Casimir effect at finite density

Fujii, Daisuke; Nakayama, Katsumasa*; Suzuki, Kei   

In this talk, I discuss the general features of the Casimir effect induced from quantum fields at finite chemical potential, particularly at finite density. Historically, the thermal Casimir effect has been well-established by the cooperation between theory and experiment, whereas its counterpart at finite chemical potential is still not. This is because it is usually difficult to control the chemical potential of photons in equilibrium experimentally. On the other hand, if one focuses on fermionic systems, their chemical potentials may be a tunable parameter for the Casimir effect. In addition, various quantum many-body phenomena realized at finite fermion density can modify the typical property of the Casimir effect. Within some theoretical frameworks, we evaluate the Casimir energy for Dirac fields at finite density and particularly show an oscillatory behavior as a function of the separation of boundary conditions or the chemical potential. As physical and realistic examples of the Casimir effect at finite chemical potential, I discuss applications to fermion fields inside thin dense quark matter in hadron physics and to Dirac/Weyl semimetal thin films in solid-state physics. Such materials will be platforms to examine the fermionic Casimir effect at finite chemical potential.