arXiv subjects

S. A. Yushchenko

Publications and source records attributed to S. A. Yushchenko.

3 recordsLinked to original sources

arXiv2015

Pressure from the vacuum of confined spinor matter

Charged spinor matter field is quantized in a spatial region bounded by two parallel neutral plates. The most general set of boundary conditions ensuring the confinement of matter within the plates is considered. We study a response of the vacuum of the confined matter to the background uniform magnetic field which is directed orthogonally to the plates. It is proven that, in the case of a sufficiently strong magnetic field, the vacuum pressure onto the plates is positive and independent of the boundary condition, as well as of the distance between the plates.

hep-th↗

arXiv2014

General conditions for vanishing the current J^{z} for Dirac field on boundaries of the domain between two planes

In connection with the Casimir effect for a spinor field in presence of external magnetic field, of special interest are solutions of the Dirac equation in the domains restricted by two planes, which have vanishing the third projection of the conserved current J^{z} on two boundaries. General conditions for vanishing the current are formulated, they reduce to linear homogeneous algebraic system, for which solutions exist only when vanishing the determinant of the linear system, that is for the roots of a 4-th order algebraic equation with respect to the variable e^{2ik a}, where a is a half-distance between the planes, and k stands for the third projection of the Dirac particle momentum. All solutions of the equation have been found explicitly, each of them provides us in principle with a special possibility to get the quantization rules for parameter k; the most of produced expression for the roots can be solved with respect to parameter k only numerically. Generally, solutions e^{2ik a} depend on 4 arbitrary phase parameters which influence the appropriate wave functions with vanishing current: J^{z}(z=-z,+a)=0.

quant-ph↗

arXiv2014

The Casimir effect with quantized charged scalar matter in background magnetic field

We study the influence of a background uniform magnetic field and boundary conditions on the vacuum of a quantized charged massive scalar matter field confined between two parallel plates; the magnetic field is directed orthogonally to the plates. The admissible set of boundary conditions at the plates is determined by the requirements that the operator of one-particle energy squared be self-adjoint and positive definite. We show that, in the case of a weak magnetic field and a small separation of the plates, the Casimir force is either attractive or repulsive, depending on the choice of a boundary condition. In the case of a strong magnetic field and a large separation of the plates, the Casimir force is repulsive, being independent of the choice of a boundary condition, as well as of the distance between the plates.

hep-th↗