Experimental realization of the Yang-Baxter Equation via NMR interferometry

The Yang-Baxter equation is an important tool in theoretical physics, with many applications in different domains that span from condensed matter to string theory. Recently, the interest on the equation has increased due to its connection to quantum information processing. It has been shown that the Yang-Baxter equation is closely related to quantum entanglement and quantum computation. Therefore, owing to the broad relevance of this equation, besides theoretical studies, it also became significant to pursue its experimental implementation. Here, we show an experimental realization of the Yang-Baxter equation and verify its validity through a Nuclear Magnetic Resonance (NMR) interferometric setup. Our experiment was performed on a liquid state Iodotrifluoroethylene sample which contains molecules with three qubits. We use Controlled-transfer gates that allow us to build a pseudo-pure state from which we are able to apply a quantum information protocol that implements the Yang-Baxter equation.Comment: 10 pages and 6 figure

An improved SPH scheme for cosmological simulations

We present an implementation of smoothed particle hydrodynamics (SPH) with improved accuracy for simulations of galaxies and the large-scale structure. In particular, we combine, implement, modify and test a vast majority of SPH improvement techniques in the latest instalment of the GADGET code. We use the Wendland kernel functions, a particle wake-up time-step limiting mechanism and a time-dependent scheme for artificial viscosity, which includes a high-order gradient computation and shear flow limiter. Additionally, we include a novel prescription for time-dependent artificial conduction, which corrects for gravitationally induced pressure gradients and largely improves the SPH performance in capturing the development of gas-dynamical instabilities. We extensively test our new implementation in a wide range of hydrodynamical standard tests including weak and strong shocks as well as shear flows, turbulent spectra, gas mixing, hydrostatic equilibria and self-gravitating gas clouds. We jointly employ all modifications; however, when necessary we study the performance of individual code modules. We approximate hydrodynamical states more accurately and with significantly less noise than standard SPH. Furthermore, the new implementation promotes the mixing of entropy between different fluid phases, also within cosmological simulations. Finally, we study the performance of the hydrodynamical solver in the context of radiative galaxy formation and non-radiative galaxy cluster formation. We find galactic disks to be colder, thinner and more extended and our results on galaxy clusters show entropy cores instead of steadily declining entropy profiles. In summary, we demonstrate that our improved SPH implementation overcomes most of the undesirable limitations of standard SPH, thus becoming the core of an efficient code for large cosmological simulations.Comment: 21 figures, 2 tables, accepted to MNRA

Violation of the string hypothesis and Heisenberg XXZ spin chain

In this paper we count the numbers of real and complex solutions to Bethe constraints in the two particle sector of the XXZ model. We find exact number of exceptions to the string conjecture and total number of solutions which is required for completeness.Comment: 15 pages, 7 Postscript figure

Intensity fluctuations in bimodal micropillar lasers enhanced by quantum-dot gain competition

We investigate correlations between orthogonally polarized cavity modes of a bimodal micropillar laser with a single layer of self-assembled quantum dots in the active region. While one emission mode of the microlaser demonstrates a characteristic s-shaped input-output curve, the output intensity of the second mode saturates and even decreases with increasing injection current above threshold. Measuring the photon auto-correlation function g^{(2)}(\tau) of the light emission confirms the onset of lasing in the first mode with g^{(2)}(0) approaching unity above threshold. In contrast, strong photon bunching associated with super-thermal values of g^{(2)}(0) is detected for the other mode for currents above threshold. This behavior is attributed to gain competition of the two modes induced by the common gain material, which is confirmed by photon crosscorrelation measurements revealing a clear anti-correlation between emission events of the two modes. The experimental studies are in excellent qualitative agreement with theoretical studies based on a microscopic semiconductor theory, which we extend to the case of two modes interacting with the common gain medium. Moreover, we treat the problem by an extended birth-death model for two interacting modes, which reveals, that the photon probability distribution of each mode has a double peak structure, indicating switching behavior of the modes for the pump rates around threshold.Comment: 11 pages, 5 figures, submitted to Phys. Rev.

Stochastic Model for the Motion of a Particle on an Inclined Rough Plane and the Onset of Viscous Friction

Experiments on the motion of a particle on an inclined rough plane have yielded some surprising results. For example, it was found that the frictional force acting on the ball is viscous, {\it i.e.} proportional to the velocity rather than the expected square of the velocity. It was also found that, for a given inclination of the plane, the velocity of the ball scales as a power of its radius. We present here a one dimensional stochastic model based on the microscopic equations of motion of the ball, which exhibits the same behaviour as the experiments. This model yields a mechanism for the origins of the viscous friction force and the scaling of the velocity with the radius. It also reproduces other aspects of the phase diagram of the motion which we will discuss.Comment: 19 pages, latex, 11 postscript figures in separate uuencoded fil

Energy Dissipation and Trapping of Particles Moving on a Rough Surface

We report an experimental, numerical and theoretical study of the motion of a ball on a rough inclined surface. The control parameters are $D$, the diameter of the ball, $\theta$, the inclination angle of the rough surface and $E_{ki}$, the initial kinetic energy. When the angle of inclination is larger than some critical value, $\theta>\theta_{T}$, the ball moves at a constant average velocity which is independent of the initial conditions. For an angle $\theta < \theta_{T}$, the balls are trapped after moving a certain distance. The dependence of the travelled distances on $E_{ki}$, $D$ and $\theta$. is analysed. The existence of two kinds of mechanisms of dissipation is thus brought to light. We find that for high initial velocities the friction force is constant. As the velocity decreases below a certain threshold the friction becomes viscous.Comment: 8 pages RevTeX, 12 Postscript figure

A planar extrapolation of the correlation problem that permits pairing

It was observed previously that an SU(N) extension of the Hubbard model is dominated, at large N, by planar diagrams in the sense of 't Hooft, but the possibility of superconducting pairing got lost in this extrapolation. To allow for this possibility, we replace SU(N) by U(N,q), the unitary group in a vector space of quaternions. At the level of the free energy, the difference between the SU(N)and U(N,q) extrapolations appears only to first nonleading order in N.Comment: 8 pages, 2 figure

Local Communication Protocols for Learning Complex Swarm Behaviors with Deep Reinforcement Learning

Swarm systems constitute a challenging problem for reinforcement learning (RL) as the algorithm needs to learn decentralized control policies that can cope with limited local sensing and communication abilities of the agents. While it is often difficult to directly define the behavior of the agents, simple communication protocols can be defined more easily using prior knowledge about the given task. In this paper, we propose a number of simple communication protocols that can be exploited by deep reinforcement learning to find decentralized control policies in a multi-robot swarm environment. The protocols are based on histograms that encode the local neighborhood relations of the agents and can also transmit task-specific information, such as the shortest distance and direction to a desired target. In our framework, we use an adaptation of Trust Region Policy Optimization to learn complex collaborative tasks, such as formation building and building a communication link. We evaluate our findings in a simulated 2D-physics environment, and compare the implications of different communication protocols.Comment: 13 pages, 4 figures, version 2, accepted at ANTS 201

Chemical composition and nymphicidal effect of essential oils from fruits of four Piper species (Piperaceae) against Tibraca limbativentris nymphs (Hemiptera: Pentatomidae).

This study aimed to verify the nymphicidal action of essential oils from fruits of 4 Piperaceae species against T. limbativentris nymphs. Fruits were collected in 3 brazilian states (P malacophyllum and P. marginatum: Pará, P. aduncum: Mato Grosso and P. gaudichaudinaum: Paraná)

Energy non-equipartition in systems of inelastic, rough spheres

We calculate and verify with simulations the ratio between the average translational and rotational energies of systems with rough, inelastic particles, either forced or freely cooling. The ratio shows non-equipartition of energy. In stationary flows, this ratio depends mainly on the particle roughness, but in nonstationary flows, such as freely cooling granular media, it also depends strongly on the normal dissipation. The approach presented here unifies and simplifies different results obtained by more elaborate kinetic theories. We observe that the boundary induced energy flux plays an important role.Comment: 4 pages latex, 4 embedded eps figures, accepted by Phys Rev