The fluctuation spectra around a Gaussian classical solution of a tensor model and the general relativity

Tensor models can be interpreted as theory of dynamical fuzzy spaces. In this paper, I study numerically the fluctuation spectra around a Gaussian classical solution of a tensor model, which represents a fuzzy flat space in arbitrary dimensions. It is found that the momentum distribution of the low-lying low-momentum spectra is in agreement with that of the metric tensor modulo the general coordinate transformation in the general relativity at least in the dimensions studied numerically, i.e. one to four dimensions. This result suggests that the effective field theory around the solution is described in a similar manner as the general relativity.Comment: 29 pages, 13 figure

The lowest modes around Gaussian solutions of tensor models and the general relativity

In the previous paper, the number distribution of the low-lying spectra around Gaussian solutions representing various dimensional fuzzy tori of a tensor model was numerically shown to be in accordance with the general relativity on tori. In this paper, I perform more detailed numerical analysis of the properties of the modes for two-dimensional fuzzy tori, and obtain conclusive evidences for the agreement. Under a proposed correspondence between the rank-three tensor in tensor models and the metric tensor in the general relativity, conclusive agreement is obtained between the profiles of the low-lying modes in a tensor model and the metric modes transverse to the general coordinate transformation. Moreover, the low-lying modes are shown to be well on a massless trajectory with quartic momentum dependence in the tensor model. This is in agreement with that the lowest momentum dependence of metric fluctuations in the general relativity will come from the R^2-term, since the R-term is topological in two dimensions. These evidences support the idea that the low-lying low-momentum dynamics around the Gaussian solutions of tensor models is described by the general relativity. I also propose a renormalization procedure for tensor models. A classical application of the procedure makes the patterns of the low-lying spectra drastically clearer, and suggests also the existence of massive trajectories.Comment: 31 pages, 8 figures, Added references, minor corrections, a misleading figure replace

Distinct functional domains of neurofibromatosis type 1 regulate immediate versus long-term memory formation

Neurofibromatosis type 1 (NF1) is a dominant genetic disorder that causes tumors of the peripheral nervous system. In addition, >40% of afflicted children have learning difficulties. The NF1 protein contains a highly conserved GTPase-activating protein domain that inhibits Ras activity, and the C-terminal region regulates cAMP levels via G-protein-dependent activation of adenylyl cyclase. Behavioral analysis indicates that learning is disrupted in both Drosophila and mouse NF1 models. Our previous work has shown that defective cAMP signaling leads to the learning phenotype in Drosophila Nf1 mutants. In the present report, our experiments showed that in addition to learning, long-term memory was also abolished in Nf1 mutants. However, altered NF1-regulated Ras activity is responsible for this defect rather than altered cAMP levels. Furthermore, by expressing clinically relevant human NF1 mutations and deletions in Drosophila Nf1-null mutants, we demonstrated that the GAP-related domain of NF1 was necessary and sufficient for long-term memory, whereas the C-terminal domain of NF1 was essential for immediate memory. Thus, we show that two separate functional domains of the same protein can participate independently in the formation of two distinct memory components

The evaluation of liquefaction potential of oil-containing sand under cyclic loading

Risk and Reliability in Geotechnical Engineerin

Effects of Zeeman spin splitting on the modular symmetry in the quantum Hall effect

Magnetic-field-induced phase transitions in the integer quantum Hall effect are studied under the formation of paired Landau bands arising from Zeeman spin splitting. By investigating features of modular symmetry, we showed that modifications to the particle-hole transformation should be considered under the coupling between the paired Landau bands. Our study indicates that such a transformation should be modified either when the Zeeman gap is much smaller than the cyclotron gap, or when these two gaps are comparable.Comment: 8 pages, 4 figure

Possible Evidence for Truncated Thin Disks in the Low-Luminosity Active Galactic Nuclei M81 and NGC 4579

M81 and NGC 4579 are two of the few low-luminosity active galactic nuclei which have an estimated mass for the central black hole, detected hard X-ray emission, and detected optical/UV emission. In contrast to the canonical ``big blue bump,'' both have optical/UV spectra which decrease with increasing frequency in a $\nu L_\nu$ plot. Barring significant reddening by dust and/or large errors in the black hole mass estimates, the optical/UV spectra of these systems require that the inner edge of a geometrically thin, optically thick, accretion disk lies at roughly 100 Schwarzschild radii. The observed X-ray radiation can be explained by an optically thin, two temperature, advection-dominated accretion flow at smaller radii.Comment: emulateapj.sty, to appear in ApJ Letter

Interplay between one-dimensional confinement and crystallographic anisotropy in ballistic hole quantum wires

We study the Zeeman splitting in induced ballistic 1D quantum wires aligned along the [233] and [011] axes of a high mobility (311)A undoped heterostructure. Our data shows that the g-factor anisotropy for magnetic fields applied along the high symmetry [011] direction can be explained by the 1D confinement only. However when the magnetic field is along [233] there is an interplay between the 1D confinement and 2D crystal anisotropy. This is highlighted for the [233] wire by an unusual non-monotonic behavior of the g-factor as the wire is made narrower

Oscillatory instabilities in d.c. biased quantum dots

We consider a `quantum dot' in the Coulomb blockade regime, subject to an arbitrarily large source-drain voltage V. When V is small, quantum dots with odd electron occupation display the Kondo effect, giving rise to enhanced conductance. Here we investigate the regime where V is increased beyond the Kondo temperature and the Kondo resonance splits into two components. It is shown that interference between them results in spontaneous oscillations of the current through the dot. The theory predicts the appearance of ``Shapiro steps'' in the current-voltage characteristics of an irradiated quantum dot; these would constitute an experimental signature of the predicted effect.Comment: Four pages with embedded figure

Optimal Resource Allocation in Random Networks with Transportation Bandwidths

We apply statistical physics to study the task of resource allocation in random sparse networks with limited bandwidths for the transportation of resources along the links. Useful algorithms are obtained from recursive relations. Bottlenecks emerge when the bandwidths are small, causing an increase in the fraction of idle links. For a given total bandwidth per node, the efficiency of allocation increases with the network connectivity. In the high connectivity limit, we find a phase transition at a critical bandwidth, above which clusters of balanced nodes appear, characterised by a profile of homogenized resource allocation similar to the Maxwell's construction.Comment: 28 pages, 11 figure