定的费米子味数,费米手征凝聚随费米速度的变大而单调减小。Analogous to Quantum QCD, QED₃ has two interesting features: dynamical chiral symmetry breaking (DCSB) and confinement. By adopting the rainbow approximation, we numerically solve the fermion self-energy equation at finite temperature in the framework of Dyson-Schwinger equations and discuss the relation between chiral condensate and fermion flavor for several fermion velocities in the finite temperature QED₃. It is found that the fermion chiral condensate decreases monotonically with the fermion velocity increasing for a fixed N at finite temperature.     

Phase structure of a Z2 lattice gauge theory coupled to a radially variable scalar field

Using Monte Carlo techniques and mean field method, we study a coupled Z₂ gauge-scalar system on a lattice without freezing the radial mode of the scalar field. We find that the phase diagram for our model makes a decided contrast with that for the coupled gauge-spin model when the self-coupling of the scalar field is small. First-order phase transitions caused by the radial fluctuation of the scalar field are observed.     

Dry etching characteristics of GaN using Cl2/BCl3 inductively coupled plasmas

ICP power/RF power, operating pressure, and Cl₂/BCl₃ gas mixing ratio are altered to investigate the effect of input process parameters on the etch characteristics of GaN films. The etch selectivity of GaN over SiO₂ and photoresist is studied. Although higher ICP/RF power can obtain higher GaN/photoresist etch selectivity, it can result in faceting of sidewall and weird sidewall profile due to photoresist mask erosion. Etch rates of GaN and SiO₂ decrease with the increase of operating pressure, and etch selectivity of GaN over SiO₂ increases with the increasing operating pressure at fixed ICP/RF power and mixture component. The highest etch selectivity of GaN over SiO₂ is 7.92, and an almost vertical etch profile having an etch rate of GaN close to 845.3 nm/min can be achieved. The surface morphology and root-mean-square roughness of the etched GaN under different etching conditions are evaluated by atomic force microscopy. The plasma-induced damage of GaN is analyzed using photoluminescence (PL) measurements. The optimized etching process, used for mesa formation during the LED fabrication, is presented. The periodic pattern can be transferred into GaN using a combination of Cl₂/BCl₃ plasma chemistry and hard mask SiO₂. Patterning of the sapphire substrate for fabricating LED with improved extraction efficiency is also possible using the same plasma chemistry.     

The ν3 and 2ν3 bands of SO3, SO3, SO3, and SO3

This sixth of a series of publications on the high-resolution rotation-vibration spectra of sulfur trioxide reports the results of a systematic study of the ν₃ and 2ν₃ infrared bands of the four symmetric top isotopomers ³²S¹⁶O₃, ³²S¹⁸O₃, ³⁴S¹⁶O₃, and ³⁴S¹⁸O₃. An internal coupling between the l=0(A₁^′) and l=2(E^′) levels of the 2ν₃ states was observed. This small perturbation results in a level crossing between |k−l|=9 and 12, in consequence of which the band origins of the A₁^′,l=0 “ghost” states could be determined to a high degree of accuracy. Ground and upper state rotational constants as well as vibrational anharmonicity constants are reported. The constants for the center-of-mass substituted species ³²S¹⁶O₃ and ³⁴S¹⁶O₃ vary only slightly, as do the constants for the ³²S¹⁸O₃, ³⁴S¹⁸O₃ pair. The S-O bond lengths for the vibrational ground states of the species ³²S¹⁶O₃, ³⁴S¹⁶O₃, ³²S¹⁸O₃, and ³⁴S¹⁸O₃ are, respectively, 141.981 99(1), 141.979 38(6), 141.972 78(8), and 141.969 93(8) pm, where the uncertainties, given in parentheses, are two standard deviations and refer to the last digits of the associated quantity.     

Splitting of the near infrared absorption bands of Sm in POCl3:SnCl4, POCl3:ZrCl4 and POCl3:TiCl4

The near infrared absorption spectra of Sm³⁺ in POCl₃:SnCl₄, POCl₃:ZrCl₄ and POCl₃:TiCl₄ consist of a series of bands, attributed to the ⁶H_5/2 → ⁶F_J transitions. Each one of these absorption bands is split into three components. The extent of splitting differs slightly from state to state. For each component of the ⁶F-multiplet the splitting decreases gradually from POCl₃:SnCl₄ to POCl₃:ZrCl₄ and POCl₃:TiCl₄. Energy differences between adjacent components of the near infrared absorption bands vary from a maximum of 166 cm⁻¹ to a minimum of 123 cm⁻¹. The band half-widths of the corresponding components vary from 86 to 120 cm⁻¹. At lower temperatures the intensity of the high energy component increases whereas the intensity of the entire absorption band envelope, associated with each component of the ⁶F-multiplet, remains almost constant. The splitting observed is attributed to the Stark splitting of the ⁶H_5/2-state of Sm³⁺ into three components, in conjunction with appropriate Stark splitting of the states of the ⁶F-multiplet.     

Unitary renormalization of the Lee model Y4

The Lee model Y₄ is renormalized by unitary transformation. A norm convergent (in each sector) sequence of unitary dressing transformations, which transform a sequence of renormalized cut-off Hamiltonians to a sequence of operators converging strongly on a dense set of states, is defined. The self-adjointness and semiboundedness (in each sector) of the renormalized Hamiltonian are proved.     

EPR investigation on exchange coupled Mn2+ pairs in (CH3)4NCdCl3

EPR experiments were performed at Q-band and 300 K on Mn²⁺ doped (CH₃)₄NCdCl₃. Beside the single ion resonance many weak lines could be observed which can be attributed to nearest neighbour pairs of Mn²⁺ lying along the crystallographic c-axis. The spectra can be described using a Hamiltonian for strongly exchange coupled pairs. The obtained data show that the ionic separation varies in the different spin states. So an additional interaction occurs on the Mn²⁺ dimer, which can be interpreted as an exchange striction effect.