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1
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A New Look on the Skin Depth of the Normal Skin Effect in a Metal Submitted to a Frequency-Dependent Electromagnetic Field

100%
Olszewski S.
Acta Physica Polonica A
|
2013
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vol. 123
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issue 4
750-751
EN
The theory of the skin depth in metals is re-examined by revision of the conductivity expression entering the Maxwell equations leading to the normal skin effect. In fact this conductivity formula should be improved by considering its special behaviour at low temperatures in case of the presence of the magnetic field. For very pure specimens and very low temperatures the correction of the conductivity tensor leads to the skin depth approximately proportional to the square root of the amplitude strength of the magnetic field.
2
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Thomas-Reiche-Kuhn Sum Rule for Electron Transitions in Solids

100%
Olszewski S.
Acta Physica Polonica A
|
1998
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vol. 94
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issue 1
49-70
EN
A well-known sum rule obtained for electron transitions between the atomic states by Thomas, Reiche and Kuhn (TRK) is examined for the case of transitions between delocalized electron states in cubic lattices. A characteristic point of the original TRK sum rule for the atomic states was its lack of dependence on the initial state of transitions. This situation holds also for the free-electron states in a metal but is changed in the case of electrons influenced by the presence of the field of the crystal core. Corrections to the original TRK result can be represented as a function of the quantum parameter labelling the initial electron state. Other moments of the spectral distribution function than those leading to the TRK sum rule have been calculated. A comparison of the relations found between different spectral moments for solids with similar relations obtained by Traini for the spectral moments of the atomic states has been done.
3
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Simple Method for Calculating the Weak-Field Electron Diamagnetism in Cubic Lattices

100%
Olszewski S.
Acta Physica Polonica A
|
2002
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vol. 101
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issue 2
249-265
EN
The idea of electron wave packets moving along closed anisotropic Fermi surfaces placed in a constant magnetic field has been applied to the calculation of the orbital magnetic moment of an individual free electron and tightly-bound s-electron in a crystal lattice. In each case the magnetic moment is obtained as a derivative of the electron energy done with respect to the strength of the magnetic field. In the next step, calculations have been extended to electron ensembles. For a free-electron ensemble a thorough calculation of the weak-field magnetic moment gives a result similar to that obtained by a well-known method developed by Landau. On the other hand, calculations done for the s-band of the tightly-bound electrons of metallic iron give an absolute value of the magnetic moment much smaller than in the free-electron case. Simultaneously, the sign of the moment is changed indicating a lowering of the iron band electron energy with magnetization.
4
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Quantum Invariants Descending from the Joule-Lenz Law for the Dissipated Energy Applied in Calculating the Rate of Electron Transitions

100%
Olszewski S.
|
EN
The Joule-Lenz law for a classical expense of energy is transformed into a formula representing a quantum-mechanical invariant composed of the interval of energy connected with an electron transition and the corresponding interval of transition time between two quantum levels. Time and energy enter the invariant formula on an equal footing, moreover the time intervals converge with the time periods characteristic for the examined quantum systems. These properties imply to consider the time intervals as quanta of time having character similar to that possessed by the energy. Another result of the transformation of the Joule-Lenz law is the time rate of energy of the quantum transitions. This rate is calculated on a fully non-probabilistic way. When examined for the hydrogen atomic spectrum taken as an example, the obtained quantum rate is by many orders larger than a classical transition rate.
5
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Longitudinal Magnetoresistance of Metals Calculated οn the Basis of a Single-Band Electron Theory

100%
Olszewski S.
|
EN
The longitudinal magnetoresistance of metals at different temperatures and strengths of the external magnetic field is examined with the aid of a simple single-band theory. The calculated data are compared with the experimental ones. The theoretical ratio between the longitudinal and transversal magnetoresistance approaches unity, whereas the observed ratio is rather below that value. For some metals (Al,Pt) the theoretical results are within the range of the measured data for the transversal and longitudinal resistance, or remain close to the limits of this empirical interval. In average, a relatively good agreement between experiment and theory is obtained for Al, Pt, Cu, Ag and In metals.
6
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Cyclotron Frequencies and Quanta of the Landau Levels in Semiconductors Having Ellipsoidal Fermi Surfaces Studied in Dependence on Direction of the Magnetic Field

63%
Olszewski S., Roliński T.
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vol. 126
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issue 6
1304-1311
EN
A method of calculating the Landau levels in crystals having the ellipsoidal Fermi surfaces has been presented with an accent put on the directional dependence of the energy quanta defined by the levels. Physically the problem concerns mainly semiconductors examined in a nearly-free electron approximation. In this case the shape of the Fermi surface is defined by three different effective masses entering the electron Hamiltonian. Beyond of the masses the method, which can be applied for an arbitrary direction of the magnetic field, does contain no empirical parameters in its framework.
7
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The Hofstadter Diagram Analyzed in Terms of the Band Structure Parameters for a Planar Metal

63%
Roliński T., Olszewski S.
Acta Physica Polonica A
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2006
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vol. 109
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issue 6
753-759
EN
It is demonstrated that a wing of the Hofstadter diagram calculated for the tightly-bound s-electrons in the simple cubic lattice can be reproduced by the dispersion figure of the wave-vector square considered for the electron states of the same lattice, on the condition that the states having equal energies are taken into account. The dispersion splitting increases systematically with the distance of the states from the Brillouin zone center. A similar wing due to dispersion of the electron momentum is calculated also for the s-electron states in the body-centered cubic lattice.
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