Intermediate Coupling Region Research Articles

Analysis and Discussion About How to Determine the Variational Parameters in the Variational-Cumulant Expansion11The project supported by Doctoral Foundation of Chinese Education Commission and National Natural Science Foundation of China

Four methods of determining the variational parameter in the variational-cumulant expansion (VCE) are studied on the 2-dimensional Ising model. A comparison with the exact result shows that the main-variation method is the best one at low temperature, the complete-variational method is better than others at high temperature, the accumulation-point method is the best one to approximate the intermediate coupling region, and each of the methods is analyzed from the original formulas or conjectures. Some suggestions are given in order to get optimal results. The VCE is also analyzed from a point of view of symmetry breaking for the first time.

Some properties of large polarons with squeezed states

The effective mass of the Frohlich polaron is calculated with the two-mode squeezed states in the intermediate-coupling region and found to be in close agreement, with the results of other models. Within the same approach, the induced charge density around an electron in polar solids is calculated. Our result for this charge density contains an additional term which shows a feature in the spatial dependence as a manifestation of the squeezing effect.

Refractive index in a dilute solution of molecules with intramolecular coupling up to third order in the external field

The effect of the intramolecular coupling, on the refractive index, up to third order in the external field amplitude, is studied for a dilute aqueous solution in which the solute molecules are described by a simple model consisting of two coupled harmonic electronic potentials displaced in both equilibrium distance and energy. The effect of the intramolecular coupling on the refractive index appears to be sizeable, particularly in the weak- and intermediate-coupling region.

SU(2) Gauge System with Dynamical Fermions in Cumulant Expansion Treatment11The project supported by National Natural Science Foundation of China.

The SU(2) lattice gauge system with dynamical Wilson fermions is investigated by the variational cumulant expansion method with the novel criterion to determine the variational parameters. The agreement of calculated order parameter EP of the pure gauge sector with Monte Carlo data is much improved, especially, in the intermediate coupling region. The fermionic contributions are small to k6 hopping parameter expansion, but the general feature is in accordance with the Monte Carlo data qualitatively. The necessity of higher order calculations in the intermediate coupling region is discussed.

Critical mass in nonzero temperature QCD with staggered fermions

The behaviour of the chiral condensate in QCD is investigated by means of a study of the distribution of the zeros of the partition function in the complex quark-mass plane. Simulations are performed at fixed temperature on three different spatial volumes at β = 5.04 and at β = 4.9 and β = 5.2 on a 4 4 lattice. Evidence is found for a chirally related transition at non-zero quark mass in the intermediate coupling region for β < 5.2 but superimposed upon a smooth behaviour for the condensate. The critical mass at which this transition is found in only weakly dependent on the spatial volume and decreases with decreasing temperature.

Cumulant Expansion in Intermediate Coupling Region in U(1) Lattice Gauge Theory

Determining the parameters in the i-th order approximation in the cumulant expansion from the requirement that the correction to the zeroth order approximation is zero or the smallest, we show in the example of calculating the Polyakov line ⟨L⟩ of U(1) gauge model at finite temperature with Nτ = 1-to 5-th order that the expansion works well not only in the strong and weak coupling regions, but also in the intermediate coupling region except the very vicinity of the phase transition point. The calculated ⟨L⟩ is in agreement with Monte Carlo simulations.

CHIRAL PHASE TRANSITION IN HIGH TEMPERATURE QCD WITH MASSIVE QUARKS

The thermal phase transition in lattice QCD at finite quark mass is studied from the distribution of the zeros of the partition function in the complex quark mass plane. Results from simulations at strong and intermediate coupling are presented. Evidence for a chirally related transition at non-zero quark mass in the intermediate coupling region for β&lt;5.2. The method exhibits remarkable stability in the evaluation of the critical mass as the lattice volume increases. Conclusions regarding the possible phase structure of QCD in the mass-temperature plane are discussed.

Consistent Solutions of BCS-Gap Equation for the Hole-Pairing Mechanism by the Exchange of Soft-Magnons in a Frustrated Heisenberg Square-Lattice System

The pairing mechanism for doped holes to d 3 z 2 - r 2 orbitals of Cu 2+ ions on a CuO 2 plane is proposed so as to make clear the property of superconducting phases of high- T c superconductors where coexistence of the antiferromagnetic ordering has been recently reported. The pairing is made by the exchange of antiferromagnetic magnons for d x 2 - y 2 spins on CuO 2 plane. Here, the frustration introduced by the second nearest neighbor antiferromagnetic exchange interaction between Cu 2+ ions plays an significant role. The BCS-type gap equation is derived and self-consistent solutions are obtained numerically for various symmetries. Among them, the gaps for s and d x y symmetries are discussed in detail. By the essential contribution of the frustration, the gap can be formed even for the intermediate coupling region.

The ground-state energy of a two-level tunnelling unit in a phonon field

The ground-state energy of a truncated two-level localised tunnelling system coupled to a phonon field is studied within the framework of small-polaron theory by a variational calculation. In former similar calculations, even when treating the intermediate-coupling region and with finite-polaron bandwidth, a very large coupling-strength parameter was tacitly assumed in the variational procedure, while the ratio of the rigid-lattice tunnelling matrix element to the small-polaron binding energy was kept finite. The present calculation is extended to finite coupling strengths. This introduces dispersion in the lattice deformation parameters, leads to lower ground-state energy and produces weakest renormalisation of the tunnelling matrix element.

The Decay ρ→ππ in Lattice Gauge Theory††Project Supported in part by the Foundation of Zhongshan University Advanced Research Center and by the Science Fund of the Chinese Education Committee.

The hadronic decays are studied by using an improved Hamiltonian including 2-link interactions. We find that the formulation is effective for studying hadronic decays as well as mass spectrum. In the intermediate coupling region, the decay width of ρ meson is found to be of the right order of magnitude.

The Improved Hamiltonian and ρ-ω Mass Difference in Lattice Gauge Theory††Project supported by the Foundation of Zhongshan University, Advanced Research Center.

We formulate a Hamiltonian theory on the lattice including next-to-nearest neighbor fermion interactions. A canonical transformation is made to induce a momentum-dependent mass term. The meson spectrum is studied by using this Hamiltonian. The current algebra formula for the pion mass is derived. The ρ-ω mass ratio in the intermediate coupling region is in agreement with the experimental value.

The Effect of an E-Type Quadratic Jahn-Teller Coupling on the Eigenstates in theT×t2Vibronic States

Numerical studies of the vibronic eigenstates in the case when an orbital triplet states is coupled linearly and quadratically to a t 2 vibrational mode have been made. For a fixed value of the linear Jahn-Teller coupling strength in the intermediate coupling region, the effects of an E -type quadratic Jahn-Teller coupling strength on the vibronic eigenstates of the Jahn-Teller system have been investigated. As the quadratic Jahn-Teller coupling strength increases, the feature of an orthorhombic Jahn-Teller distortion has been clearly shown in the vibronic properties in the sixfold degenerate ground state.

On the true quasiparticle structure of the conduction band of a ferromagnetic semiconductor

In order to clarify controversial discussions concerning the electronic excitation spectrum of ferromagnetic semiconductors such as EuO and EuS exact T=0 results for the spectral density and the quasiparticle density of states are presented and discussed within the framework of the sf model. The physics of the sf model turns out to be strikingly different in the strong-coupling region g/W>or approximately=0.5 (atomic-like behaviour, g is the sf exchange constant and W is the Bloch bandwidth), in the intermediate-coupling region 0.1>or approximately=g/W. It has been overlooked in the past that typical magnetic semiconductors (e.g. europium chalcogenides) are spread over all three regions. Mean-field treatments are reasonable in a certain sense for weakly coupled systems such as EuO but are, however, completely inappropriate for more strongly coupled systems such as EuS. Due to the sf exchange the conduction band consists of several quasiparticle sub-bands, overlapping in the weak-coupling but with real gaps between them in the intermediate- and strong-coupling regions.

Mass gap of lattice O(3) non-linear σ-model with naive and improved actions

We evaluate the strong coupling expansion for the mass gap of the euclidean lattice O(3) non-linear σ-model in two dimensions with the naive action and with the tree level improved action. For the naive action the expansion series exhibits scaling behaviour in the weak coupling region. For the tree level improved action, our series is consistent with Monte Carlo data in the intermediate coupling region but is too short to reproduce the scaling.

Vortex free energy and string tension at strong and intermediate coupling

We present results of high temperature expansions up to order g −24 for the vortex free energy respectively string tension in pure lattice gauge theories with gauge groups SU(2) and Z 2 in 3 and 4 dimensions. For SU(2) in 4 dimensions the result is compared with Monte Carlo calculations of Creutz and is in good agreement. An intermediate coupling region is seen, where the string tension smoothly interpolates between strong coupling and weak coupling behaviour.

Analysis of Satellite Lines of the GR1 Band in Diamond by Quadratic Jahn-Teller Coupling

The quadratic Jahn-Teller effect has been studied in the intermediate linear coupling region in the E - e system. Reduction factors, E - A separation and the zero-phonon intensity for E → T transition have been calculated by diagonalizing the vibronic Hamiltonian including both the linear and the quadratic coupling. From comparison of these calculated results with experimental data on the GR1 band in diamond, values of vibronic parameters for the GR1 center have been extracted.

Non-adiabatic transitions in two-state curve crossing systems

The transition amplitudes for passage through a potential curve crossing are calculated by means of the first order Magnus approximation to the coupled equations in the momentum representation, together with a semiclassical mapping prescription. The cases of potentials with similar or different slopes at the crossing point require a different treatment: for similar slopes the semiclassical Magnus approximation is practically identical with the exponential uniform distorted wave approximation (EUDWBA); for slopes with different signs a new probability conserving approximation is obtained, which differs from the EUDWBA and leads to a substantial improvement of the transition probabilities in the weak and intermediate coupling region. The present approximation can easily be extended to multistate crossings.

Analysis of the generalized Stueckelberg method of non-adiabatic transitions

The generalized Stueckelberg model of non-adiabatic transitions is applied to the linear curve crossing problem. It is shown that the theory can be analytically continued for all energies, thus reproducing the adiabatic asymptotic formulae derived by the Nikitin school for the Landau-Zener model. Comparisons are made with exact numerical calculations and excellent agreement is obtained in the adiabatic regime. The method is less accurate for low energies in the intermediate non-adiabatic coupling region.

Dynamic Jahn-Teller vibronic coupling for an orbital triplet:T×τ2andT×(τ2+ε)

Numerical solutions of the vibronic problem for an electronic triplet state coupled to ${\ensuremath{\tau}}_{2}$ vibrations in cubic symmetry have been investigated in detail by Lanczos's method for the diagonalization of a sparse matrix. Ham's reduction factors and zero-phonon intensity have been calculated and compared with the previous results. Good agreement between our results and the previous ones has been found. Our method has been sucessfully extended to the general problem of a $T\ifmmode\times\else\texttimes\fi{}({\ensuremath{\tau}}_{2}+\ensuremath{\epsilon})$ system in which the coupling to the two modes is assumed different. The vibronic energy scheme for the lower states of this system are obtained in the intermediate-coupling region. The properties of the lowest state are also investigated.

Phonon-Correlation Effects in the Optical-Absorption Spectra of Free Polarons

The influence of correlation between the optical phonons on the one- and two-phonon contribution to the free-polaron absorption spectrum in polar semiconductors ($\ensuremath{\alpha}&lt;1$) is evaluated by extending the Lee-Low-Pines formalism. This correlation can be related to the concept of the relaxed excited state in the intermediate and strong electron-phonon coupling region ($\ensuremath{\alpha}&gt;3$).