Dynamics of Two-Level System Interacting with Random Classical Field

The dynamics of a particle interacting with random classical field in a two-well potential is studied by the functional integration method. The probability of particle localization in either of the wells is studied in detail. Certain field-averaged correlation functions for quantum-mechanical probabilities and the distribution function for the probabilities of final states (which can be considered as random variables in the presence of a random field) are calculated. The calculated correlators are used to discuss the dependence of the final state on the initial state. One of the main results of this work is that, although the off-diagonal elements of density matrix disappear with time, a particle in the system is localized incompletely (wave-packet reduction does not occur), and the distribution function for the probability of finding particle in one of the wells is a constant at infinite time.Comment: 5 page

Mathematical Model for the Formation of University Contingents on the Basis of Population Dynamics Equations

The mathematical model of two competitive universities for limited contingent of applicants, offered by L.A. Serkov, has been simplified up to level, allowing to investigate it by methods of the qualitative theory of dynamic systems. 8 critical points of the simplified dynamic system are defined and the analysis of their stability are made. It has allowed receiving all regimes of education system’s behavio

Methodology for comparative analysis of university rankings, with the Mediterranean and Black sea region countries taken as an example

The article develops quantitative methodology of comparative analysis of global university rankings for the Mediterranean and Black Sea region. In its frameworks three analytical procedures are proposed. They are used to build university and country matricesyesBelgorod State Universit

Josephson Frequency Singularity in the Noise of Normal Metal-Superconductor Junctions

A singularity at the Josephson frequency in the noise spectral density of a disordered normal metal -- superconductor junction is predicted for bias voltages below the superconducting gap. The non-stationary Aharonov-Bohm effect, recently introduced for normal metals, is proposed as a tool for detecting this singularity. In the presence of a harmonic external field, the derivative of the noise with respect to the voltage bias reveals jumps when the applied frequency is commensurate with the Josephson frequency associated with this bias. The height of these jumps is non-monotonic in the amplitude of the periodic field. The superconducting flux quantum enters this dependence. Additional singularities in the frequency dependent noise are predicted above gap.Comment: 4 pages, 2 figures, revised versio

N-particle scattering matrix for electrons interacting on a quantum dot

We present a non-perturbative expression for the scattering matrix of $N$ particles interacting inside a quantum dot. Characterizing the dot by its resonances, we find a compact form for the scattering matrix in a real-time representation. We study the transmission probabilities and interaction-induced orbital entanglement of two electrons incident on the dot in a spin-singlet state.Comment: 4 page

Dynamical correlations in electronic transport through a system of coupled quantum dots

Current auto- and cross-correlations are studied in a system of two capacitively coupled quantum dots. We are interested in a role of Coulomb interaction in dynamical correlations, which occur outside the Coulomb blockade region (for high bias). After decomposition of the current correlation functions into contributions between individual tunneling events, we can show which of them are relevant and lead to sub-/supper-Poissonian shot noise and negative/positive cross-correlations. The results are differentiated for a weak and strong inter-dot coupling. Interesting results are for the strong coupling case when electron transfer in one of the channel is strongly correlated with charge drag in the second channel. We show that cross-correlations are non-monotonic functions of bias voltage and they are in general negative (except some cases with asymmetric tunnel resistances). This is effect of local potential fluctuations correlated by Coulomb interaction, which mimics the Pauli exclusion principle

Bibliometric Analysis of Urban Runoff Study with help of Google Scholar

The paper discuses the dynamics of research frontiers on urban runoff problems. The outbursts of digitized and indexed Google Scholar publications on the subject under study happened in the 1960s-1970s and in 1994-199

Model of Quantum Measurement, which Leads to Reduction of Wave Function

In this paper, a mathematical model of reduction of the wave function is proposed. The model is based on ideas developed by Klimontovich and apply the method of stochastic quantization in the formulation of Haken. The equation takes into account the stochastic nature of the interaction of a quantum system and the measuring device during the measurement. From this equation, an equation of the Fokker- Planck was received. The solution of which show a reduction of wave functionyesBelgorod State Universit

Excess Noise in Biased Superconducting Weak Links

Non-equilibrium excess noise of a short quasi one-dimensional constriction between two superconductors is considered. A general expression for the current-current correlation function valid for arbitrary temperatures and bias voltages is derived. This formalism is applied to a current-carrying quantum channel with perfect transparency. Contrary to a transparent channel separating two normal conductors, a weak link between two superconductors exhibits a finite level of noise. The source of noise is fractional Andreev scattering of quasiparticles with energies $|E|$ greater than the half-width $\Delta$ of the superconducting gap. For high bias voltages, $V \gg \Delta /e$, the relation between the zero-frequency limit of the noise spectrum, $S(0)$, and the excess current $I_{\text{exc}}$ reads $S(0)=(1/5)|e|I_{\text{exc}}$. As $\Delta \rightarrow 0$ both the excess noise and the excess current vanish linearly in $\Delta$, %$\propto \Delta$, their ratio being constant.Comment: 8 pages (Latex), 1 figur

Theorem about the number and structure of the singular points n-dimensional dynamical system of population dynamics Lotka-Volterra in context of informational analysis and modeling

By elementary methods of combinatorial mathematics and uniqueness of solutions systems of linear algebraic equations for non degenerate cases proved a theorem about the number and structure of the singular points of n-dimensional dynamical system of population a dynamics Lotka-Volterra model. Showed that the number of singular points for this system is equal to 2 and their structure on a combination of zero nand nonzero coordinates coincides with the binomial coefficientsyesBelgorod State Universit