arXiv subjects
Publications and source records attributed to R. Tsekov.
A new discrete model for energy relaxation of a quantum particle is described via a projection operator, causing the wave function collapse. Power laws for the evolution of the particle coordinate and momentum dispersions are derived. A new dissipative Schrodinger equation is proposed and solved for particular cases. A new dissipative Liouville equation is heuristically constructed.
It is shown that quantum entanglement is the only force able to maintain the fourth state of matter, possessing fixed shape at an arbitrary volume. Accordingly, a new relativistic Schrodinger equation is derived and transformed further to the relativistic Bohmian mechanics via the Madelung transformation. Three dissipative models are proposed as extensions of the quantum relativistic Hamilton-Jacobi equation. The corresponding dispersion relations are obtained.
The quantum Liouville equation, which describes the phase space dynamics of a quantum system of fermions, is analyzed from statistical point of view as a particular example of the Kramers-Moyal expansion. Quantum mechanics is extended to the relativistic domain by generalizing the Wigner-Moyal equation. Thus, an expression is derived for the relativistic mass in the Wigner quantum phase space presentation. The diffusion with an imaginary diffusion coefficient is also discussed. An imaginary stochastic process is proposed as the origin of quantum mechanics.
The dependence of the surface plasmons resonance (SPR) frequency on the size of gold nanoparticles (GNPs) is experimentally studied. The measured data for the SPR frequency by UV-Vis spectroscopy and GNPs diameter by Dynamic Light Scattering (DLS), Transmission Electron Microscopy (TEM) and Atomic Force Microscopy (AFM) are collected in the course of classical citrate GNPs synthesis. The relationship between the GNPs size and the blue shift of the light absorption is presented. They are fitted by an equation with a single free parameter, the dielectric permittivity of the surrounding media. Thus, the refractive index of the surrounding media is determined, which characterizes the GNPs surface shell.
Thermodynamically, bosons and fermions differ by their statistics only. A general entropy functional is proposed by superposition of entropic terms, typical for different quantum gases. The statistical properties of the corresponding Janus particles are derived by variation of the weight of the boson/fermion fraction. It is shown that di-bosons and anti-fermions separate in gas and liquid phases, while three-phase equilibrium appears for poly-boson/fermion Janus particles.
The Klein-Kramers equation, governing the Brownian motion of a classical particle in quantum environment under the action of an arbitrary external potential, is derived. Quantum temperature and friction operators are introduced and at large friction the corresponding Smoluchowski equation is obtained. Introducing the Bohm quantum potential, this Smoluchowski equation is extended to describe the Brownian motion of a quantum particle in quantum environment.
A Brownian harmonic oscillator, which dissipates energy either by friction or via emission of electromagnetic radiation, is considered. This Brownian emitter is driven by the surrounding thermo-quantum fluctuations, which are theoretically described by the fluctuation-dissipation theorem. It is shown how the AbrahamLorentz force leads to dependence of the half-width on the peak frequency of the oscillator amplitude spectral density. It is also found that for the case of a charged particle, moving in vacuum at zero temperature, its root-mean-square velocity fluctuation is a universal constant, equal to roughly 1/18 of the speed of light. The relevant Klein-Kramers and Smoluchowski equations are derived as well.
It is demonstrated how quantum mechanics emerges from the stochastic dynamics of force-carriers. It is shown that the quantum Moyal equation corresponds to some dynamic correlations between the momentum of a real particle and the position of a virtual particle, which are not present in classical mechanics. The new concept throws light on the physical meaning of quantum theory, showing that the Planck constant square is a second-second cross-cumulant.
The finite size effect of electron and nucleus is accounted for in the model of atom. Due to their hard sphere repulsion the energy of the 1s orbital decreases and the corrections amount up to 8% in Uranium. Several models for boundary conditions on the atomic nucleus surface are discussed as well.
In the frames of the DLVO theory the root mean square amplitude of capillary waves in a thin liquid film is calculated and its dependence on some important physical parameters is unveiled. Two important models are considered: films with classical interfaces and films between lipid bilayers. The performed numerical analysis demonstrates essential difference in their behavior due to the different elastic properties of the film surfaces. It is shown that the film lifetime is significantly long at some magic film radii.
The simplest density functional theory due to Thomas, Fermi, Dirac and Weizsacker is employed to describe the non-equilibrium thermodynamic evolution of an electron gas. The temperature effect is introduced via the Fermi-Dirac entropy, while the irreversible dynamics is described by a nonlinear diffusion equation. A dissipative Kohn-Sham equation is also proposed, which improves the Thomas-Fermi-Weizsacker kinetic functional.
The tribology of a bubble rubbing on a solid surface is studied via interferometry. A unique experimental setup is designed for monitoring the thickness profiles of a wetting film, intercalated between the bubble and hydrophilic glass moving with speed up to 412 um/s. The determination of the 3D film thickness profiles allows us to calculate 3D maps over the wetted surface of the local capillary, disjoining and lift pressures, viscous stress and friction force. In this way the average friction force and the corresponding friction coefficient are obtained. A theoretical model for the dependence of the friction coefficient on the film thickness is developed. The relevant slip coefficient, being a measure for the slip between liquid and solid, is determined as a function of the speed of the solid surface. It is found out that below 170 um/s a friction regime exists which formally resembles dry friction, while at larger speed the friction force between the bubble and solid passes through a maximum. Furthermore, the friction coefficient has a large value at low speed of the solid and reduces substantially with the speed increase.
Phase-formation of surface alloying by spinodal decomposition has been studied for the first time at an electrified interface. For this aim Zn was electrodeposited on Au(111) from the ionic liquid AlCl3-MBIC (58:42) containing 1 mM Zn(II) at different potentials in the underpotential range corresponding to submonolayer up to monolayer coverage. Structure evolution was observed by in situ electrochemical scanning tunneling microscopy (STM) at different times after starting the deposition via potential jumps and at temperatures of 298 K and 323 K. Spinodal or labyrinth two-dimensional structures predominate at middle coverage, both in deposition and dissolution experiments. They are characterized by a length scale of typically 5 nm which has been determined from the power spectral density of the STM images. Structure formation and surface alloying is governed by slow kinetics with a rate constant k with activation energy of 120 meV and preexponential factor of 0.17 Hz. The evolution of the structural features is described by a continuum model and is found to be in good agreement with the STM observations. From the experimental and model calculation results we conclude that the two-dimensional phase-formation in the Zn on Au(111) system is dominated by surface alloying. The phase separation of a Zn-rich and a Zn-Au alloy phase is governed by 2D spinodal decomposition.
The intra-crystalline diffusion of normal alkanes in LTL and ZSM-12 zeolite was experimentally studied via gravimetric measurements performed at different temperatures. A periodic dependence of the diffusion coefficient on the number of carbon atoms in alkane was detected, which is an experimental proof for resonant diffusion. The present observations were described on the base of the existing theory of the resonant diffusion and several important parameters of the alkane-zeolite interaction and zeolite vibrations were obtained. In the considered temperature region the diffusion coefficient follows the Arrhenius law with periodic dependences of the pre-exponential factor and activation energy on the number of carbon atoms in alkanes. A compensation effect of simultaneous increases of the pre-exponential factor and the activation energy was also established.
It is demonstrated that the dynamic structure is very important for the rate of drainage of a thin liquid film and it can be effectively taken into account by a dynamic fractal dimension. It is shown that the latter is a powerful tool for description of the film drainage and classifies all the known results from the literature. The obtained general expression for the thinning rate is a heuristic one and predicts variety of drainage models, which are even difficult to simulate in practice. It is a typical example of a scaling law, which explains the origin of the complicate dependence of the thinning rate on the film radius.
The diffusion of superoxide radical anions on the surface of TiO2 catalysts is theoretically considered as an important step in the kinetics of photocatalytic oxidation of toxic pollutants. A detailed analysis is performed to discriminate the effects of rotation, anion and adsorption bonds vibrations on the diffusion coefficient. A resonant dependence of the diffusivity on the lattice parameters of the TiO2 surface is discovered showing that the most rapid diffusion takes place when the lattice parameters are twice larger than the bond length of the superoxide radical anions. Whereas the rotation and vibrations normal to the catalyst surface are important, the anion bond vibrations do not affect the diffusivity due to their low amplitudes as compared to the lattice parameters.
The Brownian motion of a light quantum particle in a heavy classical gas is theoretically described and a new expression for the friction coefficient is obtained for arbitrary temperature. At zero temperature it equals to the de Broglie momentum of the mean free path divided by the mean free path. Alternatively, the corresponding mobility of the quantum particle in the classical gas is equal to the square of the mean free path divided by the Planck constant. The Brownian motion of a quantum particle in a quantum environment is also discussed.
The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Ito and Stratonovich forms, is introduced. It is shown that the new presentation is more appropriate for the description of thermodynamic fluctuations. The range of validity of the Boltzmann-Einstein principle is also discussed and a generalized alternative is proposed. Both expressions coincide in the small fluctuation limit, providing a normal distribution density.