Zhu Yue-Jin

Solving Generalized Non-degenerate Two-Mode Two-Photon Jaynes–Cummings Model by Supersymmetric Unitary Transformation*

Based on supersymmetric quantum mechanics theory, we introduced a supersymmetric unitary transformation to diagonalize the Hamiltonian of non-degenerate two-mode two-photon Jaynes–Cummings models which include any forms of intensity-dependent coupling, field-dependent detuning, and field nonlinearity. Its eigenvalue, eigenstates, and time evolution of state vector are obtained.

Self-consistent field theory of adsorption of flexible polyelectrolytes onto an oppositely charged sphere

The adsorption of flexible polyelectrolyte (PE) with the smeared charge distribution onto an oppositely charged sphere immersed in a PE solution is studied numerically with the continuum self-consistent field theory. The power law scaling relationships between the boundary layer thickness and the surface charge density and the charge fraction of PE chains revealed in the study are in good agreement with the existing analytical result. The curvature effect on the degree of charge compensation of the total amount of charges on the adsorbed PE chains over the surface charges is examined, and a clear understanding of it based on the dependences of the degree of charge compensation on the surface charge density and the charge fraction of PE chains is established.

Finite size effect of ions and dipoles close to charged interfaces

The modified dipolar Poisson–Boltzmann (MDPB) equation, where the electrostatics of the dipolar interactions of solvent molecules and also the finite size effects of ions and dipolar solvent molecules are explicitly taken into account on a mean-field level, is studied numerically for a two-plate system with oppositely charged surfaces. The MDPB equation is solved numerically, using the nonlinear Multigrid method, for one-dimensional finite volume meshes. For a high enough surface charge density, numerical results of the MDPB equation reveal that the effective dielectric constant decreases with the increase of the surface charge density. Furthermore, increasing the salt concentration leads to the decrease of the effective dielectric constant close to the charged surfaces. This decrease of the effective dielectric constant with the surface charge density is opposite to the trend from the dipolar Poisson–Boltzmann (DPB) equation. This seemingly inconsistent result is due to the fact that the mean-field approach breaks down in such highly charged systems where the counterions and dipoles are strongly attracted to the charged surfaces and form a quasi two-dimensional layer. In the weak-coupling regime with the electrostatic coupling parameter (the ratio of Bjerrum length to Gouy–Chapman length) Ξ < 1, where the MDPB equation works, the effective dielectric constant is independent of the distance from the charged surfaces and there is no accumulation of dipoles near the charged surfaces. Therefore, there are no physical and computational advantages for the MDPB equation over the modified Poisson–Boltzmann (MPB) equation where the effect of dipolar interactions of solvent dipoles is implicitly taken into account in the renormalised dielectric constant.

Quantum Fluctuation of a Mesoscopic Inductance Coupling Circuit at Finite Temperature

We study the quantization of mesoscopic inductance coupling circuit and discuss its time evolution. By means of the thermal field dynamics theory we study the quantum fluctuation of the system at finite temperature.

EXACT SOLITARY WAVE SOLUTIONS OF THE COUPLED NONLINEAR SCALAR FIELD EQUATIONS

Because of the arbitrary property of the singular manifold, the usual singularity analysis can be extended to a different form. Using a nonstandard truncation approach, five special types of exact solution of the coupled nonlinear scalar field equations are obtained.

Exact Solution of the Milburn Equation for the Coupled-Channel Cavity QED Model*

We give the exact solution of Milburn equation for a coupled-channel cavity QED model which includes the Stark term and the frequency detuning, and study the influence of the intrinsic decoherence on the atomic inversion of the system.

Phase Properties of Nonlinear Coherent States

Using the Pegg–Barnett formalism we study the phase probability distributions and the squeezing effects of measured phase operators in the nonlinear coherent states introduced by R.L. de Matos Filho and W. Vogel to describe the center-of mass motion of a trapped ion and the q-coherent states. Moreover, we have obtained the completeness relation of nonlinear coherent states and proved that the q-Fock state introduced in many papers is, in fact, the usual Fock state.

Painlevé Nonstandard Truncation Expansion Solutions of Dynamics Equation of Diblock Copolymer

Through Pickerings and extended Painleve nonstandard truncated expansion method, this paper solves the phase-separating dynamics equation of diblock copolymer, and obtains various exact solutions. We discuss non-complex special solutions which can be made up of hyperbolic functions or elliptic functions.

Structure of a Phase-Separating System in the Presence of Oscillatory Particles*

We numerically simulate the processing of the phase separation of the polymer blend-particle system under fluctuating fields by new discretizations form. Due to the presence of oscillatory particles which have an affinity for one of the components, the ordering mechanism of phase separation will be changed. By changing the oscillatory frequency ω and amplitude γ, we can find the formation of the striped structures either parallel or perpendicular to the oscillatory direction and obtain a diagram describing the orientational ordering of the domain structures.

N-Particle Entangled States of Continuum Variables*

We construct the n-particle entangled states in n-mode Fock space, and examine their completeness relation and partly non-orthonormal property. Their Schmidt decomposition and entangled operator are manifestly shown. Finally, we discuss their application.