Casimir Energy for a Coupled Fermion-Kink System and its stability

Abstract

We compute the Casimir energy for a system consisting of a fermion and a pseudoscalar field in the form of a prescribed kink. This model is not exactly solvable and we use the phase shift method to compute the Casimir energy. We use the relaxation method to find the bound states and the Runge-Kutta-Fehlberg method to obtain the scattering wavefunctions of the fermion in the whole interval of $x$. The resulting phase shifts are consistent with the weak and strong forms of the Levinson theorem. Then, we compute and plot the Casimir energy as a function of the parameters of the pseudoscalar field, i.e. the slope of $\varphi (x)$ at x=0 ($\mu$) and the value of $\varphi (x)$ at infinity (${\theta }_0$). In the graph of the Casimir energy as a function of $\mu$ there is a sharp maximum occurring when the fermion bound state energy crosses the line of E=0. Furthermore, this graph shows that the Casimir energy goes to zero for $\mu \to 0$, and also for $\mu \to \infty$ when ${\theta }_0$ is an integer multiple of $\pi$. Moreover, the graph of the Casimir energy as a function of ${\theta }_0$ shows that this energy is on the average an increasing function of ${\theta }_0$ and has a cusp whenever there is a zero fermionic mode. We finally compute the total energy of a system consisting of a valence fermion in the ground state. Most importantly, we show that this energy (the sum of the Casimir energy and the energy of the fermion) is minimum when the background field has winding number one, independent of the details of the background profile. Throughout the paper we compare our results with those of a simple exactly solvable model, where a piece-wise linear profile approximates the kink. We find that the kink is an almost reflectionless barrier for the fermions, within the context of our model.

revtex4, 10 pages, 9 figures

References in corpus (48)

• Precision Measurement of the Casimir Force from 0.1 to 0.9 microns
• Measurement of the Casimir force between parallel metallic surfaces
• Precise comparison of theory and new experiment for the Casimir force leads to stronger constraints on thermal quantum effects and long-range interactions
• Template-stripped gold surfaces with 0.4 nm rms roughness suitable for force measurements. Application to the Casimir force in the 20-100 nm range
• Constraining New Forces in the Casimir Regime Using the Isoelectronic Technique
• Casimir energies for massive fields in the bag
• Casimir effect for a $D$-dimensional sphere
• Exact Casimir interaction between eccentric cylinders
• Mode-by-mode summation for the zero point electromagnetic energy of an infinite cylinder
• Limits on Nonstandard Forces in the Submicrometer Range
• Casimir interaction between two concentric cylinders: exact versus semiclassical results
• Heat kernels and zeta-function regularization for the mass of the supersymmetric kink
• Fermionic Casimir effect for parallel plates in the presence of compact dimensions with applications to nanotubes
• No saturation of the quantum Bogomolnyi bound by two-dimensional supersymmetric solitons
• Direct mode summation for the Casimir energy of a solid ball
• Fermionic Casimir densities in toroidally compactified spacetimes with applications to nanotubes
• Thermal correction to the Casimir force, radiative heat transfer, and an experiment
• Casimir Energy for a Purely Dielectric Cylinder by the Mode Summation Method
• Casimir force between sharp-shaped conductors
• Heat kernel Coefficients and Divergencies of the Casimir Energy for the Dispersive Sphere
• Casimir effect within D=3+1 Maxwell-Chern-Simons electrodynamics
• Quantum and thermal Casimir interaction between a sphere and a plate: Comparison of Drude and plasma models
• Heavy Fermion Stabilization of Solitons in 1+1 Dimensions
• Casimir force between eccentric cylinders
• Nonvanishing quantum corrections to the mass and central charge of the N=2 vortex and BPS saturation
• One-loop surface tensions of (supersymmetric) kink domain walls from dimensional regularization
• General stationary charged black holes as charged particle accelerators
• Casimir effect between two spheres at small separations
• Local Casimir Energy For Solitons
• The Dirichlet Casimir effect for ${\varphi }^4$ theory in (3+1) dimensions: A new renormalization approach
• Spectral Zeta Functions for a Cylinder and a Circle
• A new renormalization approach to the Dirichlet Casimir effect for ϕ^4 theory in (1+1) dimensions
• Low noise cryogenic system for the measurement of Casimir energy in rigid cavities
• Semiclassical Scaling Functions of Sine--Gordon Model
• A Heavy Fermion Can Create a Soliton: A 1+1 Dimensional Example
• Casimir force in brane worlds: coinciding results from Green's and Zeta function approaches
• Casimir Energies of Cylinders: Universal Function
• Rigorous proof of attractive nature for Casimir force of p-odd hypercube
• Radiative Correction to the Dirichlet Casimir Energy for $\lambda {\varphi }^4$ Theory in Two Spatial Dimensions
• Quantum Kinks: Solitons at Strong Coupling
• A Direct Approach to the Electromagnetic Casimir Energy in a Rectangular Waveguide
• The Casimir effect for parallel plates involving massless Majorana fermions at finite temperature
• Dynamical Casimir effect with cylindrical waveguides
• Casimir Energy for a Coupled Fermion-Soliton System
• Fermionic Casimir effect with helix boundary condition
• Casimir Energy of 5D Electro-Magnetism and Sphere Lattice Regularization
• Exact Solutions of a Fermion-Soliton System in Two Dimensions
• The Casimir Effect in Spheroidal Geometries

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