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The Jaynes-Cummings model (JCM) is studied in the absence of the rotating-wave approximation (RWA) by a coherent-state expansion technique. In comparison with the previous paper in which the coherent-state expansion was performed only to the third order, we carry out in this paper a complete expansion to demonstrate exactly the dynamics of the JCM without the RWA. Our study gives a systematic method to solve the non-RWA problem, which would be useful in various physical systems, e.g., in a system with an ultracold trapped ion experiencing the running waves of lasers.

In this paper the coherent-state approximation (CA) method is used to deal with the problem of the decoherence of the entangled states of two two-state systems. As the base of the discussion, the dissipation of one two-state system has been investigated at first. The improved results calculated by CA are given in the paper. It is shown that the right approaching behavior and scaling law have been obtained when CA is applied to the problem of dissipation of two two-state systems coupled with environment. The whole evolution process and calculated results of the decoherence of the entangled states show also the scaling law, right approaching behavior, and rich phenomenon.

The quaritum behavior of a precooled cantilever canbe probed higlily efficiently by electrostatically coupling to a trapped ultracold ion, in which a fast cooling of the cantilever down to the ground vibrational state is possible. Within a simple model with an ultracold ion coupled to a cantilever with only few vibrational quanta, we solve tile dynamics of the coupling system by a squeezed-state expansion technique, and can in principle obtain the exact solution of the time-evolution of the coupling system in the absence of the rotating-wave approximation. Comparing to the treatment under the rotating wave approximation, we present a more accurate description of the quantum behavior of the cantilever.

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+∑'c†k1σ1h†k2σ2c†k3σ3h†k4σ4∏exp(ρc†k1σ1h†k2σ2)]0, where and ρ are the coupling constants. Our results are then compared to those of variational 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.

By a model of a two-level particle coupled with boson field, we made it clear that an evolution problem can be solved beyond the rotating wave approximation. We have applied the coherent approximation method, which had been proved to be effective in dealing with stationary state problems of polaron, to the evolution problem of the system mentioned above. The results obtained showed that the coherent approximation method is effective to treat the evolution problem and, in general cases, the non-rotating wave terms in Hamiltonian should not be ignored. Our results may provide a deep physical insight for further experiments to test the effects of non-rotating wave terms.

Recently, a generalization of Laughlin's wave function expressed in Haldane's spherical geometry is constructed in 4D quantum Hall effect. In fact, it is a membrane wave function in CP3 space. In this article, we use non-Abelian Berry phase to analyze the statistics of this membrane wave function. Our results show that the membrane wave function obeys fractional statistics. It is the rare example to realize fractional statistics in higher-dimensional space than 2D. And, it will help to make clear the unresolved problems in 4D quantum Hall effect.

A new ansatz is presented for analytic study of the properties of the Holstein model. New analytic results for the polaronic band structure, ground state energy, phonon distribution, hopping probability of electron, and effective masses, of the Holstein molecular crystal model, are given in one dimension. All the analytic results obtained are in accord with the numerical results completed recently and valid both in the adiabatic and nonadiabatic regimes, and accurate enough in the region of validity.

Behaviour of a simple model polariton system is restudied. The distribution of phonons in polariton never is sub-Poisson given by computation of the thermal counterpart of the Q parameter and the matrix m(3). The polariton complex as a whole shows non-classical behaviour below a threshold temperature, which depends on the photon-phonon coupling strength, when the distribution of phonons is always classical at any temperature.

Based on the relativistic Bethe–Salpeter (BS) equation, the positronium wavefunctions in Euclidean momentum space are obtained. Meanwhile the energy levels of positronium ground states 11S0 and 13S1 are fitted to be 6.7934 eV and 6.7929 eV respectively, which qualitatively agree with the previous theoretical values. It is shown that the BS theory is valid and reliable to treat positronium.

The kaon electromagnetic form factor is calculated in the framework of coupled Schwinger–Dyson equation in rainbow approximation and Bethe–Salpeter equation in ladder approximation with the modified flat-bottom potential, which is the combination of the flat-bottom potential with considerations for the infrared and ultraviolet asymptotic behaviours of the effective quark-gluon coupling. All our numerical results give good fit to experimental values and other theoretical results.

The kaon meson electromagnetic form factor is calculated in the framework of coupled Schwinger-Dyson and Bethe-Salpeter formulation in simplified impulse approximation (dressed vertex) with modified flat-bottom potential, which is a combination of the flat-bottom potential taking into consideration the infrared and ultraviolet asymptotic behaviours of the effective quark-gluon coupling. All the numerical results give a good fit to experimental values.

Using every realization of the Virasoro-type symmetry algebra , we can obtain various high-dimensional integrable models under the meaning that they possess infinitely many symmetries. By means of a concrete realization, many -dimensional equations which possess Kac?Moody?Virasoro-type infinite dimensional symmetry algebras are obtained.

The ground-state energy of polarons in strong- and weak-coupling surface, interface materials is investigated by a concise purely two-dimensional polaron model. Phonon correlation is introduced in phonon coherent state to represent the wavefunction of the system. A self-consistent integral nonlinear equation satisfied by the distribution function of the energy is derived. Numerical calculations for the ground-state energy and binding energy of polarons in different type materials are performed using iteration method. Results are obtained in a wide range of coupling constant and are found to be lower than those of previous calculations.

In the framework of phonon-plasmon cooperative effect mechanism, the differential equation for the wavefunction of the travelling soliton-like bi-plasma polaron (BPP) is derived. Then it is proven that the solution can be simply one-dimensional form. Meanwhile, the velocity range of the travelling soliton-like BPP is studied, thereby, we found that the quantity of the materials, where the travelling soliton-like BPP can exist, should be very small, i.e. . This result is consistent with the recently reported ones. Finally, an analytic approximation solution is given.

The static kinks and their low energy excited states in scalar field theories with are studied in a function-series method. We give a universal formal solution, and a universal approach to find the low energy excited states as well. Excellent agreement between the FS solution and the exact answer is found. This confirms our predicted results of the energies of the excited quantum states by considering small oscillations about the kink motion.

Using 1+1 soliton-like polaron model of a deformable continuum, the critical temperature and the energy gap in high-temperature superconductors Y1-xCaxBa2Cu3-xMxO7-δ(M=Fe, Ni) are studied in the framework of finite temperature Green's function theory. The ratio 2Δ/kBTc=3.9 is obtained. Theoretical results are found in good agreement with the experimental data.

The resonant transition in the Paul trap is studied by the time-space transformation and function series expansion. A new selection rule for the transition in the trap is derived strictly. The probability in the ground state and some transition rates to the excited states are calculated. The comparison with the former studies shows that our results are more accurate and credible.

Based on the former studies, the time-dependent characteristics of the wave packets of a Paul-trapped ion are investigated explicitly in cylindrical coordinates by the method of function series expansion (FSE). It is shown that the present work relates the quantum motion of a Paul-trapped ion to the orbit of the classical motion and presents a more clear physical picture than the former studies.

The wavefunctions of the bound state of the charged kaon are obtained from the Bethe-Salpeter equation with the phenomenological vector-vector-type flat-bottom potential. The physical space-like electromagnetic form factor of the charged kaon is calculated. The results calculated give a good fit to the experimental values.

With time and space transformation, we first solve the Schrodinger equation of the time-dependent harmonic oscillator (TDHO) system. The properties of the squeezing in the case of , i.e., the Paul trap and , namely a stable frequency interfered by a single-pulsing-type disturbance, are investigated by using function series expansion. Results in the former case are compared with the numerical calculations carried out before. It is found that the condition related to the most strong squeezing is the direct result of our method, not any approximation is needed. Solutions of the latter one are valuable for the study of the ion trap, where different cases are studied in detail. Finally we made a discussion for the measurement and observation of a trapped ion by using squeezing properties.

A new concise polaron model is proposed to study the ground state of polarons in some strong-and weak-coupling polar crystals. The ground-state energy and binding energy of these materials are calculated numerically by iteration method. Results are in close agreement with the experimental data.

The magnetic properties of icosahedral clusters are studied using the discrete-variational local-spin-density-functional method, where M = V, Cr, Mn, Fe, Co, and Ni. The results show that all of the clusters, just like the case for the cluster, have double magnetic solutions. In contrast to the moment of for the cluster, the total magnetic moments of the clusters, ranging from to , have been changed greatly by the substitution of the central Ru atom with M. Among them, the cluster has a giant moment of . Furthermore, the cluster has nondegenerate ground state and could be expected to be remarkably stable. Therefore, for the purpose of enhancing the magnetic moment of the cluster, Ni is a promising candidate as a dopant. Finally, we predict that all the clusters except might belong to the class in which the magnetization of the cluster increases with temperature.

A novel variational approach is presented for the calculation of the ground-state energy of the polaron in arbitrary N dimensions in the strong-coupling limit. By using the phonon coherent state to represent the wavefunction of phonons, a self-consistent integro-differential equation for the electron wavefunction is derived. The calculated results of the ground-state energy for N = 1, 2 and 3 agree well with the best results in the literature. It is also found that, for arbitrary N, the present results are less than the Feynman path integral ones by small percentages. It is proposed that this approach should be universal for systems involving polarons in the strong-coupling regime.

The effective mass of a large polaron is calculated using the extended phonon coherent state proposed in our previous paper. In the weak-coupling limit, the mass expansion obtained can reproduce the fourth-order perturbative result. Moreover, in the intermediate-coupling range, the calculated results are in good agreement with those of other approaches.

The site occupation and electronic structure of an interstitial Mn2+ impurity in GaP are studied using the discrete-variational local-spin-density-functional method with cluster models. The results verify the conjecture of van Gisbergen et al. that the Mn2+ impurity prefers the interstitial site surrounded by four nearest-neighbour Ga atoms and show that a small host crystal relaxation and a large formation energy of the impurity measured with respect to GaP and Mn2+ occur. Two deep donor levels are found in the host crystal band gap owing to the presence of the impurity. The behaviour of the impurity is analysed and compared with results of the EPR experiment.

We calculated the decay constant and radius of the pion in the framework of the Bethe-Salpeter equation with the vector-vector-type flat-bottom potential. The calculated results, f pi = 102 MeV and [r(pi)(2)](1/2) = 0.632 fm, are close to experimental values of f(pi) = 93 MeV and [r(pi)(2)](1/2) = 0.663 +/- 0.023 fm.

A refined approach where the wave function is gradually improved is developed in the one-dimensional (1D) large-Frohlich-polaron problem. The results for the ground-state energy, the effective mass, and the average number of virtual phonons are obtained for a wide range of the coupling constant It, and are in agreement with those of the Feynman path-integral formalism. In addition, in the weak-coupling limit, the expansions of these observables in powers of the coupling constant are exactly calculated up to the alpha 3-term. They are E=- alpha -0.06066 alpha 2-0.00844 alpha 3, m*=1+0.5 alpha +0.19194 alpha 2+0.06912 alpha 3, and N=0.5 alpha +0.12132 alpha 2+0.029540 alpha 3, which agree with the known results of the fourth-order perturbation theory.

The electronic structure of Ti8C12 clusters with three possible geometric structures suggested in the literature is studied using the discrete-variational local-density-functional method. The results show that the ground states of the clusters are all degenerate, which means further Jahn-Teller distortions for the geometric structures of clusters. The results also indicate that the distorted dodecahedral Ti8C12 cluster, which is proposed by Guo et al. and optimized by the first principle calculations, is the most stable one among the clusters we considered and its electronic structure can explain the experimental observations. In this cluster, there is a strong pd bonding between Ti and C atoms, and the density of states at the Fermi energy is high.

By using the standard truncated Painleve analysis, a Backlund transformation is used to obtain some new types of multi-soliton solutions of the (2+1)-dimensional integrable Konopelchenko-Dubrovsky equation from the trivial vacuum solution.

The modified flat-bottom potential (MFBP) is given by the combination of the flat-bottom potential with considerations for the infrared and ultraviolet asymptotic behaviour of the effective quark-gluon coupling. The π meson electromagnetic form factor is calculated in the framework of the coupled Schwinger-Dyson equation and the Bethe-Salpeter equation in the simplified impulse approximation (dressed vertex) with the MFBP. All our numerical results give a good fit to experimental values.

For pt.I see ibid., vol.23, p.3923 (1990). The authors use the method previously presented to obtain the exact solutions for some coupled nonlinear equations.

The authors present a certain type of exact solutions for the two nonlinear equations by making an ansatz for the solution.

We study the interaction between holes and molecular vibrations on dry DNA by using the extended Firsov's model. The ground state energy, calculated by using two Hilbert spaces, Fock state space and coherent state space, is confirmed. The polaron binding energy, defined with the ground state energy, is 0.014 eV, much less than the thermal energy 0.026eV at room temperature 300K, which means that polarons are difficult to form self-trapping at room temperature and Anderson localization will prevent a metallic state on dry DNA. The results are consistent with the available experiments.

The eigenenergy spectrum of the Jaynes–Cummings (JC) model with and without the rotating-wave approximation (RWA) is investigated. The numerical analysis indicates that the non-RWA spectrum can only be approximated by the RWA in the range of sufficiently small coupling constant and detuning. In other region, the counter-rotating terms remarkably change the nature of the RWA energy spectrum. A simple expression with high accuracy for ground eigenenergy and eigenvector for non-RWA is available. The ground eigenvector for non-RWA shows that the ground state is not a dark state and very different from that of RWA which is a dark state.

In this paper we have calulated the Higgs potential with the one-loop correction in the SU(3) and SU(5) gauge models. The result shows that the arbitrary gauge hierarchy is doubtful in the peiturbation theory. This is in contradiction with the conclusion obtained by Mohaptra et al.

In an spontaneously broken gauge theory with a Higgs triplet, the mass effect of an isospin 1/2 fermion on the fermion-monopole bound states is discussed. It is shown that when the direct coupling between fermion and Higgs field approaches zero, but the Dirac mass remains finiteness, the necessary condition of the fermion-monopole bound state cannot be satisfied. This result means that the Rubakov effect is absent for monopole because of the Dirac mass.