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1
Content available remote

Time Evolution of SU(1,1) Coherent States

100%
Zaleśny J.
Acta Physica Polonica A
|
2000
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vol. 98
|
issue 1-2
11-22
EN
Mathematical aspects of the SU(1,1) group parameter ξ dynamics governed by Hamiltonians exhibiting some special types of time dependence was presented on an elementary level from the point of view of the Möbius transformation of complex plane. The trajectories of ξ in continuous and mappings in discrete dynamics are considered. Some simple examples were examined. Analytical considerations and numerical results were given.
2
Content available remote

Nonclassical Properties of Para-Bose Superposition States

100%
Yu Y., Wang D.
Acta Physica Polonica A
|
2009
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vol. 115
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issue 3
613-616
EN
We investigate the nonclassical properties of para-Bose superposition states which involve the vacuum and one- or two-photon state of paraboson. It is found that these para-Bose superposition states exhibit stronger squeezing and antibunching. The amplitude-squared squeezing for these states is also examined.
3
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Exact Solution of Klein-Gordon with the Pöschl-Teller Double-Ring-Shaped Coulomb Potential

80%
Hassanabadi H., Ikot A., Zarrinkamar S.
Acta Physica Polonica A
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2014
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vol. 126
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issue 3
647-652
EN
Analytical solution of the Klein-Gordon equation under the equal scalar and vector Pöschl-Teller double-ring-shaped Coulomb potentials is obtained. We have used the Nikiforov-Uvarov method in our calculations. The radial wave function in terms of the Laguerre polynomials is presented and the angular wave functions are expressed in terms of the Jacobi polynomials. We have also considered some special cases of the Pöschl-Teller double-ring-shaped Coulomb potential and represented the energy eigenvalues and the corresponding wave functions.
4
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Spectroscopic Studies on Distorted Structure Nanomolecules by Using Lie Algebraic Model

80%
Rao Karumuri S., Girija Sravani K., Vijayshekar J., Reddy L.
Acta Physica Polonica A
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2012
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vol. 122
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issue 1
49-52
EN
We have applied Lie algebraic model to distorted structure molecules to determine the vibrational spectra of different stretching and bending vibrational modes. The the Lie algebraic model of the Hamiltonian expression is H = E_0 + ∑_{i = 1}^{n} A_{i} C_{i} + ∑_{i < j}^{n} A_{ij} C_{ij} + ∑_{i < j}^{n} λ_{ij} M_{ij}}. By using the Lie algebraic method, the stretching vibrational energies of fullerene (C_{80}) are calculated in the one-dimensional [U(2)] framework. Using the model Hamiltonian so constructed, we have calculated the local mode vibrational energy levels of the fullerene (C_{80}) accurately.
5
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A Survey on the Classical Limit of Quantum Dynamical Entropies

80%
Cappellini V.
Acta Physica Polonica A
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2007
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vol. 112
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issue 4
589-605
EN
We analyze the behavior of quantum dynamical entropies production from sequences of quantum approximants approaching their (chaotic) classical limit. The model of the quantized hyperbolic automorphisms of the 2-torus is examined in detail and a semi-classical analysis is performed on it using coherent states, fulfilling an appropriate dynamical localization property. Correspondence between quantum dynamical entropies and the Kolmogorov-Sinai invariant is found only over timescales that are logarithmic in the quantization parameter.
6
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Vibrational Spectroscopy of H_2O by Lie Algebraic Methods

80%
Karumuri S., Srinivas G., Sunil Babu K., Sundara Siva Kumar V., Hanumaiah A.
|
EN
An algebraic model of coupled anharmonic oscillators is introduced, capable of describing the stretching vibrations of medium-size molecules. This model is applied to the calculation of O-H vibrational modes of water molecules. In this paper, we have reported the stretching and bending vibrational energy levels of water molecule using the algebraic and density functional theory method. The results obtained by theoretical models show good agreement with the experimental values.
7
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Complete Analytical Solutions of the Mie-Type Potentials in N-Dimensions

80%
Agboola D.
Acta Physica Polonica A
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2011
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vol. 120
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issue 3
371-377
EN
The exact solutions of the N-dimensional Schrödinger equation with the Mie-type potentials are obtained. The energy levels are worked out and the corresponding wave functions are obtained in terms of the Laguerre polynomial. Some energy levels of some diatomic molecules are given using the modified Kratzer-type potential. The expectation values 〈r^{-1}〉 and 〈r^{-2}〉 and the virial theorem are also obtained in N-dimensions using the Hellmann-Feynman theorem. The ladder operators are also constructed for the Mie-type potentials in N-dimensions and the matrix elements of some operators r and r·d/dr are analytically obtained from the ladder operators. The general results reduce to the 3-dimensional case when N = 3.
8
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A Study of Vibrational Spectra of Fullerene C_{70} and~C_{80}: An Algebraic Approach

80%
Sen R., Kalyan A., Subhra Paul R., Sarkar N., Bhattacharjee R.
Acta Physica Polonica A
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2011
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vol. 120
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issue 3
407-411
EN
Using the Lie algebraic method, the stretching vibrational energies of fullerenes C_{70} and C_{80} are calculated in the one-dimensional U(2) framework. By constructing the model Hamiltonian with the help of Casimir and Majorana invariant operators in this frame work, we calculated the local mode vibrational energy levels of the fullerenes C_{70} and C_{80}.
9
Content available remote

Double Reflection of Electron Spin in Semiconductors

80%
Dargys A.
Acta Physica Polonica A
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2011
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vol. 119
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issue 2
161-163
EN
Reflection of spin-polarized electron from a potential barrier in bulk semiconductor in the presence of spin-orbit interaction is considered. The spin-orbit interaction brings about double electron reflection at oblique incidence of electronic beam onto the barrier. The competition between the Rashba and Dresselhaus spin-orbit mechanisms during double reflection is discussed. The problem was solved within the Clifford algebra framework, which allows one to describe the spin in a real Euclidean ℰ_3 space rather than in an abstract Hilbert space.
10
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Some Exact Results in the One-Dimensional Attractive Hubbard Model

80%
Jakubczyk D.
Acta Physica Polonica A
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2015
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vol. 128
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issue 2
170-172
EN
The one-dimensional attractive Hubbard model (Ułl 0) is discussed for the chains of N nodes and the same number of electrons, where N-1 of them have the same spin projection, assuming periodic boundary conditions and the half-filling case. Based on the analysis of the eigenvalue problem we provided the general analytical expression for the eigenvalues, for any number N. This formula implies the existence of two elementary particles with mutually dependent momenta on the ring with N sites the same number of electrons including N-1 of the same spin projection.
11
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Content available

Application of Contractor Renormalization Group to the Heisenberg Zig-Zag and the Hubbard Chain

80%
Cichy K., Tomczak P.
Acta Physica Polonica A
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2007
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vol. 111
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issue 5
773-780
EN
The contractor renormalization group method was devised in 1994 by Morningstar and Weinstein. It was primarily aimed at extracting the physics of lattice quantum field theories (like lattice quantum chromodynamics). However, it is a general method of analyzing Hamiltonian lattice systems, e.g. Ising, Heisenberg or Hubbard models. The aim of this work is to show the application of contractor renormalization group method to one-dimensional quantum systems - the Heisenberg zig-zag model and the Hubbard chain. As a test of the method, the ground state energy of these systems will be calculated.
12
Content available remote

Solutions of One-Dimensional Effective Mass Schrödinger Equation for PT-Symmetric Scarf Potential

80%
Zhang A., Shi P., Ling Y., Hua Z.
Acta Physica Polonica A
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2011
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vol. 120
|
issue 6
987-991
EN
The one-dimensional effective mass Schrödinger equation for PT-symmetric Scarf potential is investigated. The analytical expressions of energy eigenvalue and corresponding wave function are presented. They are accomplished by using an appropriate coordinate transformation to map the transformed exactly solvable one-dimensional Schrödinger equation with constant mass into the position-dependent mass equation. In the computation, three different forms of mass distributions are considered.
13
Content available remote

Product of Projective Representations in Description of Multi-Electron States in An External Magnetic Field

80%
Florek W.
Acta Physica Polonica A
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1999
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vol. 95
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issue 6
871-880
EN
In this paper all inequivalent irreducible projective representations of the two-dimensional translation group for a given factor system are determined. A normalized, i.e. corresponding to the Landau gauge, factor system is considered. Obtained representations directly lead to concept of magnetic cells and to periodicity with respect to the charge of a moving particle. It is also shown that the quantization condition is imposed on the product qH of the charge q and the magnitude of magnetic field H. The Kronecker product of such representations is considered and it is proven that the multiplication of representations corresponds to the addition of charges of particles moving in a given external magnetic field. In general, coupling of d representations corresponds to d-particle states. Presented results can be applied in any problem related to two-dimensional electron gas in a magnetic field, for example in the fractional quantum Hall effect or high temperature superconductivity.
14
Content available remote

Paths vs. Winding Numbers for the Two-Magnon Sector of the XXX Heisenberg Magnet

80%
Labuz M.
Acta Physica Polonica A
|
2015
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vol. 128
|
issue 2
190-192
EN
Bethe Ansatz is the famous method of determination of eigenstates and eigenenergies for a wide range of quantum problems, e.g. for the Heisenberg XXX s=1/2 model. The Bethe equations applied to solve the problem of N nodes and r overturned spins on a magnetic chain are labeled by sets of winding numbers {n_i}, however the condition for admissible sets give an overcomplete number of results. On the other hand, combinatorial objects, so called "paths", give the exact number of eigenvectors for the problem described by (N,r) values. The paper presents the method of determining the set of winding numbers from the appropriate path for the sector of r=2 spin deviations.
15
Content available remote

On the q-Analogue of a Black Body Radiation

80%
Babinec P.
Acta Physica Polonica A
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1992
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vol. 82
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issue 6
957-960
EN
A statistical distribution function and spectral energy density are derived for the q-analogue of a black body radiation. These functions are different from the usual ones for q ≠ 1 and they have singularities. The reason for these singularities is also discussed.
16
Content available remote

Magnetic Pentagonal Ring - Galois Extensions and Crystallography

70%
Labuz M., Lulek T.
Acta Physica Polonica A
|
2017
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vol. 132
|
issue 1
97-99
EN
The Galois symmetry of exact Bethe Ansatz eigenstates for magnetic pentagonal ring is shown to bear a close analogy to some crystallographic constructions. Automorphisms of number field extensions associated with these eigenstates prove to be related to choices of the Bravais cells in the finite crystal lattice ℤ₂×ℤ₂, responsible for extension of the cyclotomic field by the Bethe parameters.
17
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Some New Approaches of the XXX Heisenberg Model of the Two-Magnon Sector

70%
Łabuz M., Milewski J., Lulek T.
Acta Physica Polonica A
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2018
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vol. 133
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issue 3
444-446
EN
XXX Heisenberg s-1/2 model has been examined in detail during last decades, however, recently one may find some new insights into that issue. Among several approaches describing the eigenproblem for the finite case, a close look into the structure of Bethe equations (BE) for the two-magnon sector case seems to be particularly interesting. BE enable us to evaluate parameters labeling eigenstates of a magnet, however to find appropriate sets of winding numbers, which parametrize BE, one has to apply the Inverse Bethe Ansatz method. On the other hand, one may choose a different - combinatoric approach - which also parametrizes Bethe eigenstates, with the use of rigging numbers describing string configurations. We present an idea of comparison of the concepts mentioned above for the particular case of two-spin deviations sector.
18
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Point Group Interpretation of Galois Symmetry of Bethe Ansatz Solutions of Magnetic Pentagonal Ring

70%
Lulek B., Lulek T., Łabuz M., Milewski J.
Acta Physica Polonica A
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2015
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vol. 127
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issue 2
336-338
EN
Exact solutions of the eigenproblem of the magnetic pentagonal ring exhibit the arithmetic symmetry expressed in terms of a Galois group of a finite extension of the prime field Q of rationals. We propose here a geometric interpretation of this symmetry in the interior of the Brillouin zone, in terms of point groups. Explicitly, it is a subgroup of the direct product C₄ × D₄. We present also the appropriate irreducible representations of the group.
19
Content available remote

Homotopy of the classical configuration space for the two-magnon sector of a magnetic Heisenberg ring

51%
Lulek B., Jakubczyk D.
Open Physics
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2003
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vol. 1
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issue 1
132-144
EN
A finite Heisenberg magnetic ring with an arbitrary single-node spin and two spin deviations from the ferromagnetic saturation is considered as the system of two Bethe pseudoparticles. The set of all relevant magnetic configurations spans a surface which can be recognised as a Mőbius strip. The dynamics of the system imposes the double twist of all regular orbits of the translation symmetry group.
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