Birth of the Universe as quantum scattering in string cosmology

In a Wheeler-DeWitt approach to quantum string cosmology, the present state of the Universe arises from the scattering and reflection of the wave function representing the initial string vacuum in superspace. This scenario is described and compared with the more conventional quantum cosmology picture, in which the birth of the Universe is represented as a process of tunnelling from nothing in superspace.This essay received the third award from the Gravity Research Foundation, 1996-Ed.     

Quantized magnetic flux through the ground-state orbit of the hydrogen atom

We have investigated the spin-dependent quantized magnetic fluxes through the ground-state electronic orbit of the hydrogen atom. We show that the corresponding fluxes are (1/2)Φ₀ for the spin-up case and (3/2)Φ ₀ for the spin-down case, respectively, where Φ₀ = hc/e is the flux quantum. Using the energy-flux proportionality, we also show that the spin-up case (where the electron spin is antiparallel to the proton spin, resulting in zero total spin) is the spin-dependent ground state of the hydrogen atom. The present result helps to understand the spin flip-flop in excitonic transitions in nanostructures.     

Quantum black hole and the modified uncertainty principle

Recently Ali et al. (2009) [13] proposed a Generalized Uncertainty Principle (or GUP) with a linear term in momentum (accompanied by Planck length). Inspired by this idea we examine the Wheeler-DeWitt equation for a Schwarzschild black hole with a modified Heisenberg algebra which has a linear term in momentum. We found that the leading contribution to mass comes from the square root of the quantum number n which coincides with Bekenstein?s proposal. We also found that the mass of the black hole is directly proportional to the quantum number n when quantum gravity effects are taken into consideration via the modified uncertainty relation but it reduces the value of mass for a particular value of the quantum number.     

Quantum Cosmological Perfect Fluid Models

Perfect fluid Friedmann-Robertson-Walker quantum cosmological models for an arbitrary barotropic equation of state p = are constructed using Schutz's variational formalism. In this approach the notion of time can be recovered. By superposition of stationary states, finite-norm wave-packet solutions to the Wheeler-DeWitt equation are found. The behaviour of the scale factor is studied by applying the many-worlds and the ontological interpretations of quantum mechanics. Singularity-free models are obtained for < 1. Accelerated expansion at present requires –1/3 > > – 1.     

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

The Einstein＇s genera/relativity is formulated in the Hamiltonian form for a spatia/ly Bat, 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 spatia/ly fiat Friedmann equation for the early universe where the scale factor of the universe is taken to be sufilcientlv small.     

Quantized Conductance in Heteronanocontacts Between Iron Tip and Perovskite Electrode Under High-Bias Voltages

We studied the conductance of a point contact between a mechanically sharpened iron tip and a surface of the La_0.7Sr_0.3MnO₃ perovskite electrode. The tip is fixed to a piezoelectric element and the conductance is measured as a function of the piezo voltage, which controls the tip pressing on the electrode. The height of steps between conductance plateaus is a multiple of the integer quantum e ²/h, characteristic for ferromagnetic materials in which the spin degeneracy is lifted.     

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.     

Deformation of Towers of Algebras and Quantized Intersection Cardinality Functions

The inductive limit of a tower of separable algebras is unchanged, up to isomorphism, by consistent deformations but the inductive limit of a corresponding tower of modules may be nontrivially deformed, thereby quantizing the limit module. In the case of the inductive limit of the complex group algebras of the symmetric groups and their deformations, the Hecke algebras, this quantization preserves properties of the finite case which disappear in the absence of quantization.     

Hamiltonian Formalism of the Derivative Nonlinear Schrodinger Equation

A particular form of poisson bracket is introduced for the derivative nonlinear Schrodinger (DNLS) equation.And its Hamiltonian formalism is developed by a linear combination method. Action-angle variables are found.     

Quantized charge transport in adiabatic pumping by a driven double δ-barrier

We investigate the condition that the charge carried by quantum parametric pumping per cycle is quantized in units of the electron charge e and the role of adiabaticity in charge quantization. Using a driven double-δ-potential model and a Floquet scattering approach, it is found that the quantization phenomenon occurs only at very low frequencies of the oscillating potential and adiabaticity of the potential modulation is crucial for quantization.     

Wavelength-Multiplexing Diffractive Phase Element with Quantized Phase Structure

We have reported on the design algorithm of the wavelength-multiplexing diffractive phase element (WMDPE) capable of generating independent spot patterns for more than two wavelengths. [J. Opt. Soc. Am. A 18 (2001) 1082] In this paper, the stepwise quantization method proposed by F. Wyrowski [J. Opt. Soc. Am. A 7 (1990) 961] is built into the algorithm to design the WMDPE with quantized phase structure. Validity of the method is verified by the WMDPE for 7 wavelengths with 9 phase levels. The optical experiment demonstrates that the fabricated WMDPE generates correct patterns for different wavelengths. Performance dependence of the WMDPE on the number of quantized phase levels is discussed based on the simulation results.This paper was originally presented at the 2nd International Conference on Optical Design and Fabrication, ODF2000 which was held on November 15-17, 2000 at the International Conference Center, Tokyo, Waseda University, Japan.     

KDP晶体三倍频实验和分析

报道了ＫＤＰ晶体中的三倍频产生的实验研究，计算了比较了直接三倍频过程和级联过程对ＫＤＰ晶体三阶有效非线性系数的贡献，并探讨了ＫＤＰ作为非线性晶体材料三阶非线性系数测量基准的可行性。     

六极磁铁的三级Lie映射

用Lie代数方法分析了相对论带电粒子在六极磁铁中的运动,得到在六维相空间中粒子的三级近似轨迹.     

Adaptive Feedback Stabilization with Quantized State Measurements for a Class of Chaotic Systems

We investigate asymptotical stabilization for a class of chaotic systems by means of quantization measurements of states. The quantizer adopted in this paper takes finite many values. In particular, one zoomer is placed at the input terminal of the quantizer, and another zoomer is located at the output terminal of the quantizer. The zoomers possess a common adjustable time-varying parameter. By using the adaptive laws for the time-varying parameter and estimating boundary error of values of quantization, the stabilization feedback controller with the quantized state measurements is proposed for a class of chaotic systems. Finally, some numerical examples are given to demonstrate the validity of the proposed methods.     

螺线管透镜的三级李映射

用李代数方法分析了带电粒子在螺线管透镜中的运动,得到六维相空间中粒子轨迹的三级近似解,并包含了运动的相对论效应.当需要时,还可以扩展到更高级像差.     

Quantized vortex stability and interaction in the nonlinear wave equation

The stability and interaction of quantized vortices in the nonlinear wave equation (NLWE) are investigated both numerically and analytically. A review of the reduced dynamic law governing the motion of vortex centers in the NLWE is provided. The second order nonlinear ordinary differential equations for the reduced dynamic law are solved analytically for some special initial data. Using 2D polar coordinates, the transversely highly oscillating far field conditions can be efficiently resolved in the phase space, thus giving rise to an efficient and accurate numerical method for the NLWE with non-zero far field conditions. By applying this numerical method to the NLWE, we study the stability of quantized vortices and find numerically that the quantized vortices with winding number m=±1 are dynamically stable, and resp. |m|>1 are dynamically unstable, in the dynamics of NLWE. We then compare numerically quantized vortex interaction patterns of the NLWE with those from the reduced dynamic law qualitatively and quantitatively. Some conclusive findings are obtained, and discussions on numerical and theoretical results are made to provide further understanding of vortex stability and interactions in the NLWE. Finally, the vortex motion under an inhomogeneous potential in the NLWE is also studied.     

Hamiltonian Formalism of mKdV Equation with Non-vanishing Boundary Values

Hamiltonian formalism of the mKdV equation with non-vanishing boundary value is re-examined by a revised form of the standard procedure. It is known that the previous papers did not give the final results and involved some questionable points [T.C. Au Yeung and P.C.W. Fung, J. Phys. A 21 （1988） 3575]. In this note, simple results are obtained in terms of an affine parameter and a Galileo transformation is introduced to ensure the results compatible with those derived from the inverse scattering transform.     

Hamiltonian Formalism of mKdV Equation with Non-vanishing Boundary Values

Hamiltonian formalism of the mKdV equation with non-vanishing boundary valueis re-examined by a revised form of the standard procedure. It is known that the previous papers did not give the final results and involved some questionable points [T.C. Au Yeung and P.C.W. Fung, J. Phys. A 21 (1988) 3575]. In this note, simple results are obtained in terms of an affine parameter and a Galileo transformation is introduced to ensure the results compatible with those derived from the inverse scattering transform.     

Quantized conductance behavior of Pt metal nanoconstrictions under electrochemical potential control

We studied the quantized conductance behavior of mechanically fabricated Pt nanoconstrictions under electrochemical potential control in H₂SO₄, Na₂SO₄, and NaOH solutions. There was no clear feature in the conductance histogram, when the electrochemical potential of the nanoconstrictions was kept at the double layer or the under potential deposited hydrogen potential. At the hydrogen evolution potential, the conductance histograms showed clear features around 0.5 and 1 G₀ in the H₂SO₄ solution. In Na₂SO₄, and NaOH solutions, a 1 G₀ feature with a shoulder appeared in the histogram. The quantized conductance behavior of Pt nanoconstrictions could be controlled by the electrochemical potential and solution pH.     

Third harmonic generation in layered media in presence of optical bistability of the fundamental

We study third harmonic generation in layered configuration when the fundamental exhibits bistable response. We consider two geometries, namely, a Fabry-Perot cavity with reflection coatings and a distributed feedback structure with alternate nonlinear layers. In both the cases for suitable choice of frequency, the power response at the fundamental frequency is bistable. We show that bistability of the fundamental leads to a multivalued character of the generated third harmonic in both the forward and backward directions. Moreover, we study frequency response in the case of the Fabry-Perot cavity and show that additional structures arise in the generated third harmonic due to frequency bistability of the fundamental. Our calculations suggest the possibility of an all optical switch at third harmonic frequency controlled by the parameters (like intensity, frequency) of the fundamental.