arXiv subjects

Pavel A. Andreev

Publications and source records attributed to Pavel A. Andreev.

75 records · Page 5Linked to original sources

arXiv2012

Quantum kinetics derivation as generalization of the quantum hydrodynamics method

We present a new way of quantum kinetic equation derivation. This method appears as a natural generalization of the many-particle quantum hydrodynamic method. Kinetic equations are derived for different system of particles. First of all we consider quantum plasma and pay special attention to the spin evolution. We show that we need a set of two kinetic equations for description of spinning particles. One of these equations is the equation for distribution function, however this equation contains new function, even in the self-consistent field approximation. This is a spin-distribution function introduced in the paper. Therefore we have to derive kinetic equation for spin distribution function evolution, which is presented here and used to construct a closed set of kinetic equations. We also present kinetic equation for system of neutral particles with a short-range interaction in the first order by the interaction radius approximation. We derive a set of kinetic equations for particles having electric dipole moment, this set analogous to the equations set for spinning particles, but it has some differences. As a special topic we find kinetic equations for graphene carriers in the vicinity of the Dirac points. Derived equations, in general case, contain two-particle distribution functions, which take into account contribution of the quantum correlations including the exchange interaction, but we restrict ourself by the self-consistent field approximation to obtain closed kinetic description, in the system of particles with the short-range interaction.

physics.plasm-ph↗

arXiv2012

Collective excitations in graphene in magnetic field

Collective excitations in graphene monolayer are studied. Equations describing collective properties of electrons in graphene are obtained. The basic ideas of the method of many-particle quantum hydrodynamics are used for the derivation. As starting point of the derivation we use the Dirac equation for massless electrons which is usually used for description of electrons in graphene [D. E. Sheehy and J. Schmalian, Phys. Rev. Lett. 99, 226803 (2007)], where the Coulomb interaction is taken into account. We study dispersion properties of collective excitations by means derived here graphene quantum hydrodynamics equations (GQHD). We consider graphene in the external magnetic field which directed at an angle to the graphene sample. We do it in a linear approximation of the GQHD equations. We observe that the magnetic field directed perpendicular to the graphene plane had no influence on dispersion of the collective excitations. For the magnetic field directed at an angle to the graphene we obtain dependence of wave dispersion on system parameters: strength of magnetic field, wave vector, direction of wave propagation relatively to the magnetic field.

cond-mat.mes-hall↗

arXiv2011

First principles derivation of NLS equation for BEC with cubic and quintic nonlinearities at non zero temperature. Dispersion of linear waves

In this work we presented a derivation of the quantum hydrodynamic equations for neutral bosons. We considered short range interaction between particles. This interaction consist binary interaction $U(\textbf{r}_{i},\textbf{r}_{j})$ and three particle interaction $U(\textbf{r}_{i},\textbf{r}_{j},\textbf{r}_{k})$, the last one does not include binary interaction between particles. From the quantum hydrodynamic (QHD) equations for Bose-Einstein condensate we derive nonlinear Schrödinger equation. This equation includes the nonlinearities of third and fifth degree. It is at zero temperature. Explicit form of the constant of three-particle interaction was taken. First of all, developed method we used for studying of dispersion of linear waves. Dispersion characteristics of linear waves were compared for the cases. It were of two-particle interaction in approximation third order to interaction radius (TOIR) and three-particle interaction, at zero temperature. We consider influence of temperature on dispersion of elementary excitations. For this aim we derive a system of QHD equations at non-zero temperature. Obtained system of equation is an analog of well-known two-fluid hydrodynamics. Moreover, it is generalization of two-fluid hydrodynamics equations due to three-particle interaction. Evident expressions of the velocities of the first and second sound via the concentrations of superfluid and noncondesate components is calculated.

cond-mat.quant-gas↗