Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

I'm working on a 2D He superfluid system with vortices. I was asked to calculate the kinetic energy of vortex-(anti-)vortex pairs and compare the two situations. One finds in literature that the vortex-vortex situation is unstable, and the vortex-antivortex pair can be stable. This is a crucial observation in what follows.

In the calculation of the energies, I came across a striking fact, which may or may not have any physical implications: the (kinetic) energy of the vortex-vortex situation had an imaginary component, while in the vortex-antivortex energy, everything imaginary nicely cancelled. It seems my results are consistent with what is expected, and certainly scale as they should for the system (energy logarithmically in the size of the system, and in the distance between the vorteces).

For now, I just "forgot" about the imaginary part of the energy, but my question is this: Can the imaginary part of the energy be interpreted as the lifetime of an unstable state in the case of a vortex-vortex situation (comparable to the lifetime of resonances in S-wave scattering, which also comes into play as the complex part of the energy of the resonance). Or is it merely a remnant of my approximate calculation and the result of logarithms in the complex plane and have I been staring at this too long?

Thanks!

PS: for those interested, the integration I performed can be viewed as a question on math.stackexchange.com. Please ignore the question itself, because it is not really an example of my intellect in this field, just some conjectures/"fleeting hope" ;) http://math.stackexchange.com/questions/32286/choosing-the-branch-of-a-logarithm

share|improve this question
    
To someone with enough rep: please add the tags "vortex", "superfluid", and "lifetime". Thanks! –  rubenvb Apr 11 '11 at 15:01

1 Answer 1

up vote 1 down vote accepted

Can the imaginary part of the energy be interpreted as the lifetime of an unstable state in the case of a vortex-vortex situation ... Yes. Vortices have repulsive interactions between them and cannot form bound states. So the result is physically reasonable. And complex energy eigenvalues do measure decay rates of resonances. This is shown in this article: "A Pedestrian Introduction to Gamow vectors". Gamow vectors are the eigenvectors corresponding to the complex energy eigenvalues.

[George Gamow was also a famous physics writer with books such as One, Two, Three Infinity and Physics: Foundations & Frontiers. Respect.]

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.