## Summary of Research Interests

The main theme in my research activities since my Ph.D.
has been the study of nonperturbative effects in
Quantum Mechanics and Field Theory. One important question that has been
addressed is the effect of complexity and chaotic behavior in
quantum systems. We showed in [2]
that answer to this question is in the correlations of the eigenvalues.
If the system is chaotic the spectral correlations do not depend on its
dynamics and are given by Random Matrix Theory.
This has been observed in
complex systems as varied as atomic nuclei, resonance cavities and the
zeros of the Riemann $\zeta$-function. Analytical results can be
obtained, for example, with the supersymmetric formalism [1].
More recently, we have applied these ideas to strongly interacting
Quantum Field Theories, in particular to QCD, the theory of the
Nuclear Forces. Typically,
nonperturbative effects in QCD are studied
in 4 Euclidean dimensions in which there is
no difference between space and time. The motion of a quark can then
be interpreted as motion in 4 spatial dimensions and 1 artificial time
dimension. One expects that its classical trajectories in the
quantum disordered Yang-Mills background field configurations
are chaotic. For example, this has been confirmed
by microcanonical simulations of lattice QCD.
From our experience with simple chaotic systems we thus expect that the
correlations of the QCD Dirac eigenvalues are given by Random Matrix Theory.
The study of this conjecture has been my main interest during the
past five years. The appropriate Random Matrix Theories have been
formulated [4] and classified
according to the global symmetries of the QCD partition function [6].
Analytical results have been derived [5] and the universality of these
results has been understood. These
ideas have been verified by explicit Monte-Carlo simulations of
the QCD partition function. Of course, the QCD partition function is much
richer than chiral Random Matrix Theory. This implies that there exists
a scale above which Random Matrix Theory is not applicable. We have identified
this scale as the equivalent of the Thouless energy in mesoscopic physics.
Other non-perturbative effects in Field Theory I have been interested in are
the study of instanton field configurations in QCD (for a summary we refer to
the page of Edward Shuryak), the study of nucleon as a topological Skyrmion
in the Skyrme model, and the study of particles with fractional statistics
(anyons). Specifically, I wish to mention
the discovery of the axially symmetric solution with
baryon number two in the Skyrme model [3].

#### Three most cited papers over all:

1. J.J.M. Verbaarschot, H.A. Weidenm\"uller and M.R. Zirnbauer,
* Grassmann integration in stochastic quantum physics:
the case of compound nucleus scattering*, Phys. Rep. {\bf 129}
(1985) 367 (323 citations)

2. T.H. Seligman, J.J.M. Verbaarschot and M.R. Zirnbauer, * Quantum
spectra and the transition from regular to chaotic classical
motion*, Phys. Rev. Lett. {\bf 53} (1984) 215 (180 citations)

3. J.J.M. Verbaarschot, * Axial symmetry of bound baryon number two
solution of the skyrme model*, Phys. Lett. {\bf B195} (1987) 235
(86 citations)

#### Three most cited papers written during the past ten years:

4. E.V. Shuryak and J.J.M. Verbaarschot, * Random matrix theory and
spectral sum rules for the Dirac operator in QCD*,
Nucl. Phys. {\bf A560} (1993) 306 (153 citations).

5. J.J.M. Verbaarschot and I. Zahed, * On the spectrum of the Dirac
operator in QCD near zero virtuality*, Phys. Rev. Lett. {\bf 70}
(1993) 3852 (133 citations).

6. J.J.M. Verbaarschot, * The spectrum of the QCD Dirac operator and
chiral random matrix theory: the threefold way*,
Phys. Rev. Lett. {\bf 72} (1994) 2531 (140 citations).