arXiv subjects

A. Yu. Bogdanov

Publications and source records attributed to A. Yu. Bogdanov.

5 recordsLinked to original sources

arXiv2012

Hyper-relativistic mechanics and superluminal particles

Recent experiments by OPERA with high energy neutrinos, as well as astrophysics observation data, may possibly prove violations of underlying principles of special relativity theory. This paper attempts to present an elementary modification of relativistic mechanics that is consistent both with the principles of mechanics and with Dirac's approach to derivation of relativistic quantum equations. Our proposed hyper-relativistic model is based on modified dispersion relations between energy and momentum of a particle. Predictions of the new theory significantly differ from the standard model, as the former implies large Lorentz gamma-factors (ratio of particle energy to its mass). First of all, we study model relationships that describe hypothetical motion of superluminal neutrinos. Next, we analyze characteristics of Cherenkov radiation of photons and non-zero mass particles in vacuum. Afterwards, we derive generalized Lorentz transformations for a hyper-relativistic case, resulting in a radical change in the law of composition of velocities and particle kinematics. Finally, we study a hyper-relativistic version of Dirac equation and some of its properties. In present paper we attempted to use plain language to make it accessible not only to scientists but to undergraduate students as well.

physics.gen-ph↗

arXiv2008

On the Informational Aspects of Interfering Quantum States

In present work we study informational measures for the problem of interference of quantum particles. We demonstrate that diffraction picture in the far field, which is given by probability density of particle momentum distribution, represents a mixture of probability densities of corresponding Schmidt modes, while the number of modes is equal to the number of slits at the screen. Also, for the first time we introduce informational measures to study the quality of interference picture and analyze the relation between visibility of interference picture and Schmidt number. Furthermore, we consider interference aspects of the problem of a quantum particle tunneling between two potential wells. This framework is applied to describing various isotopic modifications of ammonia molecule. Finally, we calculate limits on the maximum possible degree of entanglement between quantum system and its environment, which is imposed by measurements

quant-ph↗

arXiv2006

Entanglement of Quantum States, Thermodynamical Statistical Distributions and Physical Nature of Temperature

Thermodynamical equilibrium is considered as an effect of quantum entangling of the vacuum state of a system. An explicit mathematical model of multi- particle entangled pure quantum states is developed and analyzed. In the framework, the process of measurement results in probability distributions that exactly correspond to the heat equilibrium of a system in a thermostat.

quant-ph↗

arXiv2005

Schmidt information and entanglement in quantum systems

The purpose of this paper is to study entanglement of quantum states by means of Schmidt decomposition. The notion of Schmidt information which characterizes the non-randomness of correlations between two observers that conduct measurements of EPR-states is proposed. In two important particular cases - a finite number of Schmidt modes with equal probabilities and Gaussian correlations- Schmidt information is equal to Shannon information. A universal measure of a dependence of two variables is proposed. It is based on Schmidt number and it generalizes the classical Pearson correlation coefficient. It is demonstrated that the analytical model obtained can be applied to testing the numerical algorithm of Schmidt modes extraction. A thermodynamic interpretation of Schmidt information is given. It describes the level of entanglement and correlations of micro-system with its environment

quant-ph↗

arXiv2005

Analysis of localized Schmidt decomposition modes and of entanglement in atomic and optical quantum systems with continuous variables

We investigate the procedure of Schmidt modes extraction in systems with continuous variables. An algorithm based on singular value matrix decomposition is applied to the study of entanglement in an "atom-photon" system with spontaneous radiation. Also, this algorithm is applied to the study of a bi-photon system with spontaneous parametric down conversion with type-II phase matching for broadband pump. We demonstrate that dynamic properties of entangled states in an atom-photon system with spontaneous radiation are defined by a parameter equal to the product of the fine structure constant and the atom-electron mass ratio. We then consider the evolution of the system during radiation and show that the atomic and photonic degrees of freedom are entangling for the times of the same order of magnitude as the excited state life-time. Then the degrees of freedom are de-entangling and asymptotically approach to the level of small residual entanglement that is caused by momentum dispersion of the initial atomic packet.Finally, we investigate the process of coherence loss between modes in type-II parametric down conversion that is caused by non-linear crystal properties.

quant-ph↗