SciPost Phys. Core 4, 011 (2021) ·
published 4 May 2021
We derive an exact analytic expression for the high-temperature limit of the
Casimir interaction between two Drude spheres of arbitrary radii. Specifically,
we determine the Casimir free energy by using the scattering approach in the
plane-wave basis. Within a round-trip expansion, we are led to consider the
combinatorics of certain partitions of the round trips. The relation between
the Casimir free energy and the capacitance matrix of two spheres is discussed.
Previously known results for the special cases of a sphere-plane geometry as
well as two spheres of equal radii are recovered. An asymptotic expansion for
small distances between the two spheres is determined and analytical
expressions for the coefficients are given.
SciPost Phys. Core 4, 010 (2021) ·
published 29 April 2021
We study an effective Hamiltonian generating time evolution of states on
intermediate time scales in the strong-coupling limit of the spin-1/2 XXZ
model. To leading order, it describes an integrable model with local
interactions. We solve it completely by means of a coordinate Bethe Ansatz that
manifestly breaks the translational symmetry. We demonstrate the existence of
exponentially many jammed states and estimate their stability under the leading
correction to the effective Hamiltonian. Some ground state properties of the
model are discussed.