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## Bounds for the signless laplacian energy

Abreu, N.; Cardoso, D.M.; Gutman, I.; Martins, E.A.; Robbiano, M.
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
55.85%
The energy of a graph G is the sum of the absolute values of the eigenvalues of the adjacency matrix of G. The Laplacian (respectively, the signless Laplacian) energy of G is the sum of the absolute values of the differences between the eigenvalues of the Laplacian (respectively, signless Laplacian) matrix and the arithmetic mean of the vertex degrees of the graph. In this paper, among some results which relate these energies, we point out some bounds to them using the energy of the line graph of G. Most of these bounds are valid for both energies, Laplacian and signless Laplacian. However, we present two new upper bounds on the signless Laplacian which are not upper bounds for the Laplacian energy. © 2010 Elsevier Inc. All rights reserved.; FCT; FEDER/POCI 2010; CNPq; PQ-305016/2006–2007; Serbian Ministry of Science; No. 144015G; Mecesup 2 UCN 0605; Fondecyt-IC Project 11090211

## First Principles Semiclassical Calculations of Vibrational Eigenfunctions

Ceotto, Michele; Valleau, Stéphanie; Tantardini, Gian Franco; Aspuru-Guzik, Alán
Fonte: American Institute of Physics Publicador: American Institute of Physics
Tipo: Artigo de Revista Científica
EN_US
Relevância na Pesquisa
75.91%
Vibrational eigenfunctions are calculated on-the-fly using semiclassical methods in conjunction with ab initio density functional theory classical trajectories. Various semiclassical approximations based on the time-dependent representation of the eigenfunctions are tested on an analytical potential describing the chemisorption of CO on Cu(100). Then, first principles semiclassical vibrational eigenfunctions are calculated for the (CO_2) molecule and its accuracy evaluated. The multiple coherent states initial value representations semiclassical method recently developed by us has shown with only six ab initio trajectories to evaluate eigenvalues and eigenfunctions at the accuracy level of thousands trajectory semiclassical initial value representation simulations.; Chemistry and Chemical Biology

## Energy spectrum and eigenfunctions through the Quantum Section Method

Espinoza Ortiz,J.S.; Egydio de Carvalho,R.
Tipo: Artigo de Revista Científica Formato: text/html
Relevância na Pesquisa
55.87%
We present the Quantum Section Method as a quantization technique to compute the eigenvalues and the eigenfunctions of quantum systems. As an instructive example we apply this procedure to quantize the annular billiard. The method uses the symmetry of the system to determine an auxiliary section separating the system into partial regions and computes the Green's functions for Schroedinger's equation, obeying the same boundary conditions imposed on the eigenfunctions of the system. The eigenvalues are obtained as zeroes of a finite real determinant and the eigenfunctions are also determined. The present analytical and numerical results are in total agreement with those obtained by other procedures, which shows the efficiency of the method.

## On the $\kappa$-Dirac Oscillator revisited

Andrade, F. M.; Silva, E. O.; Ferreira Jr., M. M.; Rodrigues, E. C.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.84%
This Letter is based on the $\kappa$-Dirac equation, derived from the $\kappa$-Poincar\'{e}-Hopf algebra. It is shown that the $\kappa$-Dirac equation preserves parity while breaks charge conjugation and time reversal symmetries. Introducing the Dirac oscillator prescription, $\mathbf{p}\to\mathbf{p}-im\omega\beta\mathbf{r}$, in the $\kappa$-Dirac equation, one obtains the $\kappa$-Dirac oscillator. Using a decomposition in terms of spin angular functions, one achieves the deformed radial equations, with the associated deformed energy eigenvalues and eigenfunctions. The deformation parameter breaks the infinite degeneracy of the Dirac oscillator. In the case where $\varepsilon=0$, one recovers the energy eigenvalues and eigenfunctions of the Dirac oscillator.; Comment: 5 pages, no figures, accepted for publication in Physics Letters B

## Eigenvalues and Eigenfunctions of the Scalar Laplace Operator on Calabi-Yau Manifolds

Braun, Volker; Brelidze, Tamaz; Douglas, Michael R.; Ovrut, Burt A.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
75.83%
A numerical algorithm for explicitly computing the spectrum of the Laplace-Beltrami operator on Calabi-Yau threefolds is presented. The requisite Ricci-flat metrics are calculated using a method introduced in previous papers. To illustrate our algorithm, the eigenvalues and eigenfunctions of the Laplacian are computed numerically on two different quintic hypersurfaces, some Z_5 x Z_5 quotients of quintics, and the Calabi-Yau threefold with Z_3 x Z_3 fundamental group of the heterotic standard model. The multiplicities of the eigenvalues are explained in detail in terms of the irreducible representations of the finite isometry groups of the threefolds.; Comment: 67 pages, 16 figures, 9 tables. v2: References added

## Exact Ultra Cold Neutrons' Energy Spectrum in Gravitational Quantum Mechanics

Pedram, Pouria
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
65.66%
We find exact energy eigenvalues and eigenfunctions of the quantum bouncer in the presence of the minimal length uncertainty and the maximal momentum. This form of Generalized (Gravitational) Uncertainty Principle (GUP) agrees with various theories of quantum gravity and predicts a minimal length uncertainty proportional to $\hbar\sqrt{\beta}$ and a maximal momentum proportional to $1/\sqrt{\beta}$, where $\beta$ is the deformation parameter. We also find the semiclassical energy spectrum and discuss the effects of this GUP on the transition rate of the ultra cold neutrons in gravitational spectrometers. Then, based on the Nesvizhevsky's famous experiment, we obtain an upper bound on the dimensionless GUP parameter.; Comment: 11 pages, 1 figure, to appear in European Physical Journal C

## On Eigenvalues and Eigenfunctions Absent in the Actual Solid State Theory

Pereyra, Pedro
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
65.92%
In this letter new, closed and compact analytic expressions for the evaluation of resonant energies, resonant bound-states, eigenvalues and eigenfunctions for both scattering and bounded $n$-cell systems are reported. It is shown that for (scattering and bounded) 1-D systems the eigenfunctions $\Psi_{\mu ,\nu}(z)$ are simple and well defined functions of the Chebyshev polynomials of the second kind $U_{n}$, and the energy eigenvalues $E_{\mu ,\nu }$ (in the $\mu$-th band) are determined by the zeros of these polynomials. New insights on the energy gap and the localization effect induced by phase coherence are shown.; Comment: 10 pages, 5 figures

## Accurate energy spectrum for the quantum Yang-Mills mechanics with nonlinear color oscillations

Pedram, Pouria
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
65.65%
Yang-Mills theory as the foundation for quantum chromodynamics is a non-Abelian gauge theory with self-interactions between vector particles. Here, we study the Yang-Mills Hamiltonian with nonlinear color oscillations in the absence of external sources corresponding to the group $SU(2)$. In the quantum domain, we diagonalize the Hamiltonian using the optimized trigonometric basis expansion method and find accurate energy eigenvalues and eigenfunctions for one and two degrees of freedom. We also compare our results with the semiclassical solutions.; Comment: 12 pages, 2 figures, to appear in International Journal of Theoretical Physics

## The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field

Pedram, Pouria; Nozari, Kourosh; Taheri, S. H.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
65.62%
The existence of a minimum observable length and/or a maximum observable momentum is in agreement with various candidates of quantum gravity such as string theory, loop quantum gravity, doubly special relativity and black hole physics. In this scenario, the Heisenberg uncertainty principle is changed to the so-called Generalized (Gravitational) Uncertainty Principle (GUP) which results in modification of all Hamiltonians in quantum mechanics. In this paper, following a recently proposed GUP which is consistent with quantum gravity theories, we study the quantum mechanical systems in the presence of both a minimum length and a maximum momentum. The generalized Hamiltonian contains two additional terms which are proportional to $\alpha p^3$ and $\alpha^2 p^4$ where $\alpha \sim 1/M_{Pl}c$ is the GUP parameter. For the case of a quantum bouncer, we solve the generalized Schrodinger equation in the momentum space and find the modified energy eigenvalues and eigenfunctions up to the second-order in GUP parameter. The effects of the GUP on the transition rate of ultra cold neutrons in gravitational spectrometers are discussed finally.; Comment: 13 pages, 1 figure, to appear in JHEP

## High-Precision Numerical Determination of Eigenvalues for a Double-Well Potential Related to the Zinn-Justin Conjecture

Alhendi, H. A.; Lashin, E. I.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
65.71%
A numerical method of high precision is used to calculate the energy eigenvalues and eigenfunctions for a symmetric double-well potential. The method is based on enclosing the system within two infinite walls with a large but finite separation and developing a power series solution for the Schr$\ddot{o}$dinger equation. The obtained numerical results are compared with those obtained on the basis of the Zinn-Justin conjecture and found to be in an excellent agreement.; Comment: Substantial changes including the title and the content of the paper 8 pages, 2 figures, 3 tables

## Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions

Berti, Emanuele; Cardoso, Vitor; Casals, Marc
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
75.78%
Spin-weighted spheroidal harmonics are useful in a variety of physical situations, including light scattering, nuclear modeling, signal processing, electromagnetic wave propagation, black hole perturbation theory in four and higher dimensions, quantum field theory in curved space-time and studies of D-branes. We first review analytic and numerical calculations of their eigenvalues and eigenfunctions in four dimensions, filling gaps in the existing literature when necessary. Then we compute the angular dependence of the spin-weighted spheroidal harmonics corresponding to slowly-damped quasinormal mode frequencies of the Kerr black hole, providing numerical tables and approximate formulas for their scalar products. Finally we present an exhaustive analytic and numerical study of scalar spheroidal harmonics in (n+4) dimensions.; Comment: 26 pages, 10 figures. Corrected typos in Eqs. (2.16f) and (2.16g)

## Eigenvalues and Eigenfunctions of Woods Saxon Potential in PT Symmetric Quantum Mechanics

Berkdemir, Ayse; Berkdemir, Cuneyt; Sever, Ramazan
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
65.78%
Using the Nikiforov Uvarov method, we obtained the eigenvalues and eigenfunctions of the Woods Saxon potential with the negative energy levels based on the mathematical approach. According to the PT Symmetric quantum mechanics, we exactly solved the time independent Shcrodinger equation for the same potential. Results are obtained for the s states.; Comment: 12 pages. submitted to Physics Letters A

## One-dimensional hydrogen atom with minimal length uncertainty and maximal momentum

Pedram, Pouria
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
65.64%
We present exact energy eigenvalues and eigenfunctions of the one-dimensional hydrogen atom in the framework of the Generalized (Gravitational) Uncertainty Principle (GUP). This form of GUP is consistent with various theories of quantum gravity such as string theory, loop quantum gravity, black-hole physics, and doubly special relativity and implies a minimal length uncertainty and a maximal momentum. We show that the quantized energy spectrum exactly agrees with the semiclassical results.; Comment: 10 pages, 1 figure

## Cosmic censorship and stationary states of half-spin particles in the field of Reissner-Nordstroem naked singularity

Gorbatenko, M. V.; Neznamov, V. P.; Popov, E. Yu.; Safronov, I. I.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
65.59%
The paper explores quantum mechanics of half-spin particle motion in the field of Reissner-Nordstroem (RN) naked singularity. It is shown that for any quantum mechanical Dirac particle, irrespective of availability and sign of its electrical charge, the RN naked singularity is separated by an infinitely high positive potential barrier. With like charges of a particle and the source of the RN naked singularity, near the origin there exists the second completely impenetrable potential barrier. It has been proved that in the field of the RN naked singularity, bound states of half-spin particles can exist. The conditions for appearance of such states were revealed and computations were performed to find energy eigenvalues and eigenfunctions.; Comment: 20 pages, 3 figures

## Property of Zero-Energy Flows and Creations and Annihilations of Vortices in Quantum Mechanics

Kobayashi, Tsunehiro
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.92%
Time-dependent processes accompanied by vortex creations and annihilations are investigated in terms of the eigenstates in conjugate spaces of Gel'fand triplets in 2-dimensions. Creations and annihilations of vortices are described by the insertions of unstable eigenstates with complex-energy eigenvalues into stable states written by the superposition of eigenstates with zero-energy eigenvalues. Some concrete examples are presented in terms of the eigenfunctions of the 2-dimensional parabolic potential barrier, i.e., $-m \gamma^2 (x^2+y^2)/2$. We show that the processes accompanied by vortex creations and annihilations can be analyzed in terms of the eigenfunctions in the conjugate spaces of Gel'fand triplets. Throughout these examinations we point out three interesting properties of the zero-energy flows. (i) Mechanisms using the zero-energy flows are absolutely economical from the viewpoint of energy consumption. (ii) An enormous amount of informations can be discriminated in terms of the infinite variety of the zero-energy flows. (iii) The zero-energy flow patterns are absolutely stable in any disturbance by inserting arbitrary decaying flows with complex-energy eigenvalues.; Comment: 13 pages and 13 figures

## Accurate calculation of eigenvalues and eigenfunctions. I: Symmetric potentials

Fernandez, Francisco M.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
65.72%
We describe a method for the calculation of accurate energy eigenvalues and expectation values of observables of separable quantum-mechanical models. We discuss the application of the approach to one-dimensional anharmonic oscillators with symmetric potential-energy functions.

## Exact Eigenvalues and Eigenfunctions of the Hulthen Potential in the PT-Symmetry for Any Angular Momentum

Ikhdair, Sameer M.; Sever, Ramazan
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
75.84%
The Schrodinger equation with the PT-symmetric Hulthen potential is solved exactly by taking into account effect of the centrifugal barrier for any l-state. Eigenfunctions are obtained in terms of the Jacobi polynomials. The Nikiforov-Uvarov method is used in the computations. Our numerical results are in good agreement with the ones obtained before. Keywords: Energy Eigenvalues and Eigenfunctions; Hulthen potential; PT-symmetry; Nikiforov-Uvarov Method.; Comment: 24 pages

## Thouless Energy and Correlations of QCD Dirac Eigenvalues

Osborn, J. C.; Verbaarschot, J. J. M.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.81%
Eigenvalues and eigenfunctions of the QCD Dirac operator are studied for gauge field configurations given by a liquid of instantons. We find that for energy differences $\delta E$ below an energy scale $E_c$ the eigenvalue correlations are given by Random Matrix Theories with the chiral symmetries of the QCD partition function. For eigenvalues near zero this energy scale shows a weak volume dependence that is not consistent with $E_c \sim 1/L^2$ which might be expected from the pion Compton wavelength and from the behavior of the Thouless energy in mesoscopic systems. However, the numerical value of $E_c$ for our largest volumes is in rough agreement with estimates from the pion Compton wavelength. A scaling behaviour consistent with $E_c\sim 1/L^2$ is found in the bulk of the spectrum. For $\delta E> E_c$ the number variance shows a linear dependence with a slope which is larger than the nonzero multifractality index of the wave functions. Finally, the average spectral density and the scalar susceptibilities are discussed in the context of quenched chiral perturbation theory. We argue that a nonzero value of the disconnected scalar susceptibility requires a linear dependence of the number variance on $\delta E$.; Comment: 19 pages...

## Coupled diabatic potential energy surfaces for studying the nonadiabatic dynamics at conical intersections in angular resolved photodetachment simulations of OHF- --> OHF+e-

Gómez Carrasco, Susana; Aguado, Alfredo; Paniagua, Miguel; Roncero, Octavio
Fonte: American Institute of Physics Publicador: American Institute of Physics
Tipo: Artículo Formato: 1553773 bytes; application/pdf
ENG
Relevância na Pesquisa
65.75%
16 pages, 14 figures, 1 table.-- PACS nrs.: 82.20.Kh; 82.30.Cf; 33.80.Eh; 82.20.Db; 82.20.Hf.; An energy-based method is proposed for the diabatization of the OH(2Π)+F(2P) --> O(3P)+HF(1Σ+) reaction. It is demonstrated that the diabatic representation obtained is regularized, i.e., the residual derivative couplings do not present singularities at the conical intersections appearing along the reaction path. This method only requires the knowledge of the 1,2 3A'' and 1 3A' eigenvalues and does not require any adjustable parameter. Thus, many convergence problems arising in other derivative-based diabatization methods are avoided, and the description of the configuration space along the reaction path is enormously simplified. Three-dimensional coupled diabatic energy surfaces are obtained by an interpolation procedure using ≈ 4000 accurate ab initio points. The angular resolved photodetachment cross sections are obtained in the diabatic and adiabatic representations using a wave packet method. An excellent agreement is obtained with recent experimental data [D. M. Neumark, Phys. Chem. Chem. Phys. 7, 433 (2005)] for high electron kinetic energies where only the triplet electronic states contribute.; This work has been supported by DGICYT (Ministerio de Educación y Ciencia...