Does Operator Ordering Need Wormhole Dominance in the Wavefunction of the Universe?

In dealing with the wavefunction of the universe there is a debate on the various proposals about the boundary condition of the wavefunction of the universe. At present we have three proposals, namely, the Hartle-Hawking proposal, the tunneling proposal and the Linde proposal. Recently it has been argued that the operator ambiguity factor has a decisive role in deciding the consequences of the various wavefunction at the zero scale factor region. In the present paper we discuss the role of operator ordering in the light of wormhole dominance proposal proposed by one of the authors and compare the results with that of others obtained earlier. We present an interpretation of operator ordering as a contribution of some sort of matter fields and discuss the role of complex path WKB analysis in avoiding the initial singularity and allowing us to incorporate the contribution of wormhole in the wavefunction of the universe.     

Accurate wavefunctions for hydrogenic donors in GaAs(Ga,Al)As quantum dots

A simple variational wavefunction is proposed for calculating the energy of nodeless quantum states of a hydrogenic donor located at the centre of a spherical GaAs(Ga,Al)As quantum dot. Energies are calculated for the 1s, 2p and 3d states for a range of values of the radius of the quantum dot. The results are compared to the “exact” energies and for the ground state with the results obtained by using the wavefunction proposed by Porras-Montenegro and Perez-Merchancano [Phys. Rev. B 46 (1992) 9780]. For the range of quantum dot radii of practical interest, it is shown that the proposed wavefunction gives results of good accuracy. For the ground state, the results from the proposed wavefunction for R ≤ 4 are considerably better than those obtained from the wavefunction used by Porras-Montenegro and Perez-Merchancano.     

On the feasibility of charged wormholes

While wormhole spacetimes are predictions of the general theory of relativity, specific solutions may not be compatible with quantum field theory. This paper modifies the charged wormhole model of Kim and Lee with the aim of satisfying an extended version of a quantum inequality due to Ford and Roman. The modified metric may be viewed as a solution of the Einstein fields equations representing a charged wormhole that is compatible with quantum field theory.     

Energy gaps for fractional quantum Hall states described by a Chern-Simons composite fermion wavefunction

The Jain's composite fermion wavefunction has proven quite succesful to describe most of the fractional quantum Hall states. Its mathematical foundation lies in the Chern-Simons field theory for the electrons in the lowest Landau level, despite the fact that such wavefunction is different from a typical mean-field level Chern-Simons wavefunction. It is known that the energy excitation gaps for fractional Hall states described by Jain's composite fermion wavefunction cannot be calculated analytically. We note that analytic results for the energy excitation gaps of fractional Hall states described by a fermion Chern-Simons wavefunction are readily obtained by using a technique originating from nuclear matter studies. By adopting this technique to the fractional quantum Hall effect we obtained analytical results for the excitation energy gaps of all fractional Hall states described by a Chern-Simons wavefunction. Received 9 March 2001     

Semi-classical wormholes are unstable

We show that Lorentzian (traversable) wormholes with semi-classical spacetimes are unstable. Semi-classicality of the energy–momentum tensor of the exotic matter used to stabilize the wormhole implies localization of its wavefunction in phase space, leading to evolution according to the classical equations of motion. Previous results related to violation of the NEC then require that the matter is unstable to small perturbations.     

Binding energy of a screened donor in a spherical quantum dot with a parabolic potential

A wavefunction is proposed for calculating the ground-state energy of a screened donor in a spherical quantum dot under a parabolic potential by a variational method. The donor is taken to be at the center of the quantum dot. Results are presented for four values of the screening parameter by the proposed wavefunction as well as for the hydrogenic donor case by a wavefunction used by Xiao et al.. To assess the accuracy of the results, ‘exact’ energies are also obtained by numerical integration of the Schrödinger equation. It is shown that the proposed wavefunction gives very good results in all cases including the hydrogenic donor case.     

具有旋量场的量子虫洞

本文利用Hawking-Page的边界条件讨论了具有费米场的量子虫洞,导出了相应的Wheeler-DeWitt方程,计算了虫洞波函数,由虫洞波函数的分析,发现虫洞在a=0处出现几率密度为零,虫洞基态最可几半径为Planck尺度.     

Cosmological Wave Function and Wormhole Wave Function with a Conformal Complex Scalar Field

Quantum cosmology and the quantum wormhole witha conformal complex scalar field are discussed, thecorresponding Wheeler-DeWitt equations are obtained, andthe cosmological wave functions and wormhole wave functions are calculated, respectively,with different boundary conditions. From thecosmological wave function it is found that theprobability density of the universe is zero at a = 0,while at the ground state the most probable radius is aboutthe Planck scale. It is also shown that there exist twodifferent types of universes, which can be connected bythe quantum tunneling effect, transiting from one region to another. It follows from thewormhole wave function that the most probable radius ofthe wormholes is about the Planck scale, which impliesthat the wormhole is steady due to the quantumeffect.     

纤锌矿GaN柱形量子点中类氢施主杂质态

在有效质量近似和变分原理的基础上,选取含两个变分参数的波函数,研究了纤锌矿结构的GaN/AlxGa1-xN单量子点中类氢施主杂质体系的结合能随量子点(QD)尺寸以及杂质在量子点中位置的变化,并与以前使用不同尝试波函数的计算结果进行了比较。结果表明:由我们选取的两变分参数波函数得到的结果与前人选取的两变分参数波函数得到的结果相比有所改进,而与选取一个变分参数波函数得到的结果一致。同时我们还计算了体系的维里定理值随量子点半径的变化情况,所得结果与前人工作结果一致,说明本文选取的两变分参数波函数能很好地描述柱形量子点中施主杂质态的运动。     

On Jastrow wavefunctions containing attractive correlations

A quantum mechanical explanation is given in support of the form of Jastrow wavefunction introduced by De Michelis and Reatto. We propose a new, simpler wavefunction which has the correct long-range behaviour.     

Self-consistency of the quantum billiard problem in wormhole spacetimes

A wormhole can be made to function as a time machine. In the context of the quantum billiard problem in the presence of a wormhole we examine whether this is compatible with the self-consistency of physics. We derive a self-consistency condition in which the classical limit corresponds to known results for the (classical) billiard problem in a wormhole space-time and that suggests that some fine-tuning of initial conditions might be necessary.     

Double-wave description of mesoscopic resistance-inductance-capacitance coupled circuit with power source

Quantum fluctuations in the mesoscopic capacitance-inductance-resistance coupled circuit with a power source are investigated using canonical transformation and a double wavefunction. We confirm that the fluctuations are not influenced by the power source. As a new method, the double wavefunction describes a single system of the coupled circuit, whereas the single wavefunction describes a quantum ensemble.     

Visualization of space charge field effect on excitons in a GaAs quantum dot by near-field optical wavefunction mapping

Near-field photoluminescence (PL) imaging spectroscopy was used to investigate multi-exciton and charged-exciton states confined in a single GaAs interface fluctuation quantum dot. We determined the origin of peaks in the PL spectra by employing a wavefunction mapping technique. We observed distortion of the exciton wavefunction due to the electric field produced by an excess electron at a nearby confined state. Near-field wavefunction mapping was demonstrated to be a powerful tool for visualizing the local environment, which affects the emission properties of quantum dots.     

A Geometrical Interpretation of Grassmannian Coordinates

A geometrical interpretation of Grassmannian anticommuting coordinates is given. They are taken to represent an indefiniteness inherent in every spacetime point on the level of the spacetime foam. This indeterminacy is connected with the fact that in quantum gravity in some approximation we do not know the following information: are two points connected by a quantum wormhole or not? It is shown that: (a) such indefiniteness can be represented by Grassmannian numbers, (b) a displacement of the wormhole mouth is connected with a change of the Grassmannian numbers (coordinates). In such an interpretation of supersymmetry the corresponding supersymmetrical fields must be described in an invariant manner on the background of the spacetimefoam.     

Basic Neutron Interference Experiments and the Information Interpretation of the Wavefunction

No Heading Two fundamental neutron interference experiments are discussed, the measurement of an unknown phase-shift and the simultaneous measurement of which-way and visibility duality. The experiments have been realized solely with unitary phase transformations in the spirit of minimal interaction between the neutron and its environment. The scope of the quantum measurements is to strengthen the information interpretation of quantum mechanics. As result the interpretation of the wavefunction, describing the information about potential measurements on single quantum systems, is confirmed, and the search for realistic scenarios tor the wavefunction and the measurement process is weakened by such basic quantum experiments.     

Supersymmetric quantum hall liquid with a deformed supersymmetry

We construct a supersymmetric quantum Hall liquid with a deformed supersymmetry. One parameter is introduced in the supersymmetric Laughlin wavefunction to realize the original Laughlin wavefunction and the Moore—Read wavefunction in two extremal limits of the parameter. The introduced parameter corresponds to the coherence factor in the BCS theory. It is pointed out that the parameter-dependent supersymmetric Laughlin wavefunction enjoys a deformed supersymmetry. Based on the deformed supersymmetry, we construct a pseudopotential Hamiltonian whose groundstate is exactly the parameter-dependent supersymmetric Laughlin wavefunction. Though the SUSY pseudopotential Hamiltonian is parameter-dependent and non-Hermitian, its eigenvalues are parameter-independent and real.     

Quantization of the space－time with topological defect

We present the classical solution of Lagrange equations for the black hole with a global monopole or with a cosmic string. Then we obtain the wavefunction of the space－time by solving the Wheeler－De Witt equation. De Broglie－Bohm interpretation applied to the wavefunction gives the quantum solution of the space－time. In the end, the quantum effect on Hawking radiation is studied.     

Simple wavefunction for an impurity in a parabolic quantum dot

A simple variational wavefunction is proposed for calculating the ground-state energy of a hydrogenic donor located at the centre of a spherical parabolic quantum dot. Binding energies are calculated for three values of the parameter which gives the strength of the confining parabolic potential by the proposed wavefunction as well as by a wavefunction used by Xiaoet al. [Superlattices and Microstructures,19, 137 (1996)]. The results are compared to the ‘exact’ energies obtained by numerical integration of the Schrodinger equation. It is shown that the proposed wavefunction gives considerably better results than the wavefunction used by Xiaoet al. in all cases.