scholarly journals INTEGRAL TRANSFORM TECHNIQUE FOR MESON WAVE FUNCTIONS

1996 ◽  
Vol 11 (20) ◽  
pp. 1611-1626 ◽  
Author(s):  
A.P. BAKULEV ◽  
S.V. MIKHAILOV
Keyword(s):  
Wave Function ◽  
Sum Rules ◽  
Integral Transform ◽  
Wave Functions ◽  
Sum Rule ◽  
New Approach ◽  
Exactly Solvable ◽  
The Stability ◽  
The Masses ◽  
Integral Transform Technique

In a recent paper1 we have proposed a new approach for extracting the wave function of the π-meson φπ(x) and the masses and wave functions of its first resonances from the new QCD sum rules for nondiagonal correlators obtained in Ref. 2. Here, we test our approach using an exactly solvable toy model as illustration. We demonstrate the validity of the method and suggest a pure algebraic procedure for extracting the masses and wave functions relating to the case under investigation. We also explore the stability of the procedure under perturbations of the theoretical part of the sum rule. In application to the pion case, this results not only in the mass and wave function of the first resonance (π′), but also in the estimation of π″-mass.

scholarly journals The scalar and pseudoscalar hidden-charm tetraquark states with QCD sum rules

2018 ◽  
Vol 33 (14n15) ◽  
pp. 1850090
Author(s):  
Zun-Yan Di ◽  
Zhi-Gang Wang
Keyword(s):  
Experimental Data ◽  
Correlation Functions ◽  
Sum Rules ◽  
Qcd Sum Rules ◽  
Sum Rule ◽  
Rule Approach ◽  
Point Correlation ◽  
The Masses ◽  
Vacuum Condensates ◽  
Conserved Currents

Based on the diquark configuration, we construct the diquark–antidiquark interpolating tetraquark currents with [Formula: see text] and [Formula: see text], which can couple to the scalar and pseudoscalar tetraquark states, respectively, since they are not conserved currents. Then, we investigate their two-point correlation functions including the contributions of the vacuum condensates up to dimension-10 and extract the masses and pole residues of the tetraquark states with [Formula: see text] and [Formula: see text] through the QCD sum rule approach. The predicted masses can be confronted with the experimental data in the future. Moreover, we briefly discuss the possible decay patterns of the tetraquark states.

scholarly journals LAUGHLIN'S WAVE FUNCTIONS, COULOMB GASES AND EXPANSIONS OF THE DISCRIMINANT

1994 ◽  
Vol 09 (24) ◽  
pp. 4257-4351 ◽  
Author(s):  
P. DI FRANCESCO ◽  
M. GAUDIN ◽  
C. ITZYKSON ◽  
F. LESAGE
Keyword(s):  
Wave Function ◽  
Sum Rules ◽  
Quantum Hall ◽  
Wave Functions ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Lowest Landau Level ◽  
Component Plasma ◽  
Coulomb Gases ◽  
Spherical Plasma

In the context of the fractional quantum Hall effect, we investigate Laughlin's ansatz for the ground state wave function at fractional filling of the lowest Landau level. Interpreting its normalization in terms of a one-component plasma, we find the effect of an additional quadrupolar field on the free energy, and derive estimates for the thermo dynamically equivalent spherical plasma. In the second part of the paper, we present various methods for expanding the wave function in terms of Slater determinants, and obtain sum rules for the coefficients. We also address the apparently simpler question of counting the number of such Slater states using the theory of integral polytopes.

Sum Rule Photodisintegration Cross Sections of 6Li

1974 ◽  
Vol 52 (3) ◽  
pp. 202-206
Author(s):  
H. L. Yadav ◽  
B. K. Srivastava
Keyword(s):  
Charge Distribution ◽  
Cross Sections ◽  
Sum Rules ◽  
Wave Functions ◽  
Radial Wave ◽  
Sum Rule ◽  
Dependent Potential ◽  
Good Agreement

We apply the sum rules of Levinger and Bethe to calculate the integrated [Formula: see text] cross sections for 6Li using the Gaussian and Irving forms of radial wave functions whose parameters are determined by fitting the r.m.s. radius of charge distribution in 6Li. For the potential in the σint calculation we use the central velocity-dependent potential of Herndon et al. Our results for σint and σb for 6Li show reasonably good agreement with experiments.

scholarly journals Hölder Inequalities and QCD Sum-Rule Bounds on the Masses of Light Quarks

2001 ◽  
Vol 16 (supp01b) ◽  
pp. 582-584
Author(s):  
T. G. Steele
Keyword(s):  
Lower Bound ◽  
Spectral Function ◽  
Sum Rules ◽  
Light Quark ◽  
Hölder Inequality ◽  
Sum Rule ◽  
Quark Masses ◽  
The Masses

QCD Laplace Sum-Rules must satisfy a fundamental Hölder inequality if they are to consistently represent an integrated hadronic spectral function. The Laplace sum-rules of pion currents is shown to violate this inequality unless the u and d quark masses are sufficiently large, placing a lower bound on mu+md, the SU(2)-invariant combination of the light-quark masses.

scholarly journals Determination of Natural Frequency and Critical Velocity of Inclined Pipe Conveying Fluid under Thermal Effect by Using Integral Transform Technique

2021 ◽  
Vol 7 (1) ◽  
pp. 41-55
Author(s):  
Jabbar Hussein Mohmmed ◽  
Mauwafak Ali Tawfik ◽  
Qasim Abbas Atiyah
Keyword(s):  
Analytical Solution ◽  
Temperature Variation ◽  
Integral Transform ◽  
Fluid Velocity ◽  
Harmful Effect ◽  
Fluid System ◽  
Flowing Fluid ◽  
Time Domain Response ◽  
The Stability ◽  
Integral Transform Technique

This study proposes an analytical solution of natural frequencies for an inclined fixed supported Euler-Bernoulli pipe containing the flowing fluid subjected to thermal loads. The integral transform technique is employed to obtain the spatial displacement-time domain response of the pipe-fluid system. Then, a closed-form analytical expression is presented. The effects of various geometric and system parameters on the vibration characteristics of pipe-fluid system with different flow velocities are discussed. The results illustrate that the proposed analytical solution agrees with the solutions achieved in previous works. The proposed model predicts that the pipe loses the stability by divergence with the increasing flow velocity. It is evident that the influences of inclination angle and temperature variation are dramatically increased at a higher aspect ratio. Additionally, it is demonstrated that the temperature variation becomes a more harmful effect than the internal fluid velocity on the stability of the pipe at elevated temperature.

\Transient Heat Diffusion Problems with Variable Thermal Properties Solved by Generalized Integral Transform Technique

2014 ◽  
Vol 8 (5) ◽  
pp. 931
Author(s):  
Marcelo Ferreira Pelegrini ◽  
Thiago Antonini Alves ◽  
Ricardo Alan Verdú Ramos ◽  
Cassio Roberto Macedo Maia
Keyword(s):  
Thermal Properties ◽  
Integral Transform ◽  
Heat Diffusion ◽  
Transient Heat Diffusion ◽  
Integral Transform Technique ◽  
Diffusion Problems

Host-Guest Interactions on Electrode Surfaces for Immobilization of Molecular Catalysts

2020 ◽  
Author(s):  
Laurent Sévery ◽  
Jacek Szczerbiński ◽  
Mert Taskin ◽  
Isik Tuncay ◽  
Fernanda Brandalise Nunes ◽  
...  
Keyword(s):  
Aqueous Media ◽  
Heterogeneous Systems ◽  
Catalytic Systems ◽  
New Approach ◽  
Molecular Systems ◽  
Electrode Surfaces ◽  
Catalytic Surfaces ◽  
Oxide Electrodes ◽  
The Stability ◽  
Molecular Catalysts

The strategy of anchoring molecular catalysts on electrode surfaces combines the high selectivity and activity of molecular systems with the practicality of heterogeneous systems. The stability of molecular catalysts is, however, far less than that of traditional heterogeneous electrocatalysts, and therefore a method to easily replace anchored molecular catalysts that have degraded could make such electrosynthetic systems more attractive. Here, we apply a non-covalent “click” chemistry approach to reversibly bind molecular electrocatalysts to electrode surfaces via host-guest complexation with surface-anchored cyclodextrins. The host-guest interaction is remarkably strong and allows the flow of electrons between the electrode and the guest catalyst. Electrosynthesis in both organic and aqueous media was demonstrated on metal oxide electrodes, with stability on the order of hours. The catalytic surfaces can be recycled by controlled release of the guest from the host cavities and readsorption of fresh guest. This strategy represents a new approach to practical molecular-based catalytic systems.

Gravity as the curvature of the wave function of the universe.

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Main Task ◽  
Reference Systems ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Principle Of Equivalence ◽  
Relative Wave Function ◽  
New Equation ◽  
The Universe

Modern general theory of relativity considers gravity as the curvature of space-time. The theory is based on the principle of equivalence. All bodies fall with the same acceleration in the gravitational field, which is equivalent to locally accelerated reference systems. In this article, we will affirm the concept of gravity as the curvature of the relative wave function of the Universe. That is, a change in the phase of the universal wave function of the Universe near a massive body leads to a change in all other wave functions of bodies. The main task is to find the form of the relative wave function of the Universe, as well as a new equation of gravity for connecting the curvature of the wave function and the density of matter.

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