scholarly journals q-SYMMETRIES IN DNLS-AL CHAINS AND EXACT SOLUTIONS OF QUANTUM DIMERS

1999 ◽  
Vol 13 (26) ◽  
pp. 3087-3106
Author(s):  
DEMOSTHENES ELLINAS ◽  
PANAGIOTIS MANIADIS
Keyword(s):  
Recurrence Relations ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Spin Model ◽  
Rate Of Change ◽  
Nonlinearity Parameter ◽  
Hamilton Operator ◽  
Central Elements ◽  
Lowering Operators ◽  
Dynamical Algebra

Dynamical symmetries of Hamiltonians quantized models of discrete nonlinear Schrödinger chain (DNLS) and of Ablowitz–Ladik chain (AL) are studied. It is shown that for n-sites the dynamical algebra of DNLS Hamilton operator is given by the su(n) algebra, while the respective symmetry for the AL case is the quantum algebra suq(n). The q-deformation of the dynamical symmetry in the AL model is due to the non-canonical oscillator-like structure of the raising and lowering operators at each site. Invariants of motions are found in terms of Casimir central elements of su(n) and suq(n) algebra generators, for the DNLS and QAL cases respectively. Utilizing the representation theory of the symmetry algebras we specialize to the n=2 quantum dimer case and formulate the eigenvalue problem of each dimer as a nonlinear (q)-spin model. Analytic investigations of the ensuing three-term nonlinear recurrence relations are carried out and the respective orthonormal and complete eigenvector bases are determined. The quantum manifestation of the classical self-trapping in the QDNLS-dimer and its absence in the QAL-dimer, is analysed by studying the asymptotic attraction and repulsion respectively, of the energy levels versus the strength of nonlinearity. Our treatment predicts for the QDNLS-dimer, a phase-transition like behaviour in the rate of change of the logarithm of eigenenergy differences, for values of the nonlinearity parameter near the classical bifurcation point.

Energy Levels and Electromagnetic Transition of 90-94mo Nuclei Using Ibm-1

2020 ◽  
pp. 149-152
Keyword(s):  
Experimental Data ◽  
Transition Probability ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Interacting Boson Model ◽  
Excitation Energies ◽  
Electromagnetic Transition ◽  
Boson Model ◽  
Energy States ◽  
Good Agreement

The energy states for the J , b , ɤ bands and electromagnetic transitions B (E2) values for even – even molybdenum 90 – 94 Mo nuclei are calculated in the present work of "the interacting boson model (IBM-1)" . The parameters of the equation of IBM-1 Hamiltonian are determined which yield the best excellent suit the experimental energy states . The positive parity of energy states are obtained by using IBS1. for program for even 90 – 94 Mo isotopes with bosons number 5 , 4 and 5 respectively. The" reduced transition probability B(E2)" of these neuclei are calculated and compared with the experimental data . The ratio of the excitation energies of the 41+ to 21+ states ( R4/2) are also calculated . The calculated and experimental (R4/2) values showed that the 90 – 94 Mo nuclei have the vibrational dynamical symmetry U(5). Good agreement was found from comparison between the calculated energy states and electric quadruple probabilities B(E2) transition of the 90–94Mo isotopes with the experimental data .

Factorization method for exact solution of the non-central modified Killingbeck potential plus a ring-shaped-like potential

2019 ◽  
Vol 34 (10) ◽  
pp. 1950072 ◽  
Author(s):  
B. Tchana Mbadjoun ◽  
J. M. Ema’a Ema’a ◽  
Jean Yomi ◽  
P. Ele Abiama ◽  
G. H. Ben-Bolie ◽  
...  
Keyword(s):  
Exact Solution ◽  
Potential Problem ◽  
Energy Levels ◽  
Factorization Method ◽  
Spherically Symmetric ◽  
Laguerre Function ◽  
Radial Part ◽  
Raising And Lowering Operators ◽  
Structure Of Molecules ◽  
Lowering Operators

In this paper, we study the Schrödinger equation with non-central modified Killingbeck potential plus a ring-shaped-like potential problem, which is not spherically symmetric. The factorization method is used to solve the hypergeometric equation types which lead to solutions with the associate Laguerre function for the radial part and Jacobi polynomial for the polar part. We introduce the raising and lowering operators to calculate the energies eigenvalues, which show that the lack of spherical symmetry removes the degeneracy of second quantum number m which is completely expected. These obtained energies are better to explain the superposition of the energy levels of the atoms in the crystalline structure of molecules.

scholarly journals Calculation of One-Electron Wave Functions and Energy Levels of N-Butane Molecule on the Basis of Slater Atomic Orbitals

2021 ◽  
Vol 75 (3) ◽  
pp. 229-233
Author(s):  
Faig Pashaev ◽  
Arzuman Gasanov ◽  
Musaver Musaev ◽  
Ibrahim Abbasov
Keyword(s):  
Group Theory ◽  
Energy Levels ◽  
Wave Functions ◽  
Electron Wave ◽  
Hamilton Operator ◽  
Atomic Orbitals ◽  
Symmetry Properties ◽  
Symmetry Transformations ◽  
Space Symmetry ◽  
Polyatomic Systems

Abstract It is known that the application of the group theory greatly simplifies the problems of polyatomic systems possessing to any space symmetry. The symmetry properties of such systems are their most important characteristics. In such systems, the Hamilton operator is invariant under unitary symmetry transformations and rearrangements of identical particles in the coordinate system. This allows to obtain information about the character of one-electron wave functions — molecular orbitals — the considered system, i.e. to symmetrise the original wave functions without solving the Schrödinger equation.

ROTATIONAL WINGS OF RAMAN BANDS AND FREE ROTATION IN LIQUID OXYGEN, NITROGEN, AND METHANE

1952 ◽  
Vol 30 (2) ◽  
pp. 81-98 ◽  
Author(s):  
M. F. Crawford ◽  
H. L. Welsh ◽  
J. H. Harrold
Keyword(s):  
Raman Spectrum ◽  
Transition Probability ◽  
Energy Levels ◽  
Anisotropic Scattering ◽  
Rotational Energy ◽  
Rate Of Change ◽  
Liquid Oxygen ◽  
Discrete Structure ◽  
Anisotropic Part ◽  
Liquid Methane

Rotation-vibrational Raman bands have been observed in liquid oxygen, nitrogen, and methane, and in solid methane. In every case the Q branches associated with isotropic Raman scattering are sharp lines; but the Q branches and rotational wings associated with anisotropic scattering form broad continuous bands, with extent and intensity distribution consistent with free molecular rotation. The lack of discrete structure in the broad bands is attributed to a removal of the m degeneracy of the rotational energy levels in the intermolecular force fields. Removal of the m degeneracy broadens those transitions for which the transition probability depends on the anisotropic part of the rate of change of the polarizability, but not those for which J and m are unchanged and for which the transition probability depends only on the isotropic part. The Raman spectrum of liquid oxygen yields no evidence for O4 aggregates. The Raman spectrum of liquid methane displays all fundamental vibrations of the molecule and two overtones, with Raman shifts (in cm.−1): 1300, band (ν4); 1535, band (ν2); 2570, line, and 2600, band (2ν4); 2906, line (ν1); 3020, band (ν3); 3053, line (2ν2).

Der effektive Spin als Modell zur Beschreibung von ESR- Hyperfeinspektren polykristalliner Systeme / The Effective Spin as a Model to describe ESR-Hyperfine Spectra of poly cry stalline Samples

1976 ◽  
Vol 31 (2) ◽  
pp. 123-127
Author(s):  
K. Dräger
Keyword(s):  
Quantum Number ◽  
Transition Probabilities ◽  
Energy Levels ◽  
Theoretical Spectrum ◽  
Hamilton Operator ◽  
Effective Spin ◽  
Cubic Symmetry ◽  
Esr Spectrum ◽  
Spin Quantum ◽  
Spin Quantum Number

Abstract Paramagnetic ions with hyperfine interaction generally have an involved ESR-spectrum. For host lattices of cubic symmetry it will be shown that while going from single crystals to powdered systems the true spin quantum number S can be substituted by an effective spin quantum number S' = ½. Using an isotropic spin Hamilton operator the energy-levels and their eigenfunctions as well as the transition probabilities are calculated explitely.The model is then applied to the ESR-spectrum of manganese-doped polycrystalline CaO. The theoretical spectrum fits the experimental up to 2·10-5 and is in every respect comparable to results of the 3rd order perturbation theory. Above all the model reproduces the true values for the g-factor and the hyperfine coupling constant A as known from single crystal investigations. This is also verified for Mn2+ -ions on cubic sites of MgO and BaO.

scholarly journals Overview of High Energy String Scattering Amplitudes and Symmetries of String Theory

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 1045 ◽  
Author(s):  
Jen-Chi Lee ◽  
Yi Yang
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Recurrence Relations ◽  
Dynamical Symmetry ◽  
High Energy ◽  
Closed String ◽  
Fixed Angle ◽  
Linear Relations ◽  
Arbitrary Mass ◽  
String Amplitudes

In this paper, we studied symmetries of string scattering amplitudes in the high energy limits of both the fixed angle or Gross regime (GR) and the fixed momentum transfer or Regge regime (RR). We calculated high energy string scattering amplitudes (SSA) at arbitrary mass levels for both regimes. We discovered the infinite linear relations among fixed angle string amplitudes and the ifinite recurrence relations among Regge string amplitudes. The linear relations we obtained in the GR corrected the saddle point calculations by Gross, Gross and Mende. In addition, for the high energy closed string scatterings, our results differ from theirs by an oscillating prefactor which was crucial to recover the KLT relation valid for all energies. We showed that all the high energy string amplitudes can be solved using the linear or recurrence relations, so that all the string amplitudes can be expressed in terms of a single string amplitude. We further found that, at each mass level, the ratios among the fixed angle amplitudes can be extracted from the Regge string scattering amplitudes. Finally, we reviewed the recent developments on the discovery of infinite number of recurrence relations valid for all energies among Lauricella SSA. The symmetries or relations among SSA at various limits obtained previously can be exactly reproduced. It leads us to argue that the known S L ( K + 3 , C ) dynamical symmetry of the Lauricella function may be crucial to probe spacetime symmetry of string theory.

Investigation of isospin excited and mixed-symmetry states in even–even N = Z nuclei

2018 ◽  
Vol 27 (08) ◽  
pp. 1850065 ◽  
Author(s):  
Falih H. Al-Khudair
Keyword(s):  
Excited States ◽  
Degrees Of Freedom ◽  
Transition Probabilities ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Systematic Investigation ◽  
Wave Functions ◽  
Mixed Symmetry ◽  
Mixed Symmetry States ◽  
Boson Model

Mixed-symmetry and isospin excited states are typical of the interacting boson model with isospin (IBM-3). With a view to look for such states, levels scheme of the IBM-3 dynamical symmetry is discussed. A systematic investigation in the proton and neutron degrees of freedom of the energy levels has been carried out. A sequence of isospin excitation bands has been identified. We have analyzed the wave functions and given the symmetrical labeling of the states. The transition probabilities between the isospin excitation states of model limits are analyzed in terms of isoscalar and isovector decompositions. The present calculations suggest that a combination of isospin excitation and mixed-symmetry states can provide substantial information on the structure of nuclear states. Calculations for [Formula: see text] and [Formula: see text] nuclei are presented and compared with the results of the shell model and available experimental data.

A COMMENT ON THE "PEIERLS SUBSTITUTION"

2000 ◽  
Vol 14 (05) ◽  
pp. 187-194
Author(s):  
M. K. FUNG ◽  
Y. F. WANG
Keyword(s):  
Perturbation Theory ◽  
Energy Levels ◽  
The Other ◽  
Raising And Lowering Operators ◽  
Lowering Operators

We present a new way of doing perturbation theory of the Landau problem. We introduce two sets of raising and lowering operators. One set is for shifting the coordinates of the center of the cyclotron orbit. The other set is for shifting the energy levels. This method is compared to that of the Peierls substitution.

scholarly journals U(6) dynamical and quasi-dynamical symmetry in strongly deformed heavy nuclei

2018 ◽  
Vol 194 ◽  
pp. 05002 ◽  
Author(s):  
H.G. Ganev
Keyword(s):  
State Space ◽  
Effective Charge ◽  
Good Description ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Microscopic Structure ◽  
Heavy Nuclei ◽  
Ground Band ◽  
Model Hamiltonian ◽  
Collective States

The low-lying collective states of the ground, β and γ bands in154Sm and238U are investigated within the framework of the microscopic proton-neutron symplectic model (PNSM). For this purpose, the model Hamiltonian is diagonalized in a U(6)-coupled basis, restricted to the symplectic state space spanned by the fully symmetric U(6) vectors. A good description of the energy levels of the three bands under consideration, as well as the intraband B(E2) transition strengths between the states of the ground band is obtained for the two nuclei without the use of an effective charge. The calculations show that when the collective quadrupole dynamics is covered already by the symplectic bandhead structure, as in the case of154Sm, the results show the presence of a very good U(6) dynamical symmetry. In the case of238U, when we have an observed enhancement of the intraband B(E2) transition strengths, then the results show small admixtures from the higher major shells and a highly coherent mixing of different irreps which is manifested by the presence of a good U(6) quasi-dynamical symmetry in the microscopic structure of the collective states under consideration.

scholarly journals Partial dynamical symmetry versus quasi dynamical symmetry examination within a quantum chaos analyses of spectral data for even–even nuclei

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
H. Sabri ◽  
S. K. Mousavi Mobarakeh ◽  
A. J. Majarshin ◽  
Yan-An Luo ◽  
Feng Pan
Keyword(s):  
Quantum Chaos ◽  
Nearest Neighbor ◽  
Matrix Theory ◽  
Chaotic Behavior ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Mass Region ◽  
Band Head ◽  
Symmetry Limit ◽  
Rotational Bands

AbstractStatistical analyses of the spectral distributions of rotational bands in 51 deformed prolate even–even nuclei in the 152 ≤ A ≤ 250 mass region $$R_{{4_{1}^{ + } /2_{1}^{ + } }} \ge 3.00$$ R 4 1 + / 2 1 + ≥ 3.00 are examined in terms of nearest neighbor spacing distributions. Specifically, the focus is on data for 0+, 2+, and 4+ energy levels of the ground, gamma, and beta bands. The chaotic behavior of the gamma band, especially the position of the $$2_{\gamma }^{ + }$$ 2 γ + band-head compared to other levels and bands, is clear. The levels are analyzed within the framework of two models, namely, a SU(3)-partial dynamical symmetry Hamiltonian and a SU(3) two-coupled quasi-dynamical symmetry Hamiltonian, with results that are further analyzed using random matrix theory. The partial and quasi dynamics both yield outcomes that are in reasonable agreement with the known experimental results. However, due to the degeneracy of the beta and gamma bands within the simplest SU(3) picture, the theory cannot be used to describe the fluctuation properties of excited bands. By changing relative weights of the different terms in the partial and quasi dynamical Hamiltonians, results are obtained that show more GOE-like statistics in the partial dynamical formalism as the strength of the pairing term is increased. Also, in the quasi-dynamical symmetry limit, more correlations are found because of the stronger couplings.

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