36,238 research outputs found
Eigenstate entanglement in the Sachdev-Ye-Kitaev model
We study the entanglement entropy of eigenstates (including the ground state)
of the Sachdev-Ye-Kitaev model. We argue for a volume law, whose coefficient
can be calculated analytically from the density of states. The coefficient
depends on not only the energy density of the eigenstate but also the subsystem
size. Very recent numerical results of Liu, Chen, and Balents confirm our
analytical results
Effective conductivity of composites of graded spherical particles
We have employed the first-principles approach to compute the effective
response of composites of graded spherical particles of arbitrary conductivity
profiles. We solve the boundary-value problem for the polarizability of the
graded particles and obtain the dipole moment as well as the multipole moments.
We provide a rigorous proof of an {\em ad hoc} approximate method based on the
differential effective multipole moment approximation (DEMMA) in which the
differential effective dipole approximation (DEDA) is a special case. The
method will be applied to an exactly solvable graded profile. We show that DEDA
and DEMMA are indeed exact for graded spherical particles.Comment: submitted for publication
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