ELFT HÍRADÓ

["Fodor Gyula" <gfodor AT rmki.kfki.hu>]

 KFKI RMKI Elméleti Főosztály Szemináriuma


 Tisztelettel meghívjuk

                  Petr Jizba
 (FNSPE, Czech Technical Un., Prague & ITP, Freie Un., Berlin)

"Path integrals and superstatistics paradigm"

         címmel tartandó szemináriumára.


 Helye: KFKI RMKI III. ép. Tanácsterem
 Ideje: 2008. október 3. péntek du 14.00 óra

Kivonat:

Probability distributions which can be obtained from superpositions of
Gaussian distributions of different variances "v" play presently a favored
role in quantum mechanics and in theory financial markets [1]. In general,
such superpositions do not necessarily obey the
Chapman-Kolmogorov semigroup relation for Markovian processes because they
often introduce memory effects. In this talk I derive the general form of
the smearing distributions in "v" which do not destroy the semigroup
property. The presented smearing technique has two immediate applications
which I wish to discuss [2,3].
Firstly, the approach permits simplifying the system of Kramers-Moyal (and
Fokker-Planck) equations for smeared and unsmeared conditional
probabilities. In the latter case the dynamics of the smearing
distribution is explicitly separated from the dynamics of the
transitional amplitude which a desirable starting point, for instance, in
quantum optics or in superstatistics.
Secondly, the smearing technique can be conveniently implemented in the
path integral calculus. This is because in many cases, the
superposition of path integrals can be evaluated much easier than the
initial path integral. To put some flesh on the bar bones I will
present three simple examples [2,3]; "microcanonical" smearing,
Heston's stochastic volatility model and relativistic scalar particle. I
will also briefly comment on the possibility of extension
of the presented technique to quantum mechanics and quantum field
theory. Finally, some comments will be also added on a natural
appearance of the Tsallis distribution in the scheme.[1]

[1] P. Jizba and H. Kleinert, arXiv:0708.3012[physics.soc-ph].
[2] P. Jizba and H. Kleinert, arXiv:0712.0083[cond-mat.stat-mech]. [3] P.
Jizba and H. Kleinert, arXiv:0802.0695[cond-mat.other]&
Phys. Rev. E 78 (2008) 031122


Szívesen látunk minden érdeklődőt.
                                          Fodor Gyula