Dirac equation in 2-dimensional curved spacetime, particle creation, and coupled waveguide arrays

详细信息    查看全文

• 作者：Christian Koke^a ; ^{christian.koke@stud.uni-heidelberg.de" class="auth_mail" title="E-mail the corresponding author} ; Changsuk Noh^b ; ^{changsuk@kias.re.kr" class="auth_mail" title="E-mail the corresponding author} ; Dimitris G. Angelakis^c ; ^d ; ^{dimitris.angelakis@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Optical simulation ; Coupled waveguide array ; Curved spacetime ; Dirac equation ; Particle creation
• 刊名：Annals of Physics
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：374
• 期：Complete
• 页码：162-178
• 全文大小：831 K

文摘

When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. A gravitational field can be incorporated as a background spacetime if the back-action of matter on the field can be neglected, resulting in modifications of the Dirac or Klein–Gordon equations for elementary fermions and bosons respectively. The semi-classical description predicts particle creation in many situations, including the expanding-universe scenario, near the event horizon of a black hole (the Hawking effect), and an accelerating observer in flat spacetime (the Unruh effect). In this work, we give a pedagogical introduction to the Dirac equation in a general 2D spacetime and show examples of spinor wave packet dynamics in flat and curved background spacetimes. In particular, we cover the phenomenon of particle creation in a time-dependent metric. Photonic analogs of these effects are then proposed, where classical light propagating in an array of coupled waveguides provides a visualisation of the Dirac spinor propagating in a curved 2D spacetime background. The extent to which such a single-particle description can be said to mimic particle creation is discussed.