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Register a new userHow does a coin toss? A look under an asymptotic microscope
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Authors
Jithin D. George
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Is flipping a coin a deterministic process or a random one? We do not allow bounces. If we know the initial velocity and the spin given to the coin, mechanics should predict the face it lands on. However, the coin toss has been everyones introduction to probability and has been assumed to be the hallmark random process. So, whats going on here? This article discusses the problem first brought up by Keller in 1986 using a perspective tangential to the one used by Keller which leads us to new insight about the probability of getting heads.
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Time evolution of an optical image of a pressureless star under gravitational collapse is studied in the geometric optics approximation. The star surface is assumed to emit radiation obeying Lamberts cosine law but with an arbitrary spectral intensity in the comoving frame. We develop a formalism for predicting observable quantities by photon counting and by radiometry, in particular, spectral photon flux and spectral radiant flux. Then, this method is applied to the two cases: One is monochromatic radiation, and the other is blackbody radiation. The two kinds of spectral flux are calculated numerically for each case. It is reconfirmed that the redshift factor remains finite and the star becomes gradually invisible due to decay of the photon flux. We also develop an approximate method to present analytic formulas that describe the late time behavior. A possible connection of our study to observation of high-energy neutrinos is briefly discussed.
In this paper we present closed-form expressions for the wave function that governs the evolution of the discrete-time quantum walk on a line when the coin operator is arbitrary. The formulas were derived assuming that the walker can either remain put in the place or proceed in a fixed direction but never move backward, although they can be easily modified to describe the case in which the particle can travel in both directions. We use these expressions to explore the properties of magnitudes associated to the process, as the probability mass function or the probability current, even though we also consider the asymptotic behavior of the exact solution. Within this approximation, we will estimate upper and lower bounds, consider the origins of an emerging approximate symmetry, and deduce the general form of the stationary probability density of the relative location of the walker.
Bluetooth (BT) mesh is a new mode of BT operation for low-energy devices that offers group-based publish-subscribe as a network service with additional caching capabilities. These features resemble concepts of information-centric networking (ICN), and the analogy to ICN has been repeatedly drawn in the BT community. In this paper, we compare BT mesh with ICN both conceptually and in real-world experiments. We contrast both architectures and their design decisions in detail. Experiments are performed on an IoT testbed using NDN/CCNx and BT mesh on constrained RIOT nodes. Our findings indicate significant differences both in concepts and in real-world performance. Supported by new insights, we identify synergies and sketch a design of a BT-ICN that benefits from both worlds.
We take a first step towards a holographic description of a black hole by means of a flow equation. We consider a free theory of multiple scalar fields at finite temperature and study its holographic geometry defined through a free flow of the scalar fields. We find that the holographic metric has the following properties: i) It is an asymptotic Anti-de Sitter (AdS) black brane metric with some unknown matter contribution. ii) It has no coordinate singularity and milder curvature singularity. iii) Its time component decays exponentially at a certain AdS radial slice. We find that the matter spreads all over the space, which we speculate to be due to thermal excitation of infinitely many massless higher spin fields. We conjecture that the above three are generic features of a black hole holographically realized by the flow equation method.
The concept of local pressure is pivotal to describe many important physical phenomena, such as buoyancy or atmospheric phenomena, which always require the consideration of space-varying pressure fields. These fields have precise definitions within the phenomenology of hydro-thermodynamics, but a simple and pedagogical microscopic description based on Statistical Mechanical is still lacking in present literature. In this paper, we propose a new microscopic definition of the local pressure field inside a classical fluid, relying on a local barometer potential that is built into the many-particle Hamiltonian. Such a setup allows the pressure to be locally defined, at an arbitrary point inside the fluid, simply by doing a standard ensemble average of the radial force exerted by the barometer potential on the gas particles. This setup is further used to give a microscopic derivation of the generalized Archimedess buoyancy principle, in the presence of an arbitrary external field. As instructive examples, buoyancy force fields are calculated for ideal fluids in the presence of: i) a uniform force field, ii) a spherically symmetric harmonic confinement field, and iii) a centrifugal rotating frame.
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