Determination of Scaling Parameter and Dynamical Resonances in Complex-Rotated Hamiltonian Ⅱ： Numerical Analysis

This paper is concerned with the determination of a unique scaling parameter in complex scaling analysis and with accurate calculation of dynamics resonances. In the preceding paper we have presented a theoretical analysis and provided a formalism for dynamical resonance calculations. In this paper we present accurate numerical results for two non-trivial dynamical processes, namely, models of diatomic molecular predissociation and of barrier potential scattering for resonances. The results presented in this paper confirm our theoretical analysis, remove a theoretical ambiguity on determination of the complex scaling parameter, and provide an improved understanding for dynamical resonance calculations in rigged Hilbert space.     

Resonances with triaxial deformation in the complex scaled Green's function method

We extend the complex scaled Green's function(CGF) method to describe resonances with triaxial deformation and present a theoretical formalism. Taking ~(43)S as an example, we elaborate numerical details and demonstrate how to determine the resonance parameters. With changes in the deformation parameters, we study the influence of the triaxial deformation parameter γ on single-particle levels. In particular, the present scheme focuses on the advantages of the complex scaling method(CSM) and the Green's function method, and is suitable for the exploration of resonances.     

A resistance formula for coherent multi-barrier structures

Using the Landauer formula and the quantum S-matrix scattering theory, we derive a resistance formula for multi-barrier structure under phase coherent transmission condition. This formula shows that when the transport is coherent, the potential wells of the structure are just like conductors contributing to the overall resistance. And because the resistance formula is derived based on the scattering theory, the barrier resistance will change with the number of scattering centres (i.e. the number of barriers) in the structure.     

Transition Temperature of Lattice Quantum Chromodynamics with Two Flavors with a Small Chemical Potential

We present the results for the transition temperature of quantum chromodynamics with two degenerate flavors （Nf=2） of Wilson quarks as a function of a small baryon chemical potential μB from Monte Carlo simulations at κ=0.175, κ is the hopping parameter. By using the imaginary chemical potential for which the fermion determinant is positive and the Ferrenberg-Swendsen reweighting method, we perform simulations on lattice 83×4 with 4 being the temporal extent. By analytic continuation of the data to the real chemical potential μ, we obtain the transition temperature for the small chemical potential, and compare our results with others.     

Angular Dispersion and Deflection Function for Heavy Ion Elastic Scattering

The differential cross sections for elastic scattering products of ^17F on ^208Pb have been measured. The angular dispersion plots of ln（dσ/dθ） versus θ^2 are obtained from the angular distribution of the elastic scattering differential cross sections. Systematical analysis on the angular dispersion for the available experimental data indicates that there is an angular dispersion turning angle at forward angular range within the grazing angle. This turning angle can be clarified as nucleal rainbow in classical deflection function. The exotic behaviour of the nuclear rainbow angle offers a new probe to investigate the halo and skin phenomena.     

Resonance properties from a coupled channel meson exchange model

In this talk, I present the results on the pole structure of pion-nucleon scattering in an analytic model based on meson exchange. The analytic properties of scattering amplitudes provide important information. Besides the cuts, the poles and zeros on the different Riemann sheets determine the global behavior of the amplitude on the physical axis. Pole positions and residues allow for a parameterization of resonances in a well-defined way, free of assumptions for the background and energy dependence of the resonance part. This is a necessary condition to relate resonance contributions in different reactions.     

Masses and Sigma Terms of Pentaquarks in Chiral Perturbation Theory

Assuming that the recently θ＋ and other exotic resonances belong to the pentaquark i0 of SU（3）I with J^P = 1/2, we constructed a relativistic effective lagrangian in the frame work of baryon chiral perturbation theory. The masses of pentaquarks under isospin symmetry is determined by calculating the propagator to one loop, where the extended on-mass-shell renormalization scheme is applied. Using the experimental data for masses of θ＋, Ξ and N, we estimated the mass of Σ and the a terms.     

TEMPERATURE-DEPENDENT ANISOTROPY IN La1.86Sr0.14CuO4

Based on the scaling rule: R(T, H, θ) = R(T, h), where h = H(sin²θ+cos²θ/γ²)^1/2 and θ is field angle with respect to the ab-plane, the scaling approach is performed to examine the c-axis resistances of single crystalline La_1.86Sr_0.14CuO₄ as functions of field and its orientation at different temperatures. The anisotropy parameter γ of the system is extracted from the scaling approach, but shows an unusual temperature-dependent behavior, which is not expected by conventional theory. A phenomenological explanation of this temperature dependence is presented.     

Proper In deposition amount for on-demand epitaxy of InAs/GaAs single quantum dots

The test-QD in-situ annealing method could surmount the critical nucleation condition of InAs/GaAs single quantum dots(SQDs) to raise the growth repeatability.Here,through many growth tests on rotating substrates,we develop a proper In deposition amount(θ) for SQD growth,according to the measured critical θ for test QD nucleation(θ_c).The proper ratio θ/θ_c,with a large tolerance of the variation of the real substrate temperature(T_(sub)),is 0.964-0.971 at the edge and 0.989 but 0.996 in the center of a 1/4-piece semi-insulating wafer,and around 0.9709 but 0.9714 in the center of a 1/4-piece N~+ wafer as shown in the evolution of QD size and density as θ/θ_c varies.Bright SQDs with spectral lines at 905 nm-935 nm nucleate at the edge and correlate with individual 7 nm-8 nm-height QDs in atomic force microscopy,among dense 1 nm-5 nm-height small QDs with a strong spectral profile around 860 nm-880 nm.The higher T_(sub) in the center forms diluter,taller and uniform QDs,and very dilute SQDs for a proper θ/θ_c:only one 7-nm-height SQD in25 μm~2.On a 2-inch(1 inch = 2.54 cm) semi-insulating wafer,by using θ/θ_c = 0.961,SQDs nucleate in a circle in 22%of the whole area.More SQDs will form in the broad high-T_(sub) region in the center by using a proper θ/θ_c.     

Calculation of the elastic scattering properties for cold and ultracold 39K atoms in a triplet state

The elastic scattering properties for collisions between cold and ultracold 39K atoms in a triplet state are investigated. Based on the recent theoretical and experimental results, the improved hybrid potential is presented for a triplet α3∑u^＋ ground state of K2. Our calculated value of the s-wave scattering length a by using the Numerov method for the triplet state is 79.578α0 and found to be in good agreement with the previous ones. The numbers of bound states are supported by the molecular potential. Pronounced shape resonances appear for the l = 3 partial waves for the α3∑u^＋ state. Furthermore, the s-wave scattering cross section, the total cross section and energy positions of shape resonances for the α3∑u^＋ state are calculated.     

Elastic Scattering of Ultracold 23Na and 39K Atoms in the Singlet State

The elastic scattering properties for collisions between ultracold 23Na and 39K atoms in the singlet state are investigated. Based on the recent theoretical and experimental results, the improved hybrid potential is presented for the singlet X1Σg＋ ground state of NaK. By means of the Numerov and semiclassical methods, the values of the s-wave scattering length a for the singlet state are calculated to be 33.3757a0 and 37.9399a0, respectively. Pronounced shape resonances appear for the l = 1 partial wave for the X1Σg＋ state. In addition, the s-wave scattering cross section, total cross section and energy positions of shape resonances for the X1Σg＋ state are discussed.     

Electron-Helium Atom Collisions in the Presence of a Bichromatic Laser Field

The differential cross section （DCS） for electron-helium atom collisions in the presence of a bichromatic CO2 laser field is investigated as a function of the scattering angle θ by employing first-Born approximation （FBA） with a simple screening electric potential. We discuss in detail the influence of the scattering geometry, the photon energy and the number of photons exchanged on the DCSs. These illustrate that the three factors have important effects on the elastic scattering and the screening electric potential is effective.     

Transmission and Dwell Time Oscillations Caused by Coexistence of Tunneling and Propagating in a Trapezoidal Barrier

Abstract A refined one of our exactly solvable trapezoidal barrier potential model [Thin Solids Films, 414 （2002） 136）] for metal-insulator-metal tunnel junctions has Seen presented. According to the refined model, the longitudinal kinetic energy （ExL） and the effective mass （m^＊L） of the electron8 in the electrode on the left of the barrier distinguish from that on the right. It is found that as ExL is greater than the shorter side of the resultant trapezoidal barrier potential, there will be a coexistence of the tunneling and propagating in the barrier. The results demonstrate that the damped oscillating electron waves localized in the propagating barrier subregion lead to the oscillation and enhancement in the transmission coefficient DT and dwell time TD. For the barrier height φ1=2.6 eV and φ2 = 1.4 eV, the width d=22 A and ExL = 1.0 eV, DT and TD have a maximum of 0.054 and 0.58x10^-15 s at V = 2.04 V and 2.18 V, respectively. This suggests that a real tunneling may be a hybrid.     

Decomposition of Gauge Potential in Ginzburg-Landau Theory

Recently, Liu et al. proposed a so-called extended Anderson-Higgs mechanism by studying the （2＋1）-dimensional Ginzburg-Landau model in the pseudogap region of high-Tc superconductor （Phys. Rev. B 65 （2002） 132513）. We revisit this problem based on a general decomposition of the U（1） gauge potential. Using the bulk superconductor and superconduct ring as examples, we obtain a simpler expression for the extended Anderson-Higgs mechanism. In the former case we indicate that all the phase field can always be ＂eaten up＂ by the pure gauge term A｜｜. In the latter case, we decompose the phase field as θ（x） = θ1（x） ＋ θ2（x） and find that only the phase field θ1 connected with Anderson-Higgs mechanism can be canceled by the pure-gauge term A｜｜. On the other hand, the remaining phase field θ2 connected with A⊥ is multi-valued, which can induce new physical effects such as A-B effect and flux quantization. It is natural to conclude that there is no longitudinal phase fluctuation effect in high-temperature superconductors since longitudinal phase θ1 is connected with pure-gauge term.     

Quantum Fisher information and spin squeezing in one-axis twisting model

We investigate the dependence of the average parameter estimation precision （APEP）, which is defined by the quantum Fisher information, on the polar angle of the initial coherent spin state ｜θ0,φ0〉 in a one-axis twisting model. Jin et al. [New J. Phys. 11 （2009） 073049] found that the spin squeezing sensitively depends on the polar angle θ0 of the initial coherent spin state. We show explicitly that the APEP is robust to the initial polar angle θ0 in the vicinity of π/2 and a near- Heisenberg limit 2IN in quantum single-parameter estimation may still be achieved for states created with the nonlinear evolution of the nonideal coherent spin states θ0- π/2. Based on this model, we also consider the effects of the collective dephasing on spin squeezing and the APEE     

Influence of Auxiliary Equation on Wave Functions for Time-Dependent Pauli Equation in Presence of Aharonov-Bohm Effect

Invariant operator method for discrete or continuous spectrum eigenvalue and unitary transformation approach are employed to study the two-dimensional time-dependent Pauli equation in presence of the Aharonov-Bohm effect （AB） and external scalar potential. For the spin particles the problem with the magnetic field is that it introduces a singularity into wave equation at the origin. A physical motivation is to replace the zero radius flux tube by one of radius R, with the additional condition that the magnetic field be confined to the surface of the tube, and then taking the limit R → 0 at the end of the computations. We point that the invariant operator must contain the step function θ（r - R）. Consequently, the problem becomes more complicated. In order to avoid this dimculty, we replace the radius R by ρ（t）R, where ρ（t） is a positive time-dependent function. Then at the end of calculations we take the limit R →0. The qualitative properties for the invariant operator spectrum are described separately for the different values of the parameter C appearing in the nonlinear auxiliary equation satisfied by p（t）, i.e., C 〉 0, C = 0, and C 〈0. Following the C＇s values the spectrum of quantum states is discrete （C 〉 0） or continuous （C ≤ 0）.     

πN Elastic Scattering and Resonances in Quark Potential Model

The quark potential model is used to investigate the low-energy elastic scattering of πN system. The model potential consists of the t-channel and s-channel one-gluon exchange potentials and the harmonic oscillator confining potential. By means of the resonating group method, a nonlocal effective potential for the πN system is derived from the interquark potentials and used to calculate the πN elastic scattering phase shifts. By considering the effect of QCD renormalization, the suppression of the spin-orbital coupling and the contribution of the color octet of the clusters （qq） and （qqq）, the numerical results are in fairly good agreement with the experimental data. The same model and method are employed to investigate the possible πN resonances. For this purpose, the resonating group equation is transformed into a standard Schrodinger equation in which the nonlocal effective πN interaction potential is included. Solving the Schrodinger equation by the variational method, we are able to reproduce the masses of some currently concerned πN resonances.     

Short-Time Dynamics of the Random n-Vector Model

Short-time critical behavior of the random n-vector model is studied by the theoretic renormalization-group approach.Asymptotic scaling laws are studied in a frame of the expansion in e = 4 - d for n ≠ 1 and for n = 1respectively.In d ＜ 4,the initial slip exponents θ′ for the order parameter and θ for the response function are calculated up to the second order in e ＝ 4 - d for n ≠ 1 and for n ＝ 1 at the random fixed point respectively.Our results show that the random impurities exert a strong influence on the short-time dynamics for d ＜ 4 and n ＜ nc.``     

Valence Quark Ratio in the Proton

Beginning with precise data on the ratio of structure functions in deep inelastic scattering（DIS） from ³ He and ³ H, collected on the domain 0.19 ≤ xB≤ 0.83, where xBis the Bjorken scaling variable, we employ a robust method for extrapolating such data to arrive at a model-independent result for the xB= 1 value of the ratio of neutron and proton structure functions. Combining this with information obtained in analyses of DIS from nuclei, corrected for target-structure depen...     

Relationship of Polaron Exchange with Ferromagnetic and Insulator--Metal Transitions in Doped Manganites

We report the experiment results and data analyses based on a polaron exchange model for La0.7Ca0.3MnO3 and Pr0.7（Sr1-xCax）0.3MnO3 epitaxial thin films. In the polaron exchange model with an energy balance condition, critical temperature of Tc for stable ferromagnetic （FM） ordering should depend on △E as kBTc = E0 exp（-△E/kBTc）, where A E denotes the potential barrier for the exchange polarons to overcome. Using the small polaron hopping model, the resistivity peak temperature Tp is a function of the hopping energy Ehop. The dependence of Tp on Ehop is similar to the dependence of Tc on AE, which reveals that the polaron exchange relates to FM and insulator-metal transitions. The result indicates that the polaron exchange model is a simple way for describing the FM ordering, and is very helpful for understanding of complex doped manganites.