|
| |
|
|
Nonequilibrium Brownian dynamics in periodic energy landscapes
Paidar, Jaroslav ; Ryabov, Artem (advisor) ; Žonda, Martin (referee)
The collective dynamics of Brownian particles in porous structures is an important topic for both theory and experiment. A good understanding of Brownian dynamics of interacting particles moving in one dimension has recently been achieved in several models. The theoretical description of these models focuses on infinitely large systems, although real systems are in usually small. This thesis studies the effect of the size of a system of interacting particles driven by a force on their transport behavior in a periodic potential. We have used simulations of a single-particle model with analytically solvable results as reference data. For this model, simulations were performed using the Euler- Maruyama method. Multi-particle simulations were performed for two different types of particle interactions. The rigid-ball type interaction served as the basis for the analysis of behavior of a smoothed-barrier type interaction potential case that allowed for the particles to pass through each other. The particle velocity and diffusion coefficient were studied as a function of various system parameters such as particle softness, size, and density or system size. 1
|
|
|
Neaditivní mezimolekulární interakce
Kovačovský, Ján ; Klimeš, Jiří (advisor) ; Žonda, Martin (referee)
Non-additive intermolecular interactions, involving three or more molecules, present a significant challenge in accurately predicting molecular behaviour and properties of materials. These interactions, characterized by their high-dimensional and unpredictable nature with molecular position, cannot be reliably estimated by simply summing pair- wise interactions between molecules. Incorporating three-body non-additive interactions into first-principles quantum mechanical approaches can greatly enhance agreement with experimental data, often achieving remarkable reductions in deviations. 1
|
|
|
Quantum interference in nanocrystals
Spitzkopf, David ; Ostatnický, Tomáš (advisor) ; Žonda, Martin (referee)
Quantum interference control has is a well described effect in bulk and infinite well super-lattice crystals. In this thesis, we describe this effect in nanocrystals. We use a 8-band model for the description of the electron band structure in the crystal. We then break its inversion symmetry with a linear potential. We then apply external electro- magnetic field and calculate its effect on the crystal with the help of perturbation theory. The fields applied are of two kinds, one harmonic, the other instant in time. We follow with the calculation of the generated current, with detailed numerical tests of several pa- rameters of the model. Conductivity for a non-linearity of the 3rd order is then formally calculated. 1
|
|
|
Reconstruction of magnetic configurations using machine learning approaches
Vargicová, Tatiana ; Baláž, Pavel (advisor) ; Žonda, Martin (referee)
Title: Reconstruction of magnetic configurations using machine learning approaches Author: Tatiana Vargicová Department: Department of Condensed Matter Physics Supervisor of the bachelor thesis: RNDr. Pavel Baláž, Ph. D. Fyzikální ústav AV ČR Abstract: This work focuses on developing an autoencoder well-suited for reconstruction of magnetic phases with a prospect of future application in phase-recognition task. Specifically, it was investigated how does the autoencoder performance change when Hamiltonian term in added to the loss function, previously computed solely from MSE error. It was found that the effect Hamiltonian inclusion on MSE error is phase specific. Notably for spiral phase, the reconstruction significantly improves. In contrast, for some of the intermediate phases, the reconstruction greatly degrades. This was especially true for the intermediate phase composed of spirals combined with merons. In addition to simple MSE error, it was also investigated whether the reconstruction conserves the energy ascribed to individual spins. It was found that the Hamiltonian term improves the spin-energy conservation for all the magnetic phases. Keywords: neural networks, autoencoder, Heisenberg model, Hamiltonian
|
|
|
Variational Neural Network Quantum States for Frustrated Magnetic Systems
Mezera, Matěj ; Žonda, Martin (advisor) ; Slobodeniuk, Artur (referee)
We investigate the Shastry-Sutherland model (SSM), i.e., spin-1/2 quantum Heisen- berg model on a Shastry-Sutherland lattice, using a newly emerging approach exploiting well-developed machine learning techniques. We utilize neural networks as variational quantum states in quantum Monte Carlo investigations of the ground state properties. We first focus on SSM without an external magnetic field. For small lattices accessible via exact diagonalization, we compare the precision of various architectures based on re- stricted Boltzmann machines (RBM) or group-convolutional neural networks. The most versatile and precise architecture, namely complex-valued RBM, is then applied for larger lattices. Here we investigate the frustrated regime. We show that the RBM is able to represent all three of the major and fundamentally different phases of SSM. Finally, we apply the complex-valued RBM for SSM in a finite external magnetic field. We find that it cannot capture the intriguing steps in magnetization typical for SSM correctly due to its tendency to prefer more ordered states with higher magnetization. 1
|
|
|
Analysis of magnetic skyrmions using machine learning methods
Dušek, Ondřej ; Baláž, Pavel (advisor) ; Žonda, Martin (referee)
Title: Analysis of magnetic skyrmions using machine learning methods Author: Ondřej Dušek Department: Department of Condensed Matter Physics Supervisor: RNDr. Pavel Baláž, Ph.D., Department of Condensed Matter Physics Abstract: In this thesis, we were examining phases of ferromagnetic lattices obtained using Monte Carlo simulations and the Heisenberg hamiltonian with machine learning methods. Methods used were Nearest Centroid method, Support Vector machines method and deep convolutional neural networks. We compared and discussed their classification accuracy and used each one of them to create a phase diagram for parameters B and D of the Heisenberg hamiltonian (a magnetic field size and the parameter D of Dzyaloshinskii-Moriya interaction). Afterwards, we visualised outputs of convolutional layers in convolutional neural networks and used them to make an estimate of phase boundaries. In comparison with other articles, we used much larger lattices and more sophisticated machine learning methods. On some of these larger lattices appeared unusual variants of examined phases, which did not appear on smaller lattices. Some simpler machine learning methods had troubles with their classification, however, the final deep convolutional neural network we created was able to not only correctly classify lattices with...
|
guest ::
