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.

Please, I would like to understand why you call the function $A(k,\omega)$ (here :The Spectral Function in Many-Body Physics and its Relation to Quasiparticles ) a spectral function? For me, as a mathematician, a spectral function is a function which writes : $F(S)=f( \lambda(S))$ where for example $S$ is a symmetric matrix and $\lambda(S)$ is the vector of eigenvalues of $S$. Thank you in advance, Sincerely.

share|improve this question

2 Answers 2

If you perform spectroscopy on a material (be it angular resolved photoemission spectroscopy (ARPES) or scanning tunneling spectroscopy (STS) or whatever method you fancy), the quantity you measure is roughly related to $A(k,\omega)$ (with additional prefactors and matrix elements depending on your method of choice.

Thus, performing spectroscopy on a sample provides you with information on $A(k,\omega)$, and hence we call it the spectral function.

share|improve this answer

The spectral function in physics tells you the probability that a particle with a certain momentum $k$ has a specific energy $\omega$. In other words, due to the Heisenberg uncertainty relation, a particle can have an energy that is distributed around a mean. The spectral function $A(k,\omega)$ describes exactly this distribution.

Therefore, in physics $\lambda(S)$ should translate into a vector that contains all the Eigenenergies of the respective system. Then the function $f(\lambda)$ should denote the distribution of energies a particle may have.

The answer given by Lagerbaer is most correct from a spectroscopist's point of view. One always measures a spectrum of energies. And the reason why one sees a spectrum of energies, is related to the uncertainty of the energy of a particle in a specific state. This distribution is just captured by the spectral function $A(k,\omega)$.

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.