Hot dense magnetized ultrarelativistic spinor matter in a slab

Properties of hot dense ultrarelativistic spinor matter in a slab of finite width, placed in a transverse uniform magnetic field, are studied. The admissible set of boundary conditions is determined by the requirement that spinor matter be confined inside the slab. In thermal equilibrium, the chiral separation effect in the slab is shown to depend on both temperature and chemical potential; this is distinct from the unrealistic case of the magnetic field filling the unbounded (infinite) medium, when the effect is temperature independent. In the realistic case of the slab, a stepwise behavior of the axial current density at zero temperature is smoothed out as temperature increases, turning into a linear behavior at infinitely large temperature. A choice of boundary conditions can facilitate either augmentation or attenuation of the chiral separation effect; in particular, the effect can persist even at zero chemical potential, if temperature is finite. Thus the boundary condition can serve as a source that is additional to the spinor matter density.

Figure 1

Contour $C_{\subset }$ enclosing the positive real semiaxis can be continuously deformed into a contour consisting of vertical lines on the complex $\omega$ plane; positions of simple poles of the integrand are indicated by crosses.

Figure 2

Poles on the complex plane are on the imaginary axis. Contour enclosing infinite number of poles on the positive real semiaxis is deformed into a contour which is infinitesimally close from the right to the imaginary axis.

Figure 3

Finite number of poles on the real axis at $-s<w<s$ is enclosed by two separate contours. Poles on the complex plane are on a vertical axis at $w=-s$. The right closed contour is deformed into a contour consisting of two vertical lines at $w=-s+\pi$ and $w=s$.

Figure 4

Contour enclosing an infinite number of poles on the real axis at $s<w<\infty$ is deformed into a contour consisting of a vertical line at $w=s$.

Figure 5

Infinite number of poles on the real axis at $s<w<\infty$ is enclosed by two separate contours, and the right one is deformed into a contour consisting of a vertical line at $w=s+\pi$. Poles on the complex plane are on a vertical line at $w=s$.