arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2004.03714hep-thcond-mat.mes-hallhep-phquant-ph
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带电费米子对轴向磁通量恒定的二维虫洞的散射

Scattering of charged fermion to two-dimensional wormhole with constant axial magnetic flux

Kulapant Pimsamarn, Piyabut Burikham, Trithos Rojjanason

摘要:

研究了在恒定轴向磁通量作用下带电费米子与$(1+2)$维虫洞的散射.通过将Dirac方程的费米子解类在虫洞曲面空间中推广到包含具有实能量和动量的简正模,得到了费米子波向虫洞散射的量子选择定则.新发现的{ \it动量-角动量关系}表明,只有动量为量子化$k=m'/a\sqrt{q}$的费米子才能通过空穴传输。允许的动量与有效角动量量子数$m'$成正比,与虫洞喉道半径$a$成反比。有效角动量量子数的通量依赖性允许我们根据它们的动量来选择可以通过的费米子。一个守恒定律也自然地强制执行的入射,反射和透射波之间的幺正性条件。随后研究了费米子态的准正规模~(QNM)在虫洞中的散射。结果发现,通过虫洞的所有方案涉及QNM的传输波大多被抑制和衰减的时间。在QNM散射的情况下,不符合么正性条件,但建立了散射系数的更一般的关系。当磁通量$ϕ=mhc/e$,即,以磁通量量子$hc/e$为单位量子化,费米子将以零反射隧穿虫洞。

英文摘要:

Scattering of charged fermion with $(1+2)$-dimensional wormhole in the presence of constant axial magnetic flux is explored. By extending the class of fermionic solutions of the Dirac equation in the curved space of wormhole surface to include normal modes with real energy and momentum, we found a quantum selection rule for the scattering of fermion waves to the wormhole. The newly found {\it momentum-angular momentum relation} implies that only fermion with the quantized momentum $k=m'/a\sqrt{q}$ can be transmitted through the hole. The allowed momentum is proportional to an effective angular momentum quantum number $m'$ and inversely proportional to the radius of the throat of the wormhole $a$. Flux dependence of the effective angular momentum quantum number permits us to select fermions that can pass through according to their momenta. A conservation law is also naturally enforced in terms of the unitarity condition among the incident, reflected, and transmitted waves. The scattering involving quasinormal modes~(QNMs) of fermionic states in the wormhole is subsequently explored. It is found that the transmitted waves through the wormhole for all scenarios involving QNMs are mostly suppressed and decaying in time. In the case of QNMs scattering, the unitarity condition is violated but a more generic relation of the scattering coefficients is established. When the magnetic flux $ϕ=mhc/e$, i.e., quantized in units of the magnetic flux quantum $hc/e$, the fermion will tunnel through the wormhole with zero reflection.

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