The Ruelle-Pollicot resonances represent the spectrum of the coarse-grained Frobenious-Perron operator and enable discussion of long time evolution of observables, which is essential for study of mixing in dynamical system. In the article we present a new stable method for calculating Ruelle-Pollicot resonances for system with finite phase space.
COBISS.SI-ID: 2189412
A class of abstract heat engines without moving parts based on thermo-electric effect is presented. It is composed of two thermo-chemical baths connected via two channels with some properties and added electrical field. The charged particles are effused from the baths and travel along the channels. We analytically solved the case of one-dimensional channel and expressed thermoelectric constants with the channel's properties. The efficiency of the heat engines can be efficiently controlled and set arbitrary near to ideal (Carnot) at the cost of small power output.
COBISS.SI-ID: 2179684
Dynamical system of the triangle map is a simplified model of classical dynamics inside of an triangle with one side strongly elongated and represents a paradigmatic example of an system with algebraic decay of correlations. Because of this atypical behavior the system is interesting from mathematical and physical side. Using numerical simulations we were able to show that the system is ergodic and mixing, when it parameters are irrational numbers. Additionally, we present a stochastic model possessing most of the properties of the system in the generic case of parameters.
COBISS.SI-ID: 2152036
A very irregular dynamics with fast time correlation decay can be effectively described by Markov chains in which dynamics is generated by Markov matrices. In general this matrices are structureless and some are statistically similar to a purely random Markov matrix, the ensemble of which I define and discuss its properties in the article. I focus in particular on spectral properties and the gap in the spectrum.
COBISS.SI-ID: 2173028