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

2014 ◽  
Vol 29 (09) ◽  
pp. 1450052 ◽  
Author(s):  
Yu. A. Sitenko ◽  
S. A. Yushchenko
Keyword(s):  
Magnetic Field ◽  
Boundary Condition ◽  
Boundary Conditions ◽  
Casimir Force ◽  
Matter Field ◽  
Particle Energy ◽  
Parallel Plates ◽  
Charged Scalar ◽  
Scalar Matter ◽  
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 requirement 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.

scholarly journals Pressure from the vacuum of confined spinor matter

2015 ◽  
Vol 30 (30) ◽  
pp. 1550184 ◽  
Author(s):  
Yu. A. Sitenko ◽  
S. A. Yushchenko
Keyword(s):  
Magnetic Field ◽  
Boundary Condition ◽  
Boundary Conditions ◽  
Strong Magnetic Field ◽  
Uniform Magnetic Field ◽  
Matter Field ◽  
Vacuum Pressure ◽  
Spatial Region ◽  
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.

scholarly journals Induced vacuum current and magnetic field in the background of a vortex

2016 ◽  
Vol 31 (06) ◽  
pp. 1650017 ◽  
Author(s):  
Volodymyr M. Gorkavenko ◽  
Iryna V. Ivanchenko ◽  
Yurii A. Sitenko
Keyword(s):  
Magnetic Field ◽  
Side Surface ◽  
Matter Field ◽  
Transverse Size ◽  
Compton Wavelength ◽  
Charged Scalar ◽  
Quantum Matter ◽  
Scalar Matter ◽  
Bohm Effect ◽  
Aharonov Bohm

A topological defect in the form of the Abrikosov–Nielsen–Olesen vortex is considered as a gauge-flux-carrying tube that is impenetrable for quantum matter. Charged scalar matter field is quantized in the vortex background with the perfectly reflecting (Dirichlet) boundary condition imposed at the side surface of the vortex. We show that a current circulating around the vortex and a magnetic field directed along the vortex are induced in the vacuum, if the Compton wavelength of the matter field exceeds considerably the transverse size of the vortex. The vacuum current and magnetic field are periodic in the value of the gauge flux of the vortex, providing a quantum-field-theoretical manifestation of the Aharonov–Bohm effect. The total flux of the induced vacuum magnetic field attains notable finite values even for the Compton wavelength of the matter field exceeding the transverse size of the vortex by just three orders of magnitude.

scholarly journals Fluid Driven by Tangential Velocity and Shear Stress: Mathematical Analysis, Numerical Experiment, and Implication to Surface Flow

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
H. S. Tang ◽  
L. Z. Zhang ◽  
J. P.-Y. Maa ◽  
H. Li ◽  
C. B. Jiang ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Shear Stress ◽  
Boundary Conditions ◽  
Steady Flow ◽  
Tangential Velocity ◽  
Surface Flow ◽  
Parallel Plates ◽  
Moving Plate ◽  
Stress Boundary Condition ◽  
Stress Boundary

This paper investigates behaviors of flows driven by tangential velocity and shear stress on their boundaries such as solid walls and water surfaces. In a steady flow between two parallel plates with one of them in motion, analytic solutions are the same when a velocity and a shear stress boundary condition are applied on the moving plate. For an unsteady, impulsively started flow, however, analysis shows that solutions for velocity profiles as well as energy transferring and dissipation are different under the two boundary conditions. In an air-water flow, if either a velocity or a stress condition is imposed at the air-water interface, the problem becomes ill-posed because it has multiple solutions. Only when both of the conditions are specified, it will have a unique solution. Numerical simulations for cavity flows are made to confirm the theoretical results; a tangential velocity and a shear stress boundary condition introduce distinct flows if one considers an unsteady flow, whereas the two conditions lead to a same solution if one simulates a steady flow. The results in this paper imply that discretion is needed on selection of boundary conditions to approximate forcing on fluid boundaries such as wind effects on surfaces of coastal ocean waters.

Effects of thermal radiation and magnetohydrodynamics on Ree-Eyring fluid flows through porous medium with slip boundary conditions

2019 ◽  
Vol 15 (2) ◽  
pp. 492-507 ◽  
Author(s):  
K. Ramesh ◽  
Sartaj Ahmad Eytoo
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Porous Medium ◽  
Boundary Conditions ◽  
Closed Form ◽  
Parallel Plates ◽  
Slip Boundary Conditions ◽  
Content Type ◽  
Closed Form Solutions ◽  
Slip Boundary

Purpose The purpose of this paper is to investigate the three fundamental flows (namely, both the plates moving in opposite directions, the lower plate is moving and other is at rest, and both the plates moving in the direction of flow) of the Ree-Eyring fluid between infinitely parallel plates with the effects of magnetic field, porous medium, heat transfer, radiation and slip boundary conditions. Moreover, the intention of the study is to examine the effect of different physical parameters on the fluid flow. Design/methodology/approach The mathematical modeling is performed on the basis of law of conservation of mass, momentum and energy equation. The modeling of the present problem is considered in Cartesian coordinate system. The governing equations are non-dimensionalized using appropriate dimensionless quantities in all the mentioned cases. The closed-form solutions are presented for the velocity and temperature profiles. Findings The graphical results are presented for the velocity and temperature distributions with the pertinent parameters of interest. It is observed from the present results that the velocity is a decreasing function of Hartmann number. Temperature increases with the increase of Ree-Eyring fluid parameter, radiation parameter and temperature slip parameter. Originality/value First time in the literature, the authors obtained closed-form solutions for the fundamental flows of Ree-Erying fluid between infinitely parallel plates with the effects of magnetic field, porous medium, heat transfer, radiation and slip boundary conditions. Moreover, the results of this paper are new and original.

scholarly journals Influence of quantized massive matter fields on the Casimir effect

2015 ◽  
Vol 30 (20) ◽  
pp. 1550099
Author(s):  
Yu. A. Sitenko
Keyword(s):  
Magnetic Field ◽  
Casimir Effect ◽  
Hamiltonian Operator ◽  
Matter Field ◽  
Parallel Plates ◽  
Vacuum Fluctuations ◽  
New Type ◽  
The Magnetic Field ◽  
External Uniform Magnetic Field ◽  
Matter Fields

Charged massive matter fields of spin-0 and spin-[Formula: see text] are quantized in the presence of an external uniform magnetic field in a spatial region bounded by two parallel plates. The most general set of boundary conditions at the plates, that is required by mathematical consistency and the self-adjointness of the Hamiltonian operator, is employed. The vacuum fluctuations of the matter field in the case of the magnetic field orthogonal to the plates are analyzed, and it is shown that the pressure from the vacuum onto the plates is positive and independent of the boundary condition, as well as of the distance between the plates. Possibilities of the detection of this new-type Casimir effect are discussed.

scholarly journals Hall instability: origin, properties and asymptotic theory for its tearing mode

2021 ◽  
Vol 87 (4) ◽  
Author(s):  
Leonid Kitchatinov
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Current Velocity ◽  
Necessary Condition ◽  
Perfect Conductor ◽  
Tearing Mode ◽  
Slab Geometry ◽  
Background Magnetic Field ◽  
Type Mode ◽  
Almost All

Hall instability in electron magnetohydrodynamics is interpreted as the shear-Hall instability driven jointly by helicoidal oscillations and shear in the electron current velocity. This explanation suggests an antiparallel orientation of the background magnetic field and vorticity of the current velocity as the necessary condition for Hall instability. The condition is tested and generally confirmed by numerical computations in plane slab geometry. Unstable eigenmodes are localized in the spatial regions of the antiparallel field and vorticity. Computations of the tearing-type mode of the instability are complemented by (and generally agree with) asymptotic analytical estimations for large Hall numbers. The stabilizing effect of perfect conductor boundary conditions is found and explained. For large Hall numbers, the growth rates approach the power-law dependence $\sigma \propto B^\alpha \eta ^{1-\alpha }$ on the magnetic field ( $B$ ) and diffusivity ( $\eta$ ). Almost all computations give the power index $\alpha = 3/4$ with one exception of the tearing-type mode with vacuum boundary conditions for which case $\alpha = 2/3$ .

scholarly journals Self-adjointness, confinement and the Casimir effect

2016 ◽  
Vol 14 (3) ◽  
pp. 319-335
Author(s):  
Yu.A. Sitenko ◽  
V.M. Gorkavenko
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Uniform Magnetic Field ◽  
Casimir Effect ◽  
Matter Field ◽  
Spinor Matter ◽  
Magnetic Field Transverse

An influence of a classical magnetic field on the vacuum of the quantized charged spinor matter field confined between two parallel material plates is studied. In the case of the uniform magnetic field transverse to the plates, the Casimir effect is shown to be repulsive, independently of a choice of boundary conditions and of a distance between the plates.

scholarly journals Casimir effect in Horava–Lifshitz-like theories

2015 ◽  
Vol 30 (36) ◽  
pp. 1550220 ◽  
Author(s):  
I. J. Morales Ulion ◽  
E. R. Bezerra de Mello ◽  
A. Yu. Petrov
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Casimir Force ◽  
Casimir Effect ◽  
Lorentz Symmetry ◽  
Space Time ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Scalar Field Theory

In this paper, we consider a Lorentz-breaking scalar field theory within the Horava–Lifshtz approach. We investigate the changes that a space–time anisotropy produces in the Casimir effect. A massless real quantum scalar field is considered in two distinct situations: between two parallel plates and inside a rectangular two-dimensional box. In both cases, we have adopted specific boundary conditions on the field at the boundary. As we shall see, the energy and the Casimir force strongly depends on the parameter associated with the breaking of Lorentz symmetry and also on the boundary conditions.

scholarly journals Casimir effect of a Lorentz-violating scalar in magnetic field

2020 ◽  
Vol 35 (31) ◽  
pp. 2050209
Author(s):  
Andrea Erdas
Keyword(s):  
Magnetic Field ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Casimir Effect ◽  
Lorentz Invariance ◽  
Neumann Boundary ◽  
Casimir Energy ◽  
Neumann Boundary Conditions ◽  
Parallel Plates ◽  
Massive Scalar Field

In this paper, I study the Casimir effect caused by a charged and massive scalar field that breaks Lorentz invariance in a CPT-even, aether-like manner. I investigate the case of a scalar field that satisfies Dirichlet or mixed (Dirichlet–Neumann) boundary conditions on a pair of very large plane parallel plates. The case of Neumann boundary conditions is straightforward and will not be examined in detail. I use the [Formula: see text]-function regularization technique to study the effect of a constant magnetic field, orthogonal to the plates, on the Casimir energy and pressure. I investigate the cases of a timelike Lorentz asymmetry, a spacelike Lorentz asymmetry in the direction perpendicular to the plates, and a spacelike asymmetry in the plane of the plates and, in all those cases, derive simple analytic expressions for the zeta function, Casimir energy and pressure in the limits of small plate distance, strong magnetic field and large scalar field mass. I discover that the Casimir energy and pressure, and their magnetic corrections, all strongly depend on the direction of the unit vector that implements the breaking of the Lorentz symmetry.

scholarly journals CASIMIR FORCE OF FERMIONS COUPLED TO MONOPOLES IN SIX-DIMENSIONAL SPACETIME

2013 ◽  
Vol 11 (01) ◽  
pp. 1450011 ◽  
Author(s):  
V. K. OIKONOMOU
Keyword(s):  
Boundary Conditions ◽  
Extra Dimensions ◽  
Casimir Force ◽  
Opposite Sign ◽  
Quantum Field ◽  
Parallel Plates ◽  
Fermion System ◽  
Extra Space ◽  
Dimensional Spacetime ◽  
Spherical Topology

We calculate the Casimir force for a fermionic quantum field in a piston geometry with three parallel plates. The fermion satisfies bag boundary conditions on the plates and the spacetime is assumed to have compact extra dimensions. The calculation is performed in the cases where the extra space has toroidal and spherical topology. We are mainly interested in the case in which the fermion is coupled non-trivially to an extra-dimensional defect, with a torus extra-dimensional topological background. We found that in certain limits, the Casimir force corresponding to the defect-fermion system and to the sphere, has opposite sign, in reference to those corresponding to the toroidal extra-dimensional spaces.

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