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Quantum thermodynamics
Sedlák, Oldřich ; Holubec, Viktor (advisor) ; Chvosta, Petr (referee)
Quantum coherence is being viewed as a possible resource that could improve the performance of quantum technologies. This thesis analyzes a quantum heat engine model inspired by Dorfman et al. (PNAS vol. 110 no. 8) while using a standard Markovian quantum optical master equation in the Lindblad form. Steady-state coherence arises from the degeneracy of the two upper energy levels and its effects become significant for near-perfect alignment of the associated transition dipole moments. For the maximum alignment, the steady-state cur- rent becomes highly dependent on the relative phase and exhibits quantum in- terference. The performed numerical calculations show some promise of possible enhancement of the current above the classical limit. 1
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Brownian motion in logarithmic potential
Berestneva, Ekaterina ; Ryabov, Artem (advisor) ; Chvosta, Petr (referee)
In this thesis we study first-passage properties of a Brownian particle diffusing under the action of logarithmic potential field U(x, t) = g(t) log(x). The main part of this thesis is de- voted to the case of time-dependent potential strength g(t). To obtain the corresponding survival probability, one may try to solve the Fokker-Planck equation. However, its exact solution for the time-dependent potential is yet unknown. In this work we propose a simple asymptotic theory which yields the long-time behaviour of the survival probability and the moments of the particle position. The survival probability exhibits a rather varied behaviour for different functions g(t). We identify three regimes of asymptotic decay: the regular regime, the marginal regime and the regime of enhanced absorption. We also address the question of how will the derived first-passage properties of Brownian motion change when the absorbing boundary is not exactly at the origin. 1
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Thermodynamics of interacting brownian particles
Herčík, Michal ; Chvosta, Petr (advisor) ; Ryabov, Artem (referee)
The thesis comprises single-file diffusion in an external time-dependent potential, the diffusion of particles in narrow channel where particles can not pass each other. We discuss the role of order statistics solving the dynamics of the particles. We focus on application of perturbation theory on Fokker- Planck equation for the combined stochastic process of position and work. The calculation of the first and second moment of work for a set of particles analytically. The comparison of these results with results based on computer simulations of trajectories. Computer simulation of marginal PDF of work for left and right particle and simultaneous PDF for a set of two external driven particles. Powered by TCPDF (www.tcpdf.org)
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Stochastic dynamics and energetics of biomolecular systems
Ryabov, Artem ; Chvosta, Petr (advisor) ; Novotný, Tomáš (referee) ; Papáček, Štěpán (referee)
Title: Stochastic dynamics and energetics of biomolecular systems Author: Artem Ryabov Department: Department of Macromolecular Physics Supervisor: prof. RNDr. Petr Chvosta, CSc., Department of Macromolecular Physics Abstract: The thesis comprises exactly solvable models from non-equilibrium statistical physics. First, we focus on a single-file diffusion, the diffusion of particles in narrow channel where particles cannot pass each other. After a brief review, we discuss open single-file systems with absorbing boundaries. Emphasis is put on an interplay of absorption process at the boundaries and inter-particle entropic repulsion and how these two aspects affect the dynam- ics of a given tagged particle. A starting point of the discussions is the exact distribution for the particle displacement derived by order-statistics argu- ments. The second part of the thesis is devoted to stochastic thermodynam- ics. In particular, we present an exactly solvable model, which describes a Brownian particle diffusing in a time-dependent anharmonic potential. The potential has a harmonic component with a time-dependent force constant and a time-independent repulsive logarithmic barrier at the origin. For a particular choice of the driving protocol, the exact work characteristic func- tion is obtained. An asymptotic analysis of...
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Theoretical description of unequilibrium energy transformation processes on the level of molecular structures
Holubec, Viktor ; Chvosta, Petr (advisor) ; Netočný, Karel (referee) ; Maass, Philipp (referee)
Title: Theoretical description of unequilibrium energy transformation processes on the level of molecular structures Author: Viktor Holubec Department: Department of Macromolecular Physics Supervisor: prof. RNDr. Petr Chvosta, CSc., Department of Macromolecular Physics Abstract: The thesis is devoted to the thermodynamics of externally driven mesoscopic sys- tems. These systems are so small that the thermodynamic limit ceases to hold and the probabilistic character of the second law cannot be ignored. Thermal forces becomes comparable to other forces acting on the system and they have to be incorporated in the underlying dynamical law, i.e., in the master equation for discrete systems, and in the Fokker-Planck equation for continuous ones. In the first part of the thesis we investigate dynamics and energetics of mesoscopic systems during non-equilibrium isothermal processes. Due to the stochastic na- ture of the dynamics, the work done on the system by the external forces must be treated as a random variable. We derive an exact analytical form of the work probability density for several model systems. In particular, the knowledge of the exact formula improves the analysis of experimental data using the recent- ly discovered fluctuation theorems. In the second part of the thesis we study a non-equilibrium...
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Selforganization and optical properties of small molecular aggregates
Sláma, Vladislav ; Mančal, Tomáš (advisor) ; Chvosta, Petr (referee)
The work deals with the description of carotenoid aggregation in water solutions. The main interactions which are involved in aggregation were analyzed and an efficient way of description of carotenoid aggregation, which leads to a speed up the computation, has been introduced. In addition, two different methods for calculation probability distribution of catotenoids configurations in solutions with variable water concentration were elaborated, and their advantages and disadvantages were discussed. Absorption spectra were calculated from these distributions, and they were compared with the experimental results. The influence of water on formation of different types of aggregates, and its impact on the shape of absorption spectra was also discussed. Results of this study will be used as a base of other, more accurate, description of carotenoids aggregation, which will include other weaker interactions between carotenoids.
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Stochastická dynamika bublin v DNA
Kaiser, Vojtěch ; Novotný, Tomáš (advisor) ; Chvosta, Petr (referee)
Název práce: Stochastická dynamika bublin v DNA Autor: Bc. Vojtěch Kaiser Katedra: Katedra fyziky kondenzovaných látek Vedoucí diplomové práce: RNDr. Tomáš Novotný, Ph.D., Katedra fyziky kondenzovaných látek Abstrakt: Bubliny v DNA jsou místa, kde se vlivem tepelných či torsních vlivů otevírá dvojšroubovice DNA. Tyto bubliny jsou považovány za důležité pro termodynamiku DNA [56] a biologické procesy s DNA spojené [23,40,43,49]. V článcích [38, 39] byla řešena stochastická dynamika bublin v DNA na zá- kladě Polandova-Scheragova modelu a získány analytické výsledky při tep- lotě denaturace DNA a pro asymptotiku dlouhých časů, zvláště pro hustotu pravděpodobnosti času setkání konců bubliny. V této práci navazujeme na tyto výsledky a počítáme celkový tvar této hustoty pravděpodobností s vy- užitím numerické inverse analytických vztahů v Laplacově obraze. Dále po- čítáme hustotu pravděpodobnosti místa setkání konců bubliny. Odpovídající výsledky jsou numericky spočteny v případě molekul DNA konečné délky. Zachycování bubliny v oblastech bohatých na AT páry je modelováno jako subdifusivní systém dle článku [42] a jsou počítány stejné veličiny jako pro difusivní model. V závěru diskutujeme tyto výsledky a možnost jejich experi- mentálního ověření. Klíčová slova: bubliny v DNA,...
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Noise-induced transitions in nonlinear dynamics of stochastic systems.
Humplík, Jan ; Chvosta, Petr (advisor) ; Šomvársky, Ján (referee)
In this thesis we focuse on one-dimensional diffusion in a random potential given by the general Markov dichotomous process. It was shown in [5] that this problem is closely related to the study of the stochastic Riccati equation. Using Kolmogorov forward equation we have a solution in the case of a semi-infinite interval. In order to overcome the restriction of a semi- infinite interval we present an approach to solution based on the method of Carleman embedding. We give an expression for the moments in the Laplace domain in terms of an infinite-dimensional matrix element and we try to evaluate it in the limit of infinite time and semi-infinite interval. However we find a discrepancy between our result, numerical simulation and different theoretical approach to the same problem. We also develop Monte Carlo simulations of the Riccati equations and we compare them to analytical results.
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