Selected topics in Planck-scale physics

We review a few topics in Planck-scale physics, with emphasis on possible manifestations in relatively low energy. The selected topics include quantum fluctuations of spacetime, their cumulative effects, uncertainties in energy-momentum measurements, and low energy quantum-gravity phenomenology. The focus is on quantum-gravity-induced uncertainties in some observable quantities. We consider four possible ways to probe Planck-scale physics experimentally: 1. looking for energy-dependent spreads in the arrival time of photons of the same energy from GRBs; 2. examining spacetime fluctuation-induced phase incoherence of light from extragalactic sources; 3. detecting spacetime foam with laser-based interferometry techniques; 4. understanding the threshold anomalies in high energy cosmic ray and gamma ray events. Some other experiments are briefly discussed. We show how some physics behind black holes, simple clocks, simple computers, and the holographic principle is related to Planck-scale physics. We also discuss a formulation of the Dirac equation as a difference equation on a discrete Planck-scale spacetime lattice, and a possible interplay between Planck-scale and Hubble-scale physics encoded in the cosmological constant (dark energy).Comment: 31 pages, 1 figure; minor changes; to appear in Mod. Phys. Lett. A as a Brief Revie

Influence of socioemotional wealth on non-family managers’ risk taking and product innovation in family businesses

Purpose: There is a growing interest in understanding family firms’ strategic behavior using the socioemotional wealth perspective. This study explores how family socioemotional wealth (SEW) dimensions influence non-family managers’ attitudes toward risk in the context of product innovation. We also examine whether managerial risk-taking mediates the relationship between SEW and product innovation. Design/methodology/approach: The study uses a sample of 150 family firms in the United Arab Emirates and collects data from family owners and non-family managers via self-administered questionnaires. We use SmartPLS structural equation modeling to test the conceptual model and the proposed hypotheses. Findings: The results indicate that SEW influences non-family managers’ risk-taking behavior in different magnitudes and directions, thus impacting firms’ product innovation. Moreover, risk-taking partially mediates the relationship between SEW dimensions and product innovation. Originality/value: While product innovation could be seen as a loss scenario for family firms due to the potential loss of SEW, growth, continuity, and reputation outweighed the desire to maintain control for the firms in this sample. Thus, these firms encourage non-family managers to take risks in product innovation

Dynamical stability of entanglement between spin ensembles

We study the dynamical stability of the entanglement between the two spin ensembles in the presence of an environment. For a comparative study, we consider the two cases: a single spin ensemble, and two ensembles linearly coupled to a bath, respectively. In both circumstances, we assume the validity of the Markovian approximation for the bath. We examine the robustness of the state by means of the growth of the linear entropy which gives a measure of the purity of the system. We find out macroscopic entangled states of two spin ensembles can stably exist in a common bath. This result may be very useful to generate and detect macroscopic entanglement in a common noisy environment and even a stable macroscopic memory.Comment: 4 pages, 1 figur

Fault-tolerant quantum computation versus Gaussian noise

We study the robustness of a fault-tolerant quantum computer subject to Gaussian non-Markovian quantum noise, and we show that scalable quantum computation is possible if the noise power spectrum satisfies an appropriate "threshold condition." Our condition is less sensitive to very-high-frequency noise than previously derived threshold conditions for non-Markovian noise.Comment: 30 pages, 6 figure

Deep Chandra Observation of the Pulsar Wind Nebula Powered by the Pulsar J1846-0258 in the Supernova Remnant Kes 75

We present the results of detailed spatial and spectral analysis of the pulsar wind nebula (PWN) in supernova remnant Kes 75 (G29.7-0.3) using a deep exposure with Chandra X-ray observatory. The PWN shows a complex morphology with clear axisymmetric structure. We identified a one-sided jet and two bright clumps aligned with the overall nebular elongation, and an arc-like feature perpendicular to the jet direction. Further spatial modeling with a torus and jet model indicates a position angle 207\arcdeg\pm8 \arcdeg for the PWN symmetry axis. We interpret the arc as an equatorial torus or wisp and the clumps could be shock interaction between the jets and the surrounding medium. The lack of any observable counter jet implies a flow velocity larger than 0.4c. Comparing to an archival observation 6 years earlier, some small-scale features in the PWN demonstrate strong variability: the flux of the inner jet doubles and the peak of the northern clump broadens and shifts 2" outward. In addition, the pulsar flux increases by 6 times, showing substantial spectral softening from $\Gamma$=1.1 to 1.9 and an emerging thermal component which was not observed in the first epoch. The changes in the pulsar spectrum are likely related to the magnetar-like bursts of the pulsar that occurred 7 days before the Chandra observation, as recently reported from RXTE observations.Comment: Accepted by ApJ, 8 figures, some of them have been scaled down in resolutio

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

On the trace of the antipode and higher indicators

We introduce two kinds of gauge invariants for any finite-dimensional Hopf algebra H. When H is semisimple over C, these invariants are respectively, the trace of the map induced by the antipode on the endomorphism ring of a self-dual simple module, and the higher Frobenius-Schur indicators of the regular representation. We further study the values of these higher indicators in the context of complex semisimple quasi-Hopf algebras H. We prove that these indicators are non-negative provided the module category over H is modular, and that for a prime p, the p-th indicator is equal to 1 if, and only if, p is a factor of dim H. As an application, we show the existence of a non-trivial self-dual simple H-module with bounded dimension which is determined by the value of the second indicator.Comment: additional references, fixed some typos, minor additions including a questions and some remark

Topological spin excitations of Heisenberg antiferromagnets in two dimensions

In this paper we discuss the construction and the dynamics of vortex-like topological spin excitations in the Schwinger-boson description of Heisenberg antiferromagnets in two dimensions. The topological spin excitations are Dirac fermions (with gap) when spin value $S$ is a half-integer. Experimental and theoretical implications of these excitations are being investigated.Comment: Latex file, no figur

Vacancy clustering and diffusion in silicon: Kinetic lattice Monte Carlo simulations

Diffusion and clustering of lattice vacancies in silicon as a function of temperature, concentration, and interaction range are investigated by Kinetic Lattice Monte Carlo simulations. It is found that higher temperatures lead to larger clusters with shorter lifetimes on average, which grow by attracting free vacancies, while clusters at lower temperatures grow by aggregation of smaller clusters. Long interaction ranges produce enhanced diffusivity and fewer clusters. Greater vacancy concentrations lead to more clusters, with fewer free vacancies, but the size of the clusters is largely independent of concentration. Vacancy diffusivity is shown to obey power law behavior over time, and the exponent of this law is shown to increase with concentration, at fixed temperature, and decrease with temperature, at fixed concentration.Comment: 14 pages, 12 figures. To appear in Physical Review

On Uniquely Closable and Uniquely Typable Skeletons of Lambda Terms

Uniquely closable skeletons of lambda terms are Motzkin-trees that predetermine the unique closed lambda term that can be obtained by labeling their leaves with de Bruijn indices. Likewise, uniquely typable skeletons of closed lambda terms predetermine the unique simply-typed lambda term that can be obtained by labeling their leaves with de Bruijn indices. We derive, through a sequence of logic program transformations, efficient code for their combinatorial generation and study their statistical properties. As a result, we obtain context-free grammars describing closable and uniquely closable skeletons of lambda terms, opening the door for their in-depth study with tools from analytic combinatorics. Our empirical study of the more difficult case of (uniquely) typable terms reveals some interesting open problems about their density and asymptotic behavior. As a connection between the two classes of terms, we also show that uniquely typable closed lambda term skeletons of size $3n+1$ are in a bijection with binary trees of size $n$.Comment: Pre-proceedings paper presented at the 27th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur, Belgium, 10-12 October 2017 (arXiv:1708.07854