An Exact Evolution Equation of the Curvature Perturbation for Closed Universe

As is well known, the exact evolution equation of the curvature perturbation plays a very important role in investigation of the inflaorresponding exacttion power spectrum of the flat universe. However, the c extension for the non-flat universes has not yet been given clearly. Interest in the non-flat, specially closed, universes has been aroused recently. The need for this extension is pressing. We start with the most elementary physical consideration and obtain finally this exact evolution equation of the curvature perturbation for the non-flat universes, as well as the evolutionary controlling parameter and the exact expression of the variable mass in this equation. We approximately perform a primitive and immature analysis on the power spectrum of non-flat universes. This analysis shows that the exact evolution equation of the curvature perturbation for the non-flat universes is very complicated, and we need to carry out many numerical and analytic works for this new equation in the future to judge whether the universe is fiat or closed by comparison of theories with observations.     

Cosmological scenario based on particle creation and holographic equipartition

We propose a cosmological scenario that describes the evolution of the universe based on particle creation and holographic equipartition. The model attempts to solve the inflation of the early universe and the accelerated expansion of the present universe without introducing the dark energy from the thermodynamical perspective.Throughout the evolution of the universe, we assume that the universe consistently creates particles, and that the holographic equipartition is always satisfied. Further, we set the creation rate of particles proportional to H~2 in the early universe and to H in the present and late universe, where H depicts the Hubble parameter. Consequently, we obtain the solutions a(t) ∝ e~(αt/3) and a(t) ∝ t~(1/2) for the early universe and solutions a(t) ∝ t~δ and a(t) ∝ e~(Ht) for the present and late universe, respectively, where α and δ are the parameters. Finally, we obtain and analyze two important thermodynamic properties for the present model.     

Multisymplectic Hamiltonian Formulation for a One-Way Seismic Wave Equation of High-order Approximation

Based on the Lagrangian density and covariant Legendre transform, we obtain the multisymplectic Hamiltonian formulation for a one-way seismic wave equation of high-order approximation. This formulation provides a new perspective for studying the one-way seismic wave equation. A multisymplectic integrator is also derived.     

Quantum Creation of Closed Universe with Both Effects of Tunnelling and Well

A new “twice loose shoe“ method in the Wheeler-DeWitt equation of the universe wavefunction on the cosmic scale factor a and a scalar field φ is suggested,We analyze both the affections coming from the tunnelling effect of α and the potential well effect of φ,and obtain the initial values α0 about a primary closed universe which is born with the largest probability in the quantum manner,Our result is able to overcome the “large field difficulty“ of the universe quantum creation probabiltiy with only tunnelling effect.This new born universe has to suffer a startup of inflation,and then comes into the usual slow rolling inflation.The universe with the largest probalility maybe has a “gentle“ inflation of an eternal chaotic infltion.this depends on a new parameter q which describes the tunnelling character.     

Lie symmetries and non-Noether conserved quantities for Hamiltonian canonical equations

This paper focuses on studying Lie symmetries and non-Noether conserved quantities of Hamiltonian dynamical systems in phase space. Based on the infinitesimal transformations with respect to the generalized coordinates and generalized momenta, we obtain the determining equations and structure equation of the Lie symmetry for Hamiltonian dynamical systems. This work extends the research of non-Noether conserved quantity for Hamilton canonical equations, and leads directly to a new type of non-Noether conserved quantities of the systems. Finally, an example is given to illustrate these results.     

Quantitative conditions for time evolution in terms of the von Neumann equation

The adiabatic theorem describes the time evolution of the pure state and gives an adiabatic approximate solution to the Schr ¨odinger equation by choosing a single eigenstate of the Hamiltonian as the initial state. In quantum systems, states are divided into pure states(unite vectors) and mixed states(density matrices, i.e., positive operators with trace one). Accordingly, mixed states have their own corresponding time evolution, which is described by the von Neumann equation. In this paper, we discuss the quantitative conditions for the time evolution of mixed states in terms of the von Neumann equation. First, we introduce the definitions for uniformly slowly evolving and δ-uniformly slowly evolving with respect to mixed states, then we present a necessary and sufficient condition for the Hamiltonian of the system to be uniformly slowly evolving and we obtain some upper bounds for the adiabatic approximate error. Lastly, we illustrate our results in an example.     

Schrdinger Equation of a Particle on a Rotating Curved Surface

We derive the Schrdinger equation of a particle constrained to move on a rotating curved surface S.Using the thin-layer quantization scheme to confine the particle on S,and with a proper choice of gauge transformation for the wave function,we obtain the well-known geometric potential V_g and an additive Coriolis-induced geometric potential in the co-rotational curvilinear coordinates.This novel effective potential,which is included in the surface Schrdinger equation and is coupled with the mean curvature of S,contains an imaginary part in the general case which gives rise to a non-Hermitian surface Hamiltonian.We find that the non-Hermitian term vanishes when S is a minimal surface or a revolution surface which is axially symmetric around the rolling axis.     

Properties of bottomonium in a semi-relativistic model

Using a semi-relativistic potential model we investigate the spectra and decays of the bottomonium (bb-) system. The Hamiltonian of our model consists of a relativistic kinetic energy term, a vector Coulomb-like potential and a scalar confining potential. Using this Hamiltonian, we obtain a spinless wave equation, which is then reduced to the form of a single particle Schrodinger equation. The spin dependent potentials are introduced as a perturbation. The three-dimensional harmonic oscillator wave function is employed as a trial wave function and the bb- mass spectrum is obtained by the variational method. The model parameters and the wave function that reproduce the the bb- spectrum are then used to investigate some of their decay properties. The results obtained are then compared with the experimental data and with the predictions of other theoretical models.     

An Approach for Solving Short-Wave Models for Camassa-Holm Equation and Degasperis-Procesi Equation

In this paper, to construct exact solution of nonlinear partial differential equation, an easy-to-use approach is proposed. By means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. To solve the ordinary differential equation, we assume the soliton solution in the explicit expression and obtain the travelling wave solution. By the transformation back to the original independent variables, the soliton solution of the original partial differential equation is derived. We investigate the short wave model for the Camassa-Holm equation and the Degasperis-Procesi equation respectively. One-cusp soliton solution of the Camassa-Flolm equation is obtained. One-loop soliton solution of the Degasperis- Procesi equation is also obtained, the approximation of which in a closed form can be obtained firstly by the Adomian decomposition method. The obtained results in a parametric form coincide perfectly with those given in the present reference. This illustrates the efficiency and reliability of our approach.     

Interacting Holographic Dark Energy in the Scalar Gauss-Bonnet Gravity

We study cosmological application of interacting holographic dark energy density in the scalar Gauss-Bonnet framework. We employ the interacting holographic model of dark energy to obtain the equation of state for the interacting holographic energy density in a spatially fiat universe. Our calculations show that taking Ω∧ = 0.73 for the present time, it is possible to have w∧^eff crossing -1. This implies that one can generate a phantom-like equation of state from the interacting holographic dark energy model in flat universe in the scalar Gauss-Bonnet cosmology framework. Then we reconstruct the potential of the scalar field.     

De Broglie-Bohm Interpretation of Canonical Quantum Cosmology Implies Early Stages of the Universe Dominated by Radiation

The Einstein's general relativity is formulated in the Hamiltonian form for a spatially flat, isotropic and homogeneous universe. Subsequently, we perform the canonical quantization procedure to the Hamiltonian to obtain the Wheeler-DeWitt equation. Solving the Wheeler-DeWitt equation and employing the de Broglie-Bohm interpretation to the wave function of the universe, we obtain a new version of spatially flat Friedmann equation for the early universe where the scale factor of the universe is taken to be sufficiently small.     

Enhanced electron positron pair creation by the frequency chirped laser pulse

Based on the quantum Vlasov equation, the effect of frequency chirp on electron-positron pair production is investigated. The cycle parameter, which characterizes the laser field cycle degree within the pulse, is also considered. In both supercycle and subcycle laser pulses the frequency chirp can greatly enhance the momentum distribution function of created pairs and the pair number density. The pair number density created by a supercycle laser pulse is larger than that by a subcycle pulse under the same laser frequency and chirping. There exists an optimal cycle parameter corresponding to the maximum value of the created pair number density for different chirp rates. It is found that the pair number density is sensitive/insensitive to chirping rate when the cycle parameter lies below/above the optimal one.     

Quantum Effect in Mesoscopic Open Electron Resonator

The open electron resonator is a mesoscopic device that has attracted considerable attention due to its remarkable behavior： conductance oscillations. In this paper, using an improved quantum theory to mesoscopic circuits developed recently by Li and Chen, the mesoscopic electron resonator is quantized based on the fundamental fact that the electric charge takes discrete value. With presentation transformation and unitary transformation, the SchrSdinger equation becomes an standard Mathieu equation. Then, the detailed energy spectrum and wave functions in the system axe obtained, which will be helpful to the observation of other characters of electron resonator. The average of currents and square of the current are calculated, the results show the existence of the current fluctuation, which causes the noise in the circuits, the influence of inductance to the noise is discussed. With the results achieved, the stability characters of mesoscopic electron resonator are studied firstly, these works would be benefit to the design and control of integrate circuit.     

Supersymmetric Quantum Mechanics and SUSY Dependent SU（2） Symmetry for a Spin-1/2 Charged Particle in a Magnetic Field

We find that in a supersymmetric quantum mechanics （SUSY QM） system, in addition to supersymmetric algebra, an associated SU（2） algebra can be obtained by using semiunitary （SUT） operator and projection operator, and the relevant constants of motion can be constructed. Two typical quantum systems are investigated as examples to demonstrate the above finding. The first example is the quantum system of a nonrelativistic charged particle moving in x-y plane and coupled to a magnetic field along z-axis. The second example is provided with the Dirac particle in a magnetic field. Similarly there exists an SUτ（2） SUσ（2） symmetry in the context of the relativistic Pauli Hamilt onian squared. We show that there exists also an SU（2） symmetry associated with the supersvmmetrv of the Dirac particle.     

Pseudospin symmetry of the Dirac equation for a MSbius square plus Mie type potential with a Coulomb-like tensor interaction via SUSYQM

We investigate the approximate solution of the Dirac equation for a combination of Mobius square and Mie type potentials under the pseudospin symmetry limit by using supersymmetry quantum mechanics. We obtain the bound-state energy equation and the corresponding spinor wave functions in an approximate analytical manner. We comment on the system via various useful figures and tables.     

Exact solution of Schrdinger equation with q-deformed quantum potentials using Nikiforov–Uvarov method

In this paper,we present the exact solution of the one-dimensional Schrdinger equation for the q-deformed quantum potentials via the Nikiforov–Uvarov method.The eigenvalues and eigenfunctions of these potentials are obtained via this method.The energy equations and the corresponding wave functions for some special cases of these potentials are briefly discussed.The PT-symmetry and Hermiticity for these potentials are also discussed.     

Quantum theory of dilaton gravity in 1+1 dimensions

We discuss the quantum theory of 1+1 dimensional dilaton gravity, which is an interesting model with features analogous to the spherically symmetric gravitational systems in 3+1 dimensions. The functional measures over the metrics and the dilaton field are explicitly evaluated and the diffeomorphism invariance is completely fixed in the conformal gauge by using the technique developed in two dimensional quantum gravity. We derive the Wheeler-DeWitt like equations as physical state conditions. In the ADM formalism the measures of fields are very ambiguous, but in our formalism they are explicitly defined. A singularity appears at ²=κ(>0), where and N is the number of matter fields. The final stage of the black hole evaporation corresponds to the region ²κ, where the Liouville term becomes important, which just comes from the measure of the metrics. If κ<0, the singularity disappears.     

Solutions of the Schrodinger Equation with Quantum Mechanical Gravitational Potential Plus Harmonic Oscillator Potential

The solutions of the Schrodinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential have been presented using the parametric Nikiforov-Uvarov method. The bound state energy eigen values and the corresponding un-normalized eigen functions are obtained in terms of Laguerre polynomials. Also a special case of the potential has been considered and its energy eigen values are obtained.     

Decoherence of a Double Quantum Dot Charge Qubit Approached with Redfield Equation

In this paper, we investigate the decoherence time of a double quantum dot （DQD） charge qubit in three kinds of baths through solving dynamics of the qubit. The dynamics of the qubit is investigated with Redfield master equation. It is shown that the decoherence time of the qubit in Ohmic bath has the same order of magnitude as the experiments reported. When the environment is modeled with the supra-Ohmic bath the decoherence time of the qubit is shorter than the experimental result. And when modeled with the sub-Ohmic bath the decoherence time of the qubit is longer than the experimental result.     

Exact Solution of Klein-Gordon Equation for Charged Particle in Magnetic Field with Shape Invariant Method

Based on the shape invariance property we obtain exact solutions of the three-dimensional relativistic Klein Gordon equation for a charged particle moving in the presence of a certain varying magnetic field, and we also show its non-relativistic limit.