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Quantum Mechanics of a Rotating Billiard
Integrability of a square billiard is spontaneously broken as it rotates
about one of its corners. The system becomes quasi-integrable where the
invariant tori are broken with respect to a certain parameter, where E is the energy of the particle inside the billiard and
is the angular frequency of rotation of billiard. We study the system
classically and quantum mechanically in view of obtaining a correspondence in
the two descriptions. Classical phase space in Poincar\'{e} surface of section
shows transition from regular to chaotic motion as the parameter is
decreased. In the Quantum counterpart, the spectral statistics shows a
transition from Poisson to Wigner distribution as the system turns chaotic with
decrease in . The wavefunction statistics however show breakdown of
time-reversal symmetry as decreases
Shear viscosity of strongly interacting fermionic quantum fluids
Eighty years ago Eyring proposed that the shear viscosity of a liquid,
, has a quantum limit where is the density of
the fluid. Using holographic duality and the AdS/CFT correspondence in string
theory Kovtun, Son, and Starinets (KSS) conjectured a universal bound
for the ratio between the shear
viscosity and the entropy density, . Using Dynamical Mean-Field Theory
(DMFT) we calculate the shear viscosity and entropy density for a fermionic
fluid described by a single band Hubbard model at half filling. Our calculated
shear viscosity as a function of temperature is compared with experimental data
for liquid He. At low temperature the shear viscosity is found to be well
above the quantum limit and is proportional to the characteristic Fermi liquid
dependence, where is the temperature. With increasing temperature
and interaction strength there is significant deviation from the Fermi
liquid form. Also, the shear viscosity violates the quantum limit near the
crossover from coherent quasi-particle based transport to incoherent transport
(the bad metal regime). Finally, the ratio of the shear viscosity to the
entropy density is found to be comparable to the KSS bound for parameters
appropriate to liquid He. However, this bound is found to be strongly
violated in the bad metal regime for parameters appropriate to lattice
electronic systems such as organic charge transfer salts.Comment: Revised manuscript with added references, 14 pages 5 figure
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