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1
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Some Exact Results in the One-Dimensional Attractive Hubbard Model

100%
Jakubczyk D.
Acta Physica Polonica A
|
2015
|
vol. 128
|
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.
2
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System Size Dependence of Entanglement in Quantum One-Dimensional Models

63%
Jakubczyk D., Jakubczyk P.
Acta Physica Polonica A
|
2017
|
vol. 132
|
issue 1
158-160
EN
We show that entanglement in one-dimensional spin and electron systems, with one excitation, depends only on the system size and has very simple form in both multipartite and bipartite case. Regarding the multipartite case, we present very simple expressions for global entanglement and N-concurrence, and show that they are mutually related. In the bipartite case, we give expressions for I-concurrence and negativity, and show that they are also dependent on each other.
3
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The Hilbert Space and the Exact Solution of the Spin-Electron Double-Tetrahedral Chain

63%
Jakubczyk D., Gálisová L.
Acta Physica Polonica A
|
2015
|
vol. 128
|
issue 2
173-175
EN
We discuss an exactly solvable double-tetrahedral chain, in which the localized Ising spins regularly alternate with triangular clusters - each available for one mobile electron. We give an exact solution for the considered hybrid system by the construction of the N-th tensor power of the Fourier transformation and using the generalized decoration-iteration mapping tranformation.
4
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Evolution of Laser Light Induced Sodium Clusters

51%
Kolwas M., Kolwas K., Jakubczyk D.
Acta Physica Polonica A
|
1994
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vol. 86
|
issue 1
257-266
EN
We investigated the growing sodium clusters, induced by the laser light resonant with a sodium dimer transition. We observed the intensity of light scattered by clusters. The clusters were produced in the stainless steel cell containing sodium vapor and helium. We obtained data on cluster mean size and dynamics from fitting the theoretical formulas to the experimental data. The model of clusters' evolution basing on the thermodynamics of the vapor-liquid transition was applied.
5
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Size Evolution of the Light Induced Sodium Clusters

51%
Hnat B., Jakubczyk D., Kolwas K., Kolwas M.
Acta Physica Polonica A
|
1992
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vol. 81
|
issue 6
629-637
EN
We report the observation of the size evolution of the laser light formed clusters. A cell containing sodium vapor and the buffer gas (He) under high pressure was used in the experiment. Changes of the radius and of the density of transient clusters were observed via the time evolution of the intensity of right-angle scattered light. The rate of the cluster radius growth was found to vary from 0.012 to 0.1 μm/s.
6
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Collective Scattering of Light on Gold Nanospheres Dispersed in Diethylene Glycol Microdroplet

51%
Kolwas M., Kolwas K., Jakubczyk D., Derkachov G.
Acta Physica Polonica A
|
2017
|
vol. 131
|
issue 2
288-293
EN
Light scattering on a freely suspended, evaporating droplet of suspension of gold nanospheres (125 nm radius) in diethylene glycol is studied, revealing both local and nonlocal properties of the system. When the average distance between the nanospheres at the droplet surface matches the wavelength of light, a (broad) maximum, associated with the collective scattering on them, is observed. The number of nanospheres at the droplet surface can be found then. A fine modulation of the maximum is associated with the whispering gallery modes of the composite droplet. The Fano profile identified in the modulation is interpreted as an interference of collective scattering and whispering gallery modes. The ultra narrow enhancement-and-quench structure recognizable in the modulation is interpreted as associated with the creation and destruction of collective oscillation of plasmons of individual nanospheres. It is proposed that this phenomenon can be perceived as whispering gallery modes-assisted creation and destruction of a global plasmon.
7
Content available remote

Evaporation of Micro-Droplets: the "Radius-Square-Law" Revisited

45%
Jakubczyk D., Kolwas M., Derkachov G., Kolwas K., Zientara M.
Acta Physica Polonica A
|
2012
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vol. 122
|
issue 4
709-716
EN
The range of applicability of a fundamental tool for studying the evolution of droplets, the "radius-square-law", was investigated both analytically and numerically, on the basis of the experimental results of our own as well as of other authors. Standard issues were briefly discussed. Departures from the "radius-square-law" caused by the influence of impurities encountered in non-ideal liquids, by the kinetic and surface tension effects encountered for small droplets or by thermal imbalance encountered in light-absorbing droplets were analysed. The entanglement between the kinetic and impurities effects was studied numerically yielding a possible explanation to evaporation coefficient discrepancies found in the literature. An unexpected "radius-square-law" persistence in case of non-isothermal evolutions of very small droplets in atmosphere nearly saturated with vapour was analysed. The coexistence of the kinetic effects and the strong effects of surface tension was found responsible for this effect.
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