Autumn · project 15 of 20

The dynamical Casimir effect

Topic: Vacuum effects and boundaries

Goal: Study the creation of real quanta from the vacuum under nonstationary boundary conditions.

  1. Consider a one-dimensional scalar field \(\phi(t,x)\) with the boundary conditions \[\phi(t,0)=\phi(t,L(t))=0,\] where \[L(t)=L_0\bigl(1+\epsilon\sin\omega t\bigr).\]

  2. Find the instantaneous modes of the field and their frequencies \(\omega_n(t)\).

  3. Show that under the resonance condition \[\omega \approx 2\omega_n\] the number of quanta grows exponentially.

  4. Compute numerically the radiated energy as a function of time.

  5. Discuss the physics: where the energy of the created quanta comes from (the work of the external force that moves the boundary) and why energy is conserved.

Autumn: all projects, PDF

← All projects