Multiple solutions and fermion mass effect in QED_3

Due to the negligible non-perturbation effect in the low-energy region, quantum chromodynamics （QCD） is limited to be applied to hadron problems in particle physics. However, QED has mature non-perturbation models which can be applied to Fermi acting-energy between quark and gluon. This paper applies quantum electrodynamics in 2 ＋ 1 dimensions （QED3） to the Fermi condensation problems. First, the Dyson-Schwinger equation which the fermions satisfy is constructed, and then the Fermi energy gap is solved. Theoretical calculations show that within the chirality limit, there exist three solutions for the energy gap; beyond the chirality limit, there are two solutions; all these solutions correspond to different fermion condensates. It can be concluded that the fermion condensates within the chirality limit can be used to analyze the existence of antiferromagnetic, pseudogap, and superconducting phases, and two fermion condensates are discovered beyond the chirality limit.

Exact Solution of Quantum Dynamics of a Cantilever Coupling to a Single Trapped Ultracold Ion

The quantum behavior ofa precooled cantilever can be probed highly 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 the 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.

Integrability of N-Component Bariev Model Under Open Boundary Conditions

N-component Bariev model for correlated hopping under open boundary conditions in one dimension is studied in the framework of Bethe ansatz method. The energy spectrum and the related Bethe ansatz equations are obtained.

Scheme for Preparation of W State Among Three Cavity Modes

We present a scheme of preparing the tripartite W state among three cavitymodes of radiation field inside high-Q superconducting cavities. Our scheme is based on theinteraction of a four-level atom with the cavity Geld for precalculated interaction times with everymode.

Solution Transformations and Their Effects on the Systems with Open Boundary Conditions

The solution transformations and properties of the -matrices for two-component systems under these transformations are analyzed in details. Not all transformed -matrices can be put into the Skalyanin's formalism. For those -matrices with all required properties, the effects of solution transformations to the six- and eight-vertex systems with open boundary conditions are discussed. These effects can be one of the following types: The Hamiltonian is invariant or transposition-invariant or made in a similarity transformation, or its coupling coefficients are multiplied by an overall factor, or the spin of the system is rotated around the axis or/and reflected with respect to some plane. In these cases, the transformed systems remain to be integrable.

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.

Generating of Conditionally Exactly Soluble Potentials by Method of Supersymmetric Quantum Mechanics

This paper suggests a systematic method based on supersymmetric quantum mechanics for generating conditionally exactly soluble potentials, and uses the variational supersymmetric WKB method to obtain the approximate values of the energy spectrum of the whole class.

Quantum Mechanical Image of Matrices' LDU Decomposition

For classical transformation （q1,q2） → （Aq1 ＋ Bq2, Cq1 ＋ Dq2）, where AD - CB ≠ 1, we find its quantum mechanical image by using LDU decomposition of the matrix （A B C D ）. The explicit operators L, D, and U axe derived and their physical meaning is revealed, this also provides a new way for disentangling some exponential operators.

Exact Solution for Phenomenon of atomic Collapse and Revival under Rotating Wave and Anti-Rotating Wave Approximation

An accurate method to solve the daynes Cummings （J-C） Hamiltonian has been investigated here. The phenomenon of atomic collapse and revival predicted by Jaynes-Cummings model is demonstrated. Solutions are consis- tent with the precious such as using the operator method. Furthermore, the Jaynes-Cummings Hamiltonian including the anti-rotating term is also solved precisely using this accurate way so that results agree with experiments better. Essences of the anti-rotating term are revealed. We discuss the relations of the phenomenon of atomic collapse and revival with the average photons number, the light field phase angle, the resonant frequency, and the size of coupling constant. The discussions may make one select suitable conditions to carry out experiment well and study the virtual light field effect on cavity quantum electrodynamics.

Elliptic Equation and Its Direct Applications to Nonlinear Wave Equations

Elliptic equation is taken as an ansatz and applied to solve nonlinear wave equations directly. More kinds of solutions are directly obtained, such as rational solutions, solitary wave solutions, periodic wave solutions and so on.It is shown that this method is more powerful in giving more kinds of solutions, so it can be taken as a generalized method.

Effects of Vibrational and Rotational Excitations on Dissociative Chemisorption Dynamics of N_(2) on Fe(111)

The dissociative chemisorption of N_(2) is the rate-limiting step for ammonia synthesis in industry.Here,we investigated the role of initially vibrational excitation and ro-tational excitation of N_(2) for its reactivity on the Fe(111)surface,based on a recently developed six-dimensional potential energy surface.Six-dimensional quantum dynamics study was carried out to investi-gate the effect of vibrational excitation for incidence energy below 1.6 eV,due to sig-nificant quantum effects for this reaction.The effects of vibrational and rotational excitations at high incidence energies were revealed by quasiclassical trajectory calculations.We found that raising the translational energy can enhance the dissociation probability to some extent,however,the vibrational excitation or rotational excitation can promote disso-ciation more efficiently than the same amount of translational energy.This study provides valuable insight into the mode-specific dynamics of this heavy diatom-surface reaction.

Biological Autonomy

We argue that genuine biological autonomy, or described at human level as free will, requires taking into account quantum vacuum processes in the context of biological teleology. One faces at least three basic problems of genuine biological autonomy： （1） if biological autonomy is not physical, where does it come from？ （2） Is there a room for biological causes？ And （3） how to obtain a workable model of biological teleology？ It is shown here that the solution of all these three problems is related to the quantum vacuum. We present a short review of how this basic aspect of the fundamentals of quantum theory, although it had not been addressed for nearly 100 years, actually it was suggested by Bohr, Heisenberg, and others. Realizing that the quantum mechanical measurement problem associated with the ＂collapse＂ of the wave function is related, in the Copenhagen Interpretation of quantum mechanics, to a process between self-consciousness and the external physical environment, we are extending the issue for an explanation of the different processes occurring between living organisms and their internal environment. Definitions of genuine biological autonomy, biological aim, and biological spontaneity are presented. We propose to improve the popular two-stage model of decisions with a biological model suitable to obtain a deeper look at the nature of the mind-body problem. In the newly emerging picture biological autonomy emerges as a new, fundamental and inevitable element of the scientific worldview.

New Exact Solutions to NLS Equation and Coupled NLS Equations

A transformation is introduced on the basis of the projective Riccati equations, and it is applied as an intermediate in expansion method to solve nonlinear Schrǒdinger (NLS) equation and coupled NLS equations. Manykinds of envelope travelling wave solutions including envelope solitary wave solution are obtained, in which some arefound for the first time.

Exact Solution of D-Dimensional Klein-Gordon Oscillator with Minimal Length

Specific modifications of the usual canonical commutation relations between position and momentumoperators have been proposed in the literature in order to implement the idea of the existence of a minimal observablelength. Here, we study a consequence of this proposal in relativistic quantum mechanics by solving in the momentumspace representation the Klein-Gordon oscillator in arbitrary dimensions. The exact bound states spectrum and thecorresponding momentum space wave function are obtained. Following Chang et al. (Phys. Rev. D 65 (2002) 125027),we discuss constraint that can be placed on the minimal length by measuring the energy levels of an electron in a penningtrap.

心是全息图

心的科学并不是大脑的特权。来自物理学、数学的探讨引起了人们的注意。根据这些探讨,有些科学家认为关于心的研究似乎并不一定非要集中在脑的研究上。 首先是曾因发现了神经元的突触电位而获诺贝尔奖的一位大脑生理学家,在1989年发表的一篇论文中,阐述了“是量子力学的概率在控制着脑中的分子生物学程序”的论点,指出了量子力学的重要性,从而在科学界引起了一场争论。

AFM study on the adsorption and aggregation behavior of dissolved humic substances on mica

Humic substances constitute the major organic fractions of soils, sediments and natural waters, and play a dominant role in the binding, mobilization, transport and ultimate fate of organic contaminants in subsurface systems. In this paper, two humic acid samples, Guanting and Tianjin, with different origin and chemical compositions have been investigated with AFM imaging for their adsorption and aggregation behaviors on mica. While the Tianjin humic sample is found to form small spheres with 250 to 330 nm in diameter at lower concentrations, irregular loop-chain assemblies of hundreds of nanometer in diameter with the chain width of about 40 nm are dominant for the Guanting humic sample, which may attribute to the more polar aliphatic fractions in the chemical composition in the latter. The heterogeneous and polydisperse nature of humic substances with multiple structural features, such as sponge-like structures, perforated sheets, aggregate of spheres, branches and chain-like assemblies etc., is apparent at higher concentrations for both humic samples, showing morphologically new evidence for the dominant view of the humic dual-mode sorption model. With naphthalene introduced, the assemblies of Guanting humic substances clearly become more compact with significantly narrowed branches and less porous the perforated sheet-like structures. It is indica- tive of that smaller nanometer scale rings present along the perforated assemblies could potentially represent hydrophobic domains, which may facilitate the adsorption and aggregation of naphthalene onto the natural particle surfaces and therefore lead to an important role of dissolved humic sub- stances in the sorption of environmental pollutants.

The Quasi-Exactly Solvable Problems in Relativistic Quantum Mechanics

We study the quasi-exactly solvable problems in relativistic quantum mechanics. We consider the problems for the two-dimensional Klein–Gordon and Dirac equations with equal vector and scalar potentials, and try to find the general form of the quasi-exactly solvable potential. After obtaining the general form of the potential, we present several examples to give the specific forms. In the examples, we show for special parameters the harmonic potential plus Coulomb potential, Killingbeck potential and a quartic potential plus Cornell potential are quasi-exactly solvable potentials.

A Semi-Analytical Solution to Classic Yang–Mills Equations with Both Asymptotical Freedom and Confining Features

It is well known that confinings and asymptotic freedom are properties of quantum chromo-dynamics （QCD）. But hints of these features can also be observed at purely classic levels. For this purpose we need to find solutions to the colorly-sourceful Yang-Mills equations with both confining and asymptotic freedom features. We provide such a solution in this paper which at the near-source region is of serial form, while at the far-away region is approximately expressed through simple elementary functions. From the solution, we derive out a classically non-perturbative beta function describing the running of effective coupling constant, which is linear in the couplings both in the infrared and ultraviolet region.