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UID:1-275@lptms.universite-paris-saclay.fr
DTSTART:20140924T100000Z
DTEND:20140924T130000Z
DTSTAMP:20140911T105525Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/soutenance-de-the
se-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 \;
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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