4,861 research outputs found
Universal deformation rings and tame blocks
Let k be an algebraically closed field of positive characteristic, and let W
be the ring of infinite Witt vectors over k. Suppose G is a finite group and B
is a block of kG of infinite tame representation type. We find all finitely
generated kG-modules V that belong to B and whose endomorphism ring is
isomorphic to k and determine the universal deformation ring R(G,V) for each of
these modules.Comment: 14 page
Quantum reservoirs with ion chains
Ion chains are promising platforms for studying and simulating quantum
reservoirs. One interesting feature is that their vibrational modes can mediate
entanglement between two objects which are coupled through the vibrational
modes of the chain. In this work we analyse entanglement between the transverse
vibrations of two heavy impurity defects embedded in an ion chain, which is
generated by the coupling with the chain vibrations. We verify general scaling
properties of the defects dynamics and demonstrate that entanglement between
the defects can be a stationary feature of these dynamics. We then analyse
entanglement in chains composed of tens of ions and propose a measurement
scheme which allows one to verify the existence of the predicted entangled
state.Comment: 14 pages, 12 figure
Spontaneous nucleation of structural defects in inhomogeneous ion chains
Structural defects in ion crystals can be formed during a linear quench of
the transverse trapping frequency across the mechanical instability from a
linear chain to the zigzag structure. The density of defects after the sweep
can be conveniently described by the Kibble-Zurek mechanism. In particular, the
number of kinks in the zigzag ordering can be derived from a time-dependent
Ginzburg-Landau equation for the order parameter, here the zigzag transverse
size, under the assumption that the ions are continuously laser cooled. In a
linear Paul trap the transition becomes inhomogeneous, being the charge density
larger in the center and more rarefied at the edges. During the linear quench
the mechanical instability is first crossed in the center of the chain, and a
front, at which the mechanical instability is crossed during the quench, is
identified which propagates along the chain from the center to the edges. If
the velocity of this front is smaller than the sound velocity, the dynamics
becomes adiabatic even in the thermodynamic limit and no defect is produced.
Otherwise, the nucleation of kinks is reduced with respect to the case in which
the charges are homogeneously distributed, leading to a new scaling of the
density of kinks with the quenching rate. The analytical predictions are
verified numerically by integrating the Langevin equations of motion of the
ions, in presence of a time-dependent transverse confinement. We argue that the
non-equilibrium dynamics of an ion chain in a Paul trap constitutes an ideal
scenario to test the inhomogeneous extension of the Kibble-Zurek mechanism,
which lacks experimental evidence to date.Comment: 19 pages, 5 figure
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