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1
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Simple Band Model of Doped Fullerene Crystal

100%
Koper A., Mucha M.
Acta Physica Polonica A
|
2000
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vol. 97
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issue 1
233-236
EN
We use quantum billiard with many scattering centers to describe conducting electrons properties in A_{n}C_{60} crystals, where A denotes alkali metal. We focus our attention on the A_{3}C_{60} crystal, for which we calculate the band structure, density of states, and conductivity for normal electrons. Conductivity shows linear dependence on temperature in this model, which agrees well with experimental data. We also discuss consequences of our results for superconductivity mechanism in A_{3}C_{60} and possibilities of analogous approach to describe electron properties in fused fullerenes and multiply connected carbon clusters.
2
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On Electrons in Quantum Chaos State in Doped Fullerene Crystal

100%
Koper A., Mucha M.
Acta Physica Polonica A
|
2000
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vol. 97
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issue 1
229-232
EN
We show that band electrons in A_{n}C_{60} crystal (C_{60} fullerene doped with alkali ions A) are in highly chaotic quantum state. We describe intensity of the chaos by means of the Shannon information entropy, which we calculate using single particle Bloch functions. The entropy provides a quantitative measure of scars as well as degree of electrons delocalization in gaps between C_{60} molecules. Implications of our results for conductivity in A_{3}C_{60} are discussed.
3
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On Stability of Frustrated Quantum Magnetic States in Fullerenes

100%
Koper A., Mucha M.
Acta Physica Polonica A
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1997
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vol. 92
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issue 2
395-398
EN
Gutzwiller variational ground states |Φ^{G}⟩ of π electrons, described by single-band half-filling Hubbard model, were determined for the molecules C_{60} and C_{70} and their energies and magnetic properties investigated. To construct these states two types of trial functions were used: generalized spin-density wave |Φ_{SD}⟩ and tight-binding wave |Φ_{ΤΒ}⟩. Our results evidently show that the Gutzwiller state |Φ^{G}_{TΒ}⟩ determined by means of function |Φ_{ΤΒ}⟩ has lower energy than the other investigated variational states |Φ^{G}_{SD}⟩. Mean values of the operators in the Gutzwiller states were calculated using Monte Carlo method.
4
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Relation of Gutzwiller Variational State with Matrix Model

100%
Koper A., Mucha M.
Acta Physica Polonica A
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1997
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vol. 91
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issue 2
391-394
EN
It is shown that mean values of electron operators in variational Gutzwiller state are equal to mean values of corresponding classical quantities calculated by means of a hermitian matrix model. In cases with small number of electrons in the system this property enables exact calculation of the mean values. In case of large number of electrons a simple and effective Monte Carlo method is formulated (within matrix model).
5
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Diblock Copolymer Melt in Spherical Unit Cells of Higher Dimensionalities

81%
Banaszak M., Koper A., Knychała P., Lewandowski K.
Acta Physica Polonica A
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2012
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vol. 121
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issue 3
703-710
EN
Using self-consistent field theory in spherical unit cells of various dimensionality, D = 1, 2, 3, and 4, we calculate phase diagram of a diblock, A-b-B, copolymer melt in 4-dimensional space, d = 4. The phase diagram is parameterized by the chain composition, f, and incompatibility between A and B, quantified by the product χ N. We predict 4 stable nanophases: layers, cylinders, 3D spherical cells, and 4D spherical cells. We also calculate order-disorder and order-order transition lines. In the strong segregation limit, that is for large χ N, the order-order transition compositions are determined by the strong segregation theory in its simplest form, for D = 1, 2, 3, and 4.
6
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Singularities of Bethe Ansatz via Robinson Numbers

81%
Koper A., Krasoń P., Milewski J.
Acta Physica Polonica A
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2018
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vol. 133
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issue 3
438-440
EN
In this work we suggest a rigorous mathematical approach for explanation of singular solutions of Bethe Ansatz by means of Robinson complex hypernumbers. There are several approaches towards these singular solutions eg. formal infinitesimals or germs of meromorphic functions. Our aim is to make them precise using non-standard analysis and show that they are essentially equivalent.
7
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Magnetic Ground State of Fullerenes

81%
Koper A., Stankowski J., Thomas M.
Acta Physica Polonica A
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1994
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vol. 85
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issue 2
351-355
EN
The classical limit of the effective antiferromagnetic Heisenberg Hamiltonian has been investigated on the series of free clusters (molecules) of C_{N} (N = 32, 44, 50, 58, 60,, 70 and 84). The valley structures of the frustrated ground states were determined. Moreover, the probability distributions of the spin correlation functions were calculated.
8
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Analysis of Magnetic Ground State in Thulium Iron Garnets

81%
Koper A., Lehmann-Szweykowska A., Wigen P. E., Bornfreund R. E.
Acta Physica Polonica A
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1997
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vol. 92
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issue 2
391-394
EN
Magnetic phase diagrams of thulium iron garnets at Τ = 0 K are obtained by means of the so-called Monte Carlo relaxation method. The diagrams are given in terms of the respective strength of the superexchange couplings. There are five different phases and one spin-flop line on the diagram obtained. Two of these phases are of a semi-spin glass type.
9
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Properties of the Semi Spin Glass Ground State of Garnets

81%
Koper A., Lehmann-Szweykowska A., Thomas M., Wojciechowski R.
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EN
A strong magnetic ordering response to valence-uncompensated doping observed experimentally in yttrium iron garnet, indicates the importance of a thorough analysis of the problem. Within the framework of the classical two-sublattice Heisenberg model the position on the ground state phase diagram, corresponding to the experimentally found values of the superexchange parameters of yttrium iron garnet, turns out to lie close to the semi spin glass region. Thus, in this paper, the magnetic structure factor, the spectrum of magnetic excitations, the density of states and a magnetic contribution to the specific heat, are calculated and discussed.
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