501 research outputs found
Toda Fields on Riemann Surfaces: remarks on the Miura transformation
We point out that the Miura transformation is related to a holomorphic
foliation in a relative flag manifold over a Riemann Surface. Certain
differential operators corresponding to a free field description of
--algebras are thus interpreted as partial connections associated to the
foliation.Comment: AmsLatex 1.1, 10 page
Boundary states for a free boson defined on finite geometries
Langlands recently constructed a map that factorizes the partition function
of a free boson on a cylinder with boundary condition given by two arbitrary
functions in the form of a scalar product of boundary states. We rewrite these
boundary states in a compact form, getting rid of technical assumptions
necessary in his construction. This simpler form allows us to show explicitly
that the map between boundary conditions and states commutes with conformal
transformations preserving the boundary and the reality condition on the scalar
field.Comment: 16 pages, LaTeX (uses AMS components). Revised version; an analogy
with string theory computations is discussed and references adde
Recursion Relations in Liouville Gravity coupled to Ising Model satisfying Fusion Rules
The recursion relations of 2D quantum gravity coupled to the Ising model
discussed by the author previously are reexamined. We study the case in which
the matter sector satisfies the fusion rules and only the primary operators
inside the Kac table contribute. The theory involves unregularized divergences
in some of correlators. We obtain the recursion relations which form a closed
set among well-defined correlators on sphere, but they do not have a beautiful
structure that the bosonized theory has and also give an inconsistent result
when they include an ill-defined correlator with the divergence. We solve them
and compute the several normalization independent ratios of the well-defined
correlators, which agree with the matrix model results.Comment: Latex, 22 page
Efficient Numerical Schemes for Computing Cardiac Electrical Activation over Realistic Purkinje Networks: Method and Verification
We present a numerical solver for the fast conduction system in the heart using both a CPU and a hybrid CPU/GPU implementation. To verify both implementations, we construct analytical solutions and show that the L2-error is similar in both implementations and decreases linearly with the spatial step size. Finally, we test the performance of the implementations with networks of varying complexity, where the hybrid implementation is, on average, 5.8 times faster
The Number of Incipient Spanning Clusters in Two-Dimensional Percolation
Using methods of conformal field theory, we conjecture an exact form for the
probability that n distinct clusters span a large rectangle or open cylinder of
aspect ratio k, in the limit when k is large.Comment: 9 pages, LaTeX, 1 eps figure. Additional references and comparison
with existing numerical results include
Perturbation Theory in Two Dimensional Open String Field Theory
In this paper we develop the covariant string field theory approach to open
2d strings. Upon constructing the vertices, we apply the formalism to calculate
the lowest order contributions to the 4- and 5- point tachyon--tachyon tree
amplitudes. Our results are shown to match the `bulk' amplitude calculations of
Bershadsky and Kutasov. In the present approach the pole structure of the
amplitudes becomes manifest and their origin as coming from the higher string
modes transparent.Comment: 26 page
Critical interfaces of the Ashkin-Teller model at the parafermionic point
We present an extensive study of interfaces defined in the Z_4 spin lattice
representation of the Ashkin-Teller (AT) model. In particular, we numerically
compute the fractal dimensions of boundary and bulk interfaces at the
Fateev-Zamolodchikov point. This point is a special point on the self-dual
critical line of the AT model and it is described in the continuum limit by the
Z_4 parafermionic theory. Extending on previous analytical and numerical
studies [10,12], we point out the existence of three different values of
fractal dimensions which characterize different kind of interfaces. We argue
that this result may be related to the classification of primary operators of
the parafermionic algebra. The scenario emerging from the studies presented
here is expected to unveil general aspects of geometrical objects of critical
AT model, and thus of c=1 critical theories in general.Comment: 15 pages, 3 figure
The Spitzer Survey of Interstellar Clouds in the Gould Belt. VI. The Auriga-California Molecular Cloud observed with IRAC and MIPS
We present observations of the Auriga-California Molecular Cloud (AMC) at
3.6, 4.5, 5.8, 8.0, 24, 70 and 160 micron observed with the IRAC and MIPS
detectors as part of the Spitzer Gould Belt Legacy Survey. The total mapped
areas are 2.5 sq-deg with IRAC and 10.47 sq-deg with MIPS. This giant molecular
cloud is one of two in the nearby Gould Belt of star-forming regions, the other
being the Orion A Molecular Cloud (OMC). We compare source counts, colors and
magnitudes in our observed region to a subset of the SWIRE data that was
processed through our pipeline. Using color-magnitude and color-color diagrams,
we find evidence for a substantial population of 166 young stellar objects
(YSOs) in the cloud, many of which were previously unknown. Most of this
population is concentrated around the LkHalpha 101 cluster and the filament
extending from it. We present a quantitative description of the degree of
clustering and discuss the fraction of YSOs in the region with disks relative
to an estimate of the diskless YSO population. Although the AMC is similar in
mass, size and distance to the OMC, it is forming about 15 - 20 times fewer
stars.Comment: (30 pages, 17 figures (2 multipage figures), accepted for publication
in ApJ
State-Dependent Accessibility of the P-S6 Linker of Pacemaker (HCN) Channels Supports a Dynamic Pore-to-Gate Coupling Model
The hyperpolarization-activated cyclic nucleotide-modulated channel gene family (HCN1-4) encodes the membrane depolarizing current that underlies pacemaking. Although the topology of HCN resembles Kv channels, much less is known about their structure-function correlation. Previously, we identified several pore residues in the S5-P linker and P-loop that are externally accessible and/or influence HCN gating, and proposed an evolutionarily conserved pore-to-gate mechanism. Here we sought dynamic evidence by assessing the functional consequences of Cys-scanning substitutions in the unexplored P-S6 linker (residues 352–359), the HCN1-R background (that is, resistant to sulfhydryl-reactive agents). None of A352C, Q353C, A354C, P355C, V356C, S357C, M358C, or S359C produced functional currents; the loss-of-function of Q353C, A354C, S357C, and M358C could be rescued by the reducing agent dithiothreitol. Q353C, A354C, and S357C, but not M358C and HCN1-R, were sensitive to Cd2+ blockade (IC50 = 3–12 μM vs. >1 mM). External application of the positively charged covalent sulfhydryl modifier MTSET irreversibly reduced I−140mV of Q353C and A354C to 27.9 ± 3.4% and 58.2 ± 13.1% of the control, respectively, and caused significant steady-state activation shifts (∆V1/2 = –21.1 ± 1.6 for Q353C and −10.0 ± 2.9 mV for A354C). Interestingly, MTSET reactivity was also state dependent. MTSET, however, affected neither S357C nor M358C, indicating site specificity. Collectively, we have identified novel P-S6 residues whose extracellular accessibility was sterically and state dependent and have provided the first functional evidence consistent with a dynamic HCN pore-to-gate model
Entropy flow in near-critical quantum circuits
Near-critical quantum circuits are ideal physical systems for asymptotically
large-scale quantum computers, because their low energy collective excitations
evolve reversibly, effectively isolated from the environment. The design of
reversible computers is constrained by the laws governing entropy flow within
the computer. In near-critical quantum circuits, entropy flows as a locally
conserved quantum current, obeying circuit laws analogous to the electric
circuit laws. The quantum entropy current is just the energy current divided by
the temperature. A quantum circuit made from a near-critical system (of
conventional type) is described by a relativistic 1+1 dimensional relativistic
quantum field theory on the circuit. The universal properties of the
energy-momentum tensor constrain the entropy flow characteristics of the
circuit components: the entropic conductivity of the quantum wires and the
entropic admittance of the quantum circuit junctions. For example,
near-critical quantum wires are always resistanceless inductors for entropy. A
universal formula is derived for the entropic conductivity:
\sigma_S(\omega)=iv^{2}S/\omega T, where \omega is the frequency, T the
temperature, S the equilibrium entropy density and v the velocity of `light'.
The thermal conductivity is Real(T\sigma_S(\omega))=\pi v^{2}S\delta(\omega).
The thermal Drude weight is, universally, v^{2}S. This gives a way to measure
the entropy density directly.Comment: 2005 paper published 2017 in Kadanoff memorial issue of J Stat Phys
with revisions for clarity following referee's suggestions, arguments and
results unchanged, cross-posting now to quant-ph, 27 page
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