Dynamic Casimir Effect

Jalal SarabadaniIASBS

May 2007, IPM

***************

July,1909 May, 2000

***************

motivationthe Casimir effectmode summation

dynamic Casimir effectcavity with two conducting platescavity with conducting and permeable plates

***************

motivation

***************

The Casimir force can be measured if the mirrors are within microns of each other [1]

weight of the water droplet

[1] A. Lambrecht, Phys. World, 29, september (2002).[2] E. Buks and M. L. Roukes and et.al., PRB 63, 033402 (2001),

Nature (London) 419, 119 (2002).

The Casimir force can cause the tiny elements inMicroelectromechanical systems (MEMS) to stick together

[2]

***************

the Casimir effect [3]mode summation

The zero point energy inside the cavity is:

[3] H. B. G. Casimir, Proc. K. Akad. Wet. 51, 793 (1948).

***************

The potential energy of the system whenthe plates are separated by a distance d is

The attractive force per unit area between the plates is

This is the Casimir force.

***************

dynamic Casimir effectcavity with two conducting plates [4]

Path-integral formalism

[4] T. Emig et al, PRA 67, 022114 (2003).

***************

Substituting Delta functionsPerforming the Gaussian integration over the

field

***************

The perpendicular forces exerted on each plate

The dissipation rate

***************

Our result using path integral formalism [5]

Result of Neto [6] using second quantization formalism

[5] J. Sarabadani and M. F. Miri, PRA 74, 023801 (2006).[6] D.F. Mundarain and P. A. Maia Neto, PRA 57, 1379 (1998).

***************

Perpendicular motion of two plates Using the Neumann B.C. [5]

Perpendicular motion of two plates Using the Dirichlet B.C. [5]

***************

dynamic Casimir effectcavity with conducting and permeable plates

[7]Second quantization formalism

[7] J. Sarabadani and M. F. Miri, Accepted in PRA (2007).

cavity with two conducting plates [5]Perpendicular motion of two plates Using the Dirichlet and Neumann B.C. in a cavity [7]

***************

-Static Casimir force between two parallel nanotubes

-Static Casimir force between a nanotube and a rough plate

-Static Casimir force at finite temperature for a cavity

***************

***************