# Is anyone here familiar with the dynamical Casimir effect?

## Main Question or Discussion Point

Just wondering if anyone here is familiar with the dynamical Casimir effect? It's part of my dissertation and have a couple of questions.

I've read that the photons produced are "always pair-produced from the vacuum in two-mode squeezed states, not in coherent states."

Since only one photon is detected can we simply say one is observable while the other is not?

Eberlein uses "an adiabatic approximation" in her calculations, this has nothing to do with an adiabatic process (as far as im aware) but is a method used for determining the result. Could someone perhaps give any insight into the term "adiabatic approximation" in terms of quantum mechanics, to what does it infer?

thanks for any ideas!

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Matterwave
Gold Member
I am not familiar with the Casimir effect (except for roughly what it is), but I can say that the "adiabatic approximation" in QM usually refers to slowly time-evolving system. In the case that the Hamiltonian is said to slowly change in time (compared with the intrinsic frequencies of the system), the system will stay, approximately, in the instantaneous eigenstates of the system. As the Hamiltonian evolves to its final state, the adiabatic approximation tells you that the system will be approximately in the corresponding eigenstate to whichever eigenstate it started out in. For example, if the system started out in the ground state, it will remain in the ground state of the new system.
However, the quantum system can pick up an additional Berry phase from this slow evolution of the Hamiltonian.

The usual example given, from a classical mechanics analogy, is the case of a pendulum with a time-varying string length (think, a pendulum attached to a ceiling with a hole where someone can pull on the string to make it shorter). If the length of the string changes very slowly, the pendulum will still approximately undergo simple harmonic motion with the new intrinsic frequency. But if the string is pulled on very quickly, the pendulum will undergo chaotic motion.

I am not familiar with the Casimir effect (except for roughly what it is), but I can say that the "adiabatic approximation" in QM usually refers to slowly time-evolving system. In the case that the Hamiltonian is said to slowly change in time (compared with the intrinsic frequencies of the system), the system will stay, approximately, in the instantaneous eigenstates of the system. As the Hamiltonian evolves to its final state, the adiabatic approximation tells you that the system will be approximately in the corresponding eigenstate to whichever eigenstate it started out in. For example, if the system started out in the ground state, it will remain in the ground state of the new system.
However, the quantum system can pick up an additional Berry phase from this slow evolution of the Hamiltonian.

The usual example given, from a classical mechanics analogy, is the case of a pendulum with a time-varying string length (think, a pendulum attached to a ceiling with a hole where someone can pull on the string to make it shorter). If the length of the string changes very slowly, the pendulum will still approximately undergo simple harmonic motion with the new intrinsic frequency. But if the string is pulled on very quickly, the pendulum will undergo chaotic motion.

could i just ask, if it's the slow evolution of a time-evolving system then why is the word adiabatic used?

Matterwave
Gold Member

could i just ask, if it's the slow evolution of a time-evolving system then why is the word adiabatic used?
I have always wondered this myself. I thought it's called adiabatic because the state will remain in an energy eigenstate. Although energy can be deposited or removed from the system by changing the energy of the eigenstates themselves, the system itself will not, for example, move to a higher energy eigenstate.

However, Wikipedia seems to say that the term used in QM is simply unrelated to the "adiabatic" we are familiar with from Thermodynamics: "Note that the term "adiabatic" is traditionally used in thermodynamics to describe processes without the exchange of heat between system and environment (see adiabatic process). The quantum mechanical definition is closer to the thermodynamical concept of a quasistatic process, and has no direct relation with heat exchange."

excellent thanks! its even more confusing when you are considering sonoluminescence of which one of the possible mechanisms is a "real" thermodynamic adiabatic compression lol