6,526 research outputs found
Normal Coordinates and Primitive Elements in the Hopf Algebra of Renormalization
We introduce normal coordinates on the infinite dimensional group
introduced by Connes and Kreimer in their analysis of the Hopf algebra of
rooted trees. We study the primitive elements of the algebra and show that they
are generated by a simple application of the inverse Poincar\'e lemma, given a
closed left invariant 1-form on . For the special case of the ladder
primitives, we find a second description that relates them to the Hopf algebra
of functionals on power series with the usual product. Either approach shows
that the ladder primitives are given by the Schur polynomials. The relevance of
the lower central series of the dual Lie algebra in the process of
renormalization is also discussed, leading to a natural concept of
-primitiveness, which is shown to be equivalent to the one already in the
literature.Comment: Latex, 24 pages. Submitted to Commun. Math. Phy
Probing many-body localization in a disordered quantum magnet
Quantum states cohere and interfere. Quantum systems composed of many atoms
arranged imperfectly rarely display these properties. Here we demonstrate an
exception in a disordered quantum magnet that divides itself into nearly
isolated subsystems. We probe these coherent clusters of spins by driving the
system beyond its linear response regime at a single frequency and measuring
the resulting "hole" in the overall linear spectral response. The Fano shape of
the hole encodes the incoherent lifetime as well as coherent mixing of the
localized excitations. For the disordered Ising magnet,
, the quality factor for spectral holes
can be as high as 100,000. We tune the dynamics of the quantum degrees of
freedom by sweeping the Fano mixing parameter through zero via the
amplitude of the ac pump as well as a static external transverse field. The
zero-crossing of is associated with a dissipationless response at the drive
frequency, implying that the off-diagonal matrix element for the two-level
system also undergoes a zero-crossing. The identification of localized
two-level systems in a dense and disordered dipolar-coupled spin system
represents a solid state implementation of many-body localization, pushing the
search forward for qubits emerging from strongly-interacting, disordered,
many-body systems.Comment: 22 pages, 6 figure
Interplay of disorder and geometrical frustration in doped Gadolinium Gallium Garnet
The geometrically-frustrated, triangular antiferromagnet GGG exhibits a rich
mix of short-range order and isolated quantum states. We investigate the
effects of up to 1% Neodymium substitution for Gallium on the ac magnetic
response at temperatures below 1 K in both the linear and nonlinear regimes.
Substitutional disorder actually drives the system towards a more perfectly
frustrated state, apparently compensating for the effect of imperfect
Gadolinium/Gallium stoichiometry, while at the same time more closely
demarcating the boundaries of isolated, coherent clusters composed of hundreds
of spins. Optical measurements of the local Nd environment substantiate the
picture of an increased frustration index with doping.Comment: 5 pages, 5 figure
Quantum and Classical Glass Transitions in
When performed in the proper low field, low frequency limits, measurements of
the dynamics and the nonlinear susceptibility in the model Ising magnet in
transverse field, , prove the existence
of a spin glass transition for = 0.167 and 0.198. The classical behavior
tracks for the two concentrations, but the behavior in the quantum regime at
large transverse fields differs because of the competing effects of quantum
entanglement and random fields.Comment: 5 pages, 5 figures. Updated figure 3 with corrected calibration
information for thermometr
Continuous and Discontinuous Quantum Phase Transitions in a Model Two-Dimensional Magnet
The Shastry-Sutherland model, which consists of a set of spin 1/2 dimers on a
2-dimensional square lattice, is simple and soluble, but captures a central
theme of condensed matter physics by sitting precariously on the quantum edge
between isolated, gapped excitations and collective, ordered ground states. We
compress the model Shastry-Sutherland material, SrCu2(BO3)2, in a diamond anvil
cell at cryogenic temperatures to continuously tune the coupling energies and
induce changes in state. High-resolution x-ray measurements exploit what
emerges as a remarkably strong spin-lattice coupling to both monitor the
magnetic behavior and the absence or presence of structural discontinuities. In
the low-pressure spin-singlet regime, the onset of magnetism results in an
expansion of the lattice with decreasing temperature, which permits a
determination of the pressure dependent energy gap and the almost isotropic
spin-lattice coupling energies. The singlet-triplet gap energy is suppressed
continuously with increasing pressure, vanishing completely by 2 GPa. This
continuous quantum phase transition is followed by a structural distortion at
higher pressure.Comment: 16 pages, 4 figures. Accepted for publication in PNA
Strange Quarks Nuggets in Space: Charges in Seven Settings
We have computed the charge that develops on an SQN in space as a result of
balance between the rates of ionization by ambient gammas and capture of
ambient electrons. We have also computed the times for achieving that
equilibrium and binding energy of the least bound SQN electrons. We have done
this for seven different settings. We sketch the calculations here and give
their results in the Figure and Table II; details are in the Physical Review
D.79.023513 (2009).Comment: Six pages, one figure. To appear in proceedings of the 2008 UCLA
coference on dark matter and dark energ
Quantum Barkhausen Noise Induced by Domain Wall Co-Tunneling
Most macroscopic magnetic phenomena (including magnetic hysteresis) are
typically understood classically. Here, we examine the dynamics of a uniaxial
rare-earth ferromagnet deep within the quantum regime, so that domain wall
motion, and the associated hysteresis, is dominated by large-scale quantum
tunneling of spins, rather than classical thermal activation over a potential
barrier. The domain wall motion is found to exhibit avalanche dynamics,
observable as an unusual form of Barkhausen noise. We observe non-critical
behavior in the avalanche dynamics that only can be explained by going beyond
traditional renormalization group methods or classical domain wall models. We
find that this ``quantum Barkhausen noise'' exhibits two distinct mechanisms
for domain wall movement, each of which is quantum-mechanical, but with very
different dependences on an external magnetic field applied transverse to the
spin (Ising) axis. These observations can be understood in terms of the
correlated motion of pairs of domain walls, nucleated by co-tunneling of
plaquettes (sections of domain wall), with plaquette pairs correlated by
dipolar interactions; this correlation is suppressed by the transverse field.
Similar macroscopic correlations may be expected to appear in the hysteresis of
other systems with long-range interactions.Comment: 11 pages, 4 figure
Inference with interference between units in an fMRI experiment of motor inhibition
An experimental unit is an opportunity to randomly apply or withhold a
treatment. There is interference between units if the application of the
treatment to one unit may also affect other units. In cognitive neuroscience, a
common form of experiment presents a sequence of stimuli or requests for
cognitive activity at random to each experimental subject and measures
biological aspects of brain activity that follow these requests. Each subject
is then many experimental units, and interference between units within an
experimental subject is likely, in part because the stimuli follow one another
quickly and in part because human subjects learn or become experienced or
primed or bored as the experiment proceeds. We use a recent fMRI experiment
concerned with the inhibition of motor activity to illustrate and further
develop recently proposed methodology for inference in the presence of
interference. A simulation evaluates the power of competing procedures.Comment: Published by Journal of the American Statistical Association at
http://www.tandfonline.com/doi/full/10.1080/01621459.2012.655954 . R package
cin (Causal Inference for Neuroscience) implementing the proposed method is
freely available on CRAN at https://CRAN.R-project.org/package=ci
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