Accelerator on a Chip

Could tiny chips no bigger than grains of rice do the job of a huge particle accelerator? At full potential, a series of these “accelerators on a chip” could boost electrons to the same high energies achieved in SLAC National Accelerator Laboratory’s 2-mile linear accelerator in a distance of just 100 feet. This could make accelerators a lot smaller and more affordable.

The Gordon and Betty Moore Foundation has awarded $13.5 million to an international collaboration led by Stanford University, to develop a working prototype of such an accelerator over the next five years. SLAC and two other national labs provide key in-kind contributions in support of this expansive university effort.

Here’s how “accelerator on a chip” works: Electrons enter the chip and travel through a microscopic tunnel that has tiny ridges carved into its walls. When scientists shine an infrared laser on the chip, the light interacts with those ridges and produces an electrical field that boosts the energy of the passing electrons. In experiments at SLAC, the chip achieved an acceleration gradient, or energy boost over a given distance, roughly 10 times higher than the SLAC linear accelerator can provide.

There’s a lot of work to do to make this technology practical for real-world use. For instance, creating a full-fledged tabletop accelerator will require a more compact way to get electrons up to speed before they enter the chip; the Moore Foundation’s funding will help scientists work on that, and ideally create a prototype the size of a shoebox.

On the plus side, the accelerator on a chip uses commercial lasers and can be manufactured with low-cost, mass-production techniques.

Scientists think a series of these tiny chips could greatly reduce the size and cost of particle accelerators for a variety of applications. For example, the technology could help make compact low-cost accelerators and X-ray devices for security scanning, medicine, biology and materials science. Small, portable X-ray sources could improve medical care for people injured in combat and reduce the cost of medical imaging in hospitals.


Duality symmetries behind solutions of the classical simple pendulum

Román Linares
The solutions that describe the motion of the classical simple pendulum have been known for very long time and are given in terms of elliptic functions, which are doubly periodic functions in the complex plane. The independent variable of the solutions is time and it can be considered either as a real variable or as a purely imaginary one, which introduces a rich symmetry structure in the space of solutions. When solutions are written in terms of the Jacobi elliptic functions the symmetry is codified in the functional form of its modulus, and is described mathematically by the six dimensional coset group Γ/Γ(2) where Γ is the modular group and Γ(2) is its congruence subgroup of second level. In this paper we discuss the physical consequences this symmetry has on the pendulum motions and it is argued they have similar properties to the ones termed as duality symmetries in other areas of physics, such as field theory and string theory. In particular a single solution of pure imaginary time for all allowed value of the total mechanical energy is given and obtained as the S-dual of a single solution of real time, where S stands for the S generator of the modular group.

The simple plane pendulum constitutes an important physical system whose analytical solutions are well known.
Historically the first systematic study of the pendulum is attributed to Galileo Galilei, around 1602. Thirty years later he discovered that the period of small oscillations is approximately independent of the amplitude of the swing, property termed as isochronism, and in 1673 Huygens published the mathematical formula for this period. However, as soon as 1636, Marin Mersenne and Rene Descartes had stablished that the period in fact does depend of the amplitude. The mathematical theory to evaluate this period took longer to be established.
The Newton second law for the pendulum leads to a nonlinear differential equation of second order whose solutions are given in terms of either Jacobi elliptic functions or Weierstrass elliptic functions …
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Earthquake power laws emerge in bamboo chopsticks

The sounds made when a bamboo chopstick is broken follow the three main power laws that describe earthquakes, yet scientists also show that they can explain this power law behavior using geometry

The sounds made when a bamboo chopstick is broken follow the three main power laws that describe earthquakes, yet scientists also show that they can explain this power law behavior using geometry

Whereas a dry twig can be broken with a single snap, breaking a bamboo chopstick produces more than 400 crackling sounds. In a new study, researchers have found similarities between the complex acoustic emission of breaking a bamboo chopstick and the three famous power laws that describe earthquake activity. The scientists also propose that the underlying mechanism behind these laws may be simpler than currently thought.

The researchers, Sun-Ting Tsai et al., from National Tsing Hua University, have published their paper on the sounds of breaking a single bamboo chopstick in a recent issue of Physical Review Letters.

Bamboo and earthquakes Continue reading Earthquake power laws emerge in bamboo chopsticks

What is the Entropy in Entropic Gravity?

Sean M. Carroll, Grant N. Remmen
We investigate theories in which gravity arises as an entropic force. We distinguish between two approaches to this idea: holographic gravity, in which Einstein’s equation arises from keeping entropy stationary in equilibrium under variations of the geometry and quantum state of a small region, and thermodynamic gravity, in which Einstein’s equation emerges as a local equation of state from constraints on the area of a dynamical lightsheet in a fixed spacetime background.
Examining holographic gravity, we argue that its underlying assumptions can be justified in part using recent results on the form of the modular energy in quantum field theory. For thermodynamic gravity, on the other hand, we find that it is difficult to formulate a self-consistent definition of the entropy, which represents an obstacle for this approach. This investigation points the way forward in understanding the connections between gravity and entanglement (…)

The idea that gravity can be thought of as an entropic force is an attractive one. In this paper we have distinguished between two different ways of implementing this idea: holographic gravity, which derives the Einstein equation from constraints on the boundary entanglement after varying over different states in the theory, and thermodynamic gravity, which relates the time evolution of a cross-sectional area to the entropy passing through a null surface in a specified spacetime.
We argued that holographic gravity is a consistent formulation and indeed that recent work on the modular hamiltonian in quantum field theory provides additional support for its underlying assumptions. The thermodynamic approach, on the other hand, seems to suffer from a difficulty in providing a self-consistent definition for what the appropriate entropy is going to be.
In the title of this work, we asked, “What is the entropy in entropic gravity?” We are now equipped to answer this question. In what we have called “holographic gravity,” the vacuum subtracted von Neumann entanglement entropy (the Casini entropy), evaluated on the null surfaces of the causal diamond, provides an appropriate formulation for an entropic treatment of gravitation. This can help guide further attempts to understand the underlying microscopic degrees of freedom giving rise to gravitation in general spacetime backgrounds.
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