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3 Journal of Applied Mathematics and Computational Mechanics

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Kinetic Monte Carlo study of structural proton diffusion along a one-dimensional path

Masłowski T., Drzewiński A., Zubaszewska M.

Journal of Applied Mathematics and Computational Mechanics

2015

Vol. 14, nr 3

59--64

We study the structural diffusion coefficient of protons in a chain-like system by the means of KMC simulations. To perform specific calculations, we adopted parameter values in our model that correspond to the benzimidazole crystal. As we have shown, the structural diffusion follows the Arrhenius-like thermal dependence with an effective activation energy of 2.01 eV.

Time evolution of the haldane state after a quantum quench

Woźniak D., Drzewiński A., Kamieniarz G.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 4

151--156

In the framework of the Matrix Product States representation the effect of a sudden quench of the uniaxial anisotropy on the time evolution of the Haldane state has been investigated. The existence of the non-vanishing string correlations in the limit of a large distance in the Haldane phase has been verified. The overlap of the initial and time-evolved states, the so-called Loschmidt echo, has been investigated.

Critical fluctuations of a confined binary mixture

Zubaszewska M., Gendiar A., Masłowski T.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 4

177-182

Exploiting the mapping between a binary mixture and the Ising model we have analyzed the critical fluctuations by means of the density-matrix renormalization group technique. The calculations have been carried out for a two-dimensional Ising strip subject to equally strong surface fields. It was found that the critical Casimir force has significantly different behavior on opposite sides of the capillary condensation line, especially below the critical temperature. It can be concluded that in real binary mixtures the most attractive force appears at temperatures near Tc and at reservoir compositions slightly away from the critical composition.