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UID:1-275@lptms.universite-paris-saclay.fr
DTSTART:20140924T100000Z
DTEND:20140924T130000Z
DTSTAMP:20140911T105525Z
URL:https://www.lptms.universite-paris-saclay.fr/seminars/soutenance-de-th
 ese-yasar-atas/
SUMMARY:Soutenance de thèse : Yasar Atas - LPTMS-batiment 100\, salle des 
 conseils - 24 Sep 14 10:00
DESCRIPTION:Some aspects of quantum chaos in many body interacting systems.
  Quantum spin chain and random matrices.\nYasar Atas\, LPTMS\nMy thesis is
  devoted to the study of some aspects of many body quantum interacting sys
 tems. In particular we focus on quantum spin chains. I addressed especiall
 y questions related to the structure of eigenfunctions\, the level densiti
 es and the spectral properties of spin chain Hamiltonians.\nIt is known th
 at the level densities of most integrable models tend to the Gaussian in t
 he thermodynamic limit. However\, it appears that in certain limits of cou
 pling of the spin chain to the magnetic field and for finite number of spi
 ns on the chain\, one observes peaks in the level density.  I show that t
 he knowledge of the first two moments of the Hamiltonian in the degenerate
  subspace associated with each peak gives a good approximation to the leve
 l density both in the case of integrable and non integrable models.\nNext\
 , I study the statistical properties of the eigenvalues of spin chain Hami
 ltonians. One of the main achievements in the study of the spectral statis
 tics of quantum complex systems concerns the universal behaviour of the fl
 uctuation of measure such as the distribution of spacing between two conse
 cutive eigenvalues. By following the Wigner surmise for the computation of
  the level spacing distribution\, I obtained approximation for the distrib
 ution of the ratio of consecutive level spacings in the three canonical en
 sembles of random matrices. The prediction are compared with numerical res
 ults obtained by exact diagonalization of spin Hamiltonians and with zeros
  of the Riemann zeta function showing excellent agreement.\nFinally\, I in
 vestigate eigenfunction statistics of some canonical spin-chain Hamiltonia
 ns. Eigenfunctions together with the energy spectrum are the fundamental o
 bjects of quantum systems: their structure is quite complicated and not we
 ll understood. Due to the exponential growth of the size of the Hilbert sp
 ace\, the study of eigenfunctions is a very difficult task from both analy
 tical and numerical points of view. I demonstrate that the groundstate eig
 enfunctions of all canonical models of spin chain are multifractal\, by co
 mputing numerically the Rényi entropy and extrapolating it to obtain the 
 multifractal dimensions.\nKey words: Quantum spin chains\, quantum Ising m
 odel\, spectral statistics\, level density\, quantum chaos\, random matric
 es\, Wigner surmise\, spacing distribution\, multifractality\, Rényi entr
 opy.\n&nbsp\;
LOCATION:LPTMS-batiment 100\, salle des conseils\, 15 Rue Georges Clemencea
 u\, Orsay\, France
GEO:48.698200;2.181770
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=15 Rue Georges Clemenceau\,
  Orsay\, France;X-APPLE-RADIUS=100;X-TITLE=LPTMS-batiment 100\, salle des 
 conseils:geo:48.698200,2.181770
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