Register to reply

Numerical real-space, real-time green's functions?

Share this thread:
icwchan
#1
Jun7-11, 12:18 PM
P: 6
Is there any numerical work on Green's functions in real-space and real-time?

The reason I ask is that it seem the self-energy diagrams correspond to much simpler expressions in space-time than in energy-momentum. However, I suspect the space-time greens functions are sort of pathological.

eg. (retarded) free particle Green's function in energy-momentum

[tex] G\left(k,E\right)=\frac{1}{E-E_{k}+i\eta}, E_{k}=\frac{\hbar^{2}k^{2}}{2m} [/tex]

seems nicely behaved, could be conceivably be numerically represented on a rectangular mesh of E and Ek values, for nonvanishing eta (suppose there's some scattering in the system).

But in space-time, it becomes a numerical abomination:

[tex]G\left(r,t\right)=\Theta\left(t\right)e^{-\eta t}\left(\frac{m}{2\pi i\hbar t}\right)^{3/2}\exp\left(-\frac{mr^{2}}{2i\hbar t}\right) [/tex]

Maybe the above expression is okay for analytical work, but how on earth does one represent it numerically? The space coordinate seems to require a t-dependent grid to avoid aliasing in space... but maybe this is doomed anyway because the oscillation frequency in space is infinite for as t approaches zero.

I'm aware that real-space, *imaginary*-time methods are popular with some models, but my own googling hasn't been fruitful on results for real-time. Any thoughts would be appreciated.
Phys.Org News Partner Physics news on Phys.org
UCI team is first to capture motion of single molecule in real time
And so they beat on, flagella against the cantilever
Tandem microwave destroys hazmat, disinfects

Register to reply

Related Discussions
No real purpose in space-time? Special & General Relativity 37
Metric space of all bounded real functions is complete Calculus & Beyond Homework 6
Fabric of space-time real? Astronomy & Astrophysics 9