arXiv subjects
Publications and source records attributed to A. Stern.
Four-dimensional manifolds with changing signature are obtained by taking the large $N$ limit of fuzzy $CP^2$ solutions to a Lorentzian matrix model. The regions of Lorentzian signature give toy models of closed universes which exhibit cosmological singularities. These singularities are resolved at finite $N$, as the underlying $CP^2$ solutions are expressed in terms of finite matrix elements.
On July 14th 2015, NASA's New Horizons mission gave us an unprecedented detailed view of the Pluto system. The complex compositional diversity of Pluto's encounter hemisphere was revealed by the Ralph/LEISA infrared spectrometer on board of New Horizons. We present compositional maps of Pluto defining the spatial distribution of the abundance and textural properties of the volatiles methane and nitrogen ices and non-volatiles water ice and tholin. These results are obtained by applying a pixel-by-pixel Hapke radiative transfer model to the LEISA scans. Our analysis focuses mainly on the large scale latitudinal variations of methane and nitrogen ices and aims at setting observational constraints to volatile transport models. Specifically, we find three latitudinal bands: the first, enriched in methane, extends from the pole to 55deg N, the second dominated by nitrogen, continues south to 35deg N, and the third, composed again mainly of methane, reaches 20deg N. We demonstrate that the distribution of volatiles across these surface units can be explained by differences in insolation over the past few decades. The latitudinal pattern is broken by Sputnik Planitia, a large reservoir of volatiles, with nitrogen playing the most important role. The physical properties of methane and nitrogen in this region are suggestive of the presence of a cold trap or possible volatile stratification. Furthermore our modeling results point to a possible sublimation transport of nitrogen from the northwest edge of Sputnik Planitia toward the south.
We obtain numerical solutions for rotating topological solitons of the nonlinear $σ$-model in three-dimensional Anti-de Sitter space. Two types of solutions, $i)$ and $ii)$, are found. The $σ$-model fields are everywhere well defined for both types of solutions, but they differ in their space-time domains. Any time slice of the space-time for the type $i)$ solution has a causal singularity, despite the fact that all scalars constructed the curvature tensor are bounded functions. No evidence of a horizon is seen for any of the solutions, and therefore the type $i)$ solutions have naked singularities. On the other hand, the space-time domain, along with the fields, for the type $ii)$ solutions are singularity free. Multiple families of solutions exhibiting bifurcation phenomena are found for this case.
Observations of the Pluto-Charon system, acquired with the ALMA interferometer on June 12-13, 2015, have yielded a detection of the CO(3-2) and HCN(4-3) rotational transitions from Pluto, providing a strong confirmation of the presence of CO, and the first observation of HCN, in Pluto's atmosphere. The CO and HCN lines probe Pluto's atmosphere up to ~450 km and ~900 km altitude, respectively. The CO detection yields (i) a much improved determination of the CO mole fraction, as 515+/-40 ppm for a 12 ubar surface pressure (ii) clear evidence for a well-marked temperature decrease (i.e., mesosphere) above the 30-50 km stratopause and a best-determined temperature of 70+/-2 K at 300 km, in agreement with recent inferences from New Horizons / Alice solar occultation data. The HCN line shape implies a high abundance of this species in the upper atmosphere, with a mole fraction >1.5x10-5 above 450 km and a value of 4x10-5 near 800 km. The large HCN abundance and the cold upper atmosphere imply supersaturation of HCN to a degree (7-8 orders of magnitude) hitherto unseen in planetary atmospheres, probably due to the slow kinetics of condensation at the low pressure and temperature conditions of Pluto's upper atmosphere. HCN is also present in the bottom ~100 km of the atmosphere, with a 10-8 - 10-7 mole fraction; this implies either HCN saturation or undersaturation there, depending on the precise stratopause temperature. The HCN column is (1.6+/-0.4)x10^14 cm-2, suggesting a surface-referred net production rate of ~2x10^7 cm-2s-1. Although HCN rotational line cooling affects Pluto's atmosphere heat budget, the amounts determined in this study are insufficient to explain the well-marked mesosphere and upper atmosphere's ~70 K temperature. We finally report an upper limit on the HC3N column density (< 2x10^13 cm-2) and on the HC15N / HC14N ratio (< 1/125).
We introduce a coupled-layer construction to describe three-dimensional topological crystalline insulators protected by reflection symmetry. Our approach uses stacks of weakly-coupled two-dimensional Chern insulators to produce topological crystalline insulators in one higher dimension, with tunable number and location of surface Dirac cones. As an application of our formalism, we turn to a simplified model of topological crystalline insulator SnTe, showing that its protected surface states can be described using the coupled layer construction.
Radio frequency tunable oscillators are vital electronic components for signal generation, characterization, and processing. They are often constructed with a resonant circuit and a 'negative' resistor, such as a Gunn-diode, involving complex structure and large footprints. Here we report that a piece of SmB6, 100 micron in size, works as a current-controlled oscillator in the 30 MHz frequency range. SmB6 is a strongly correlated Kondo insulator that was recently found to have a robust surface state likely to be protected by the topology of its electronics structure. We exploit its non-linear dynamics, and demonstrate large AC voltage outputs with frequencies from 20 Hz to 30 MHz by adjusting a small DC bias current. The behaviors of these oscillators agree well with a theoretical model describing the thermal and electronic dynamics of coupled surface and bulk states. With reduced crystal size we anticipate the device to work at higher frequencies, even in the THz regime. This type of oscillator might be realized in other materials with a metallic surface and a semiconducting bulk.
We perform a systematic search for rotationally invariant cosmological solutions to matrix models, or more specifically the bosonic sector of Lorentzian IKKT-type matrix models, in dimensions $d$ less than ten, specifically $d=3$ and $d=5$. After taking a continuum (or commutative) limit they yield $d-1$ dimensional space-time surfaces, with an attached Poisson structure, which can be associated with closed, open or static cosmologies. For $d=3$, we obtain recursion relations from which it is possible to generate rotationally invariant matrix solutions which yield open universes in the continuum limit. Specific examples of matrix solutions have also been found which are associated with closed and static two-dimensional space-times in the continuum limit. The solutions provide for a matrix resolution of cosmological singularities. The commutative limit reveals other desirable features, such as a solution describing a smooth transition from an initial inflation to a noninflationary era. Many of the $d=3$ solutions have analogues in higher dimensions. The case of $d=5$, in particular, has the potential for yielding realistic four-dimensional cosmologies in the continuum limit. We find four-dimensional de Sitter $dS^4$ or anti-de Sitter $AdS^4$ solutions when a totally antisymmetric term is included in the matrix action. A nontrivial Poisson structure is attached to these manifolds which represents the lowest order effect of noncommutativity. For the case of $AdS^4$, we find one particlular limit where the lowest order noncommutativity vanishes at the boundary, but not in the interior.
We show that fuzzy spheres are solutions of ${\it Lorentzian}$ IKKT matrix models. The fuzzy sphere solutions serve as toy models of closed noncommutative cosmologies where big bang/crunch singularities appear only after taking the commutative limit. The commutative limit of these solutions corresponds to a sphere embedded in Minkowski space. This `sphere' has several novel features. The induced metric does not agree with the standard metric on the sphere, and moreover, it does not have a fixed signature. The curvature computed from the induced metric is not constant, has singularities at fixed latitudes (not corresponding to the poles) and is negative. Perturbations are made about the solutions, and are shown to yield a scalar field theory on the sphere in the commutative limit. The scalar field can become tachyonic for a range of the parameters of the theory.
We examine solutions to the classical IKKT matrix model equations in three space-time dimensions. Closed, open and static two-dimensional universes naturally emerge from such models in the commutative limit. We show that tachyonic modes are a generic feature of these cosmological solutions.
We examine the noncommutative cylinder solution to a matrix model with a Minkowski background metric. It can be regarded as the noncommutative analogue of a static circular string. Perturbations about the solution yield a tachyonic scalar field (and an additional tachyonic fermion in the full supersymmetric version of the model) in the commutative limit. The tachyonic mode is attributed to the fact that the circular string is unstable under uniform adiabatic deformations. We obtain a stabilizing term which when added to the matrix model removes the tachyonic mass.
We examine a Chern-Simons matrix model which we propose as a toy model for studying the quantum nature of black holes in 2+1 gravity. Its dynamics is described by two $N\times N$ matrices, representing the two spatial coordinates. The model possesses an internal SU(N) gauge symmetry, as well as an external rotation symmetry. The latter corresponds to the rotational isometry of the BTZ solution, and does not decouple from SU(N) gauge transformations. The system contains an invariant which is quadratic in the spatial coordinates. We obtain its spectrum and degeneracy, and find that the degeneracy grows exponentially in the large $N$ limit. The usual BTZ black hole entropy formula is recovered upon identifying the quadratic invariant with the square of the black hole horizon radius. The quantum system behaves collectively as an integer (half-integer) spin particle for even (odd) $N$ under $2π$-rotations.
In this paper we study linear projection methods for approximating the solution and simultaneously preserving first integrals of autonomous ordinary differential equations. We show that (linear) projection methods are a subset of discrete gradient methods. In particular, each projection method is equivalent to a class of discrete gradient methods (where the choice of discrete gradient is arbitrary) and earlier results for discrete gradient methods also apply to projection methods. Thus we prove that for the case of preserving one first integral, under certain mild conditions, the numerical solution for a projection method exists and is locally unique, and preserves the order of accuracy of the underlying method. In the case of preserving multiple first integrals the relationship between projection methods and discrete gradient methods persists. Moreover, numerical examples show that similar existence and order results should also hold for the multiple integral case. For completeness we show how existing projection methods from the literature fit into our general framework.
We examine Hamiltonian formalism on Euclidean Snyder space. The latter corresponds to a lattice in the quantum theory. For any given dynamical system, it may not be possible to identify time with a real number parametrizing the evolution in the quantum theory. The alternative requires the introduction of a dynamical time operator. We obtain the dynamical time operator for the relativistic (nonrelativistic) particle, and use it to construct the generators of Poincaré (Galilei) group on Snyder space.
We obtain a minimal supersymmetric extension of the Snyder algebra and study its representations. The construction differs from the general approach given in Hatsuda and Siegel ({\tt hep-th/0311002}), and does not utilize super-de Sitter groups. The spectra of the position operators are discrete, implying a lattice description of space, and the lattice is compatible with supersymmetry transformations.
We examine basis functions on momentum space for the three dimensional Euclidean Snyder algebra. We argue that the momentum space is isomorphic to the SO(3) group manifold, and that the basis functions span either one of two Hilbert spaces. This implies the existence of two distinct lattice structures of space, on which continuous rotations and translations are unitarily implementable.
We discuss alternatives to the usual quantization of relativistic particles which result in discrete spectra for position and time operators.
We obtain the leading derivative corrections to an expression for the Seiberg-Witten map given by Banerjee and Yang and show how they affect the noncommutative deformation of the Maxwell action, as well as the matter coupling in noncommutative emergent gravity.
A relatively simple approach to noncommutative gravity utilizes the gauge theory formulation of general relativity and involves replacing the Lorentz gauge group by a larger group. This results in additional field degrees of freedom which either must be constrained to vanish in a nontrivial way, or require physical interpretation. With the latter in mind, we examine the coupling of the additional fields to point particles. Nonstandard particle degrees of freedom should be introduced in order to write down the most general coupling. The example we study is the $GL(2,C)$ central extension of gravity given by Chamseddine, which contains two U(1) gauge fields, and a complex vierbein matrix, along with the usual spin connections. For the general coupling one should then attach two U(1) charges and a complex momentum vector to the particle, along with the spin. The momenta span orbits in a four-dimensional complex vector space, and are classified by $GL(2,C)$ invariants and by their little groups. In addition to orbits associated with standard massive and massless particles, a number of novel orbits can be identified. We write down a general action principle for particles associated with any nontrivial orbit and show that it leads to corrections to geodesic motion. We also examine the classical and quantum theory of the particle in flat space-time.