10 research outputs found
Non-dissipative thermal transport in the massive regimes of the XXZ chain
We present exact results on the thermal conductivity of the one-dimensional
spin-1/2 XXZ model in the massive antiferromagnetic and ferromagnetic regimes.
The thermal Drude weight is calculated by a lattice path integral formulation.
Numerical results for wide ranges of temperature and anisotropy as well as
analytical results in the low and high temperature limits are presented. At
finite temperature, the thermal Drude weight is finite and hence there is
non-dissipative thermal transport even in the massive regime. At low
temperature, the thermal Drude weight behaves as where is the one-spinon (respectively
one-magnon) excitation energy for the antiferromagnetic (respectively
ferromagnetic) regime.Comment: 16 page
Consequences of converting graded to action potentials upon neural information coding and energy efficiency
Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na+ and K+ channels, with generator potential and graded potential models lacking voltage-gated Na+ channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na+ channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a ‘footprint’ in the generator potential that obscures incoming signals. These three processes reduce information rates by ~50% in generator potentials, to ~3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation
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On coverings of ellipsoids in Euclidean spaces
The thinnest coverings of ellipsoids are studied in the Euclidean spaces of an arbitrary dimension n. Given any ellipsoid, the main goal is to find its epsilon-entropy, which is the logarithm of the minimum number of the balls of radius e needed to cover this ellipsoid. A tight asymptotic bound on the epsilon-entropy is obtained for all but the most oblong ellipsoids, which have very high eccentricity. This bound depends only on the volume of the sub-ellipsoid spanned over all the axes of the original ellipsoid, whose length (diameter) exceeds 2\epsilon. The results can be applied to vector quantization performed when data streams from different sources are bundled together in one block