[seminar] J. Feinberg, 19.08. (ponedjeljak) 11h (c.t.), seminar ZTF-a

[Kornelija Passek-Kumericki]

                        SEMINAR  TEORIJSKE  FIZIKE


    (Zajednički seminari Fizičkog odsjeka PMF-a te Zavoda za teorijsku
     fiziku i Zavoda za eksperimentalnu fiziku IRB-a)

----------------------------------------------------------------------


Density of Eigenvalues in a generalized Joglekar-Karr Quasi-Hermitian
Matrix Model


Joshua Feinberg
Technion, Israel


    Datum:  ponedjeljak, 19. rujna 2016.
    Vrijeme: 11 sati c.t.
    Mjesto: IRB, seminar ZTFa



Sazetak:

We discuss a slight generalization of the model of random quasi-hermitian
matrices introduced by Joglekar and Karr several years ago in
Phys. Rev. E83 (2011) 031122.
This generalized ensemble is comprised of $N\times N$
matrices $M=AF$, where $A$ is a complex-hermitian matrix drawn from
the $U(N)$-invariant probability distribution
$P(A) = {1\over Z} \exp [-N{\rm Tr} V(A)]$
($Z$ is a normalization factor and $V(A)$ is typically some polynomial), and
$F$ is a strictly-positive hermitian matrix. (In the original Joglekar-Karr
model, $A$ was taken to be a  Gaussian random matrix.)  With no loss of
generality (due to $U(N)$ symmetry), $F$ can be taken to be diagonal.
The matrix $M$ is non-hermitian, of course, but can be brought to a
hermitian form $H = \sqrt{F} A \sqrt{F}$ by means of a similarity
transformation. All its eigenvalues are therefore real.
Bringing some powerful tools of Random Matrix Theory to bear, we obtain,
in the large-$N$ limit, explicit analytical expressions for the density
of eigenvalues of $M$.



Voditeljica seminara: Kornelija Passek-Kumericki (passek at irb dot hr)
-------------- next part --------------
A non-text attachment was scrubbed...
Name: sem-20160919-Feinberg.pdf
Type: application/pdf
Size: 75519 bytes
Desc: 
URL: <http://www.phy.pmf.unizg.hr/pipermail/seminar/attachments/20160914/44945346/attachment-0001.pdf>