Oscillating mushrooms: adiabatic theory for a non-ergodic system

Can elliptic islands contribute to sustained energy growth as parameters of a Hamiltonian system slowly vary with time? In this paper we show that a mushroom billiard with a periodically oscillating boundary accelerates the particle inside it exponentially fast. We provide an estimate for the rate of acceleration. Our numerical experiments confirms the theory. We suggest that a similar mechanism applies to general systems with mixed phase space.Comment: final revisio

Neel to staggered dimer order transition in a generalized honeycomb lattice Heisenberg model

We study a generalized honeycomb lattice spin-1/2 Heisenberg model with nearest-neighbor antiferromagnetic 2-spin exchange, and competing 4-spin interactions which serve to stabilize a staggered dimer state which breaks lattice rotational symmetry. Using a combination of quantum Monte Carlo numerics, spin wave theory, and bond operator theory, we show that this model undergoes a strong first-order transition between a Neel state and a staggered dimer state upon increasing the strength of the 4-spin interactions. We attribute the strong first order character of this transition to the spinless nature of the core of point-like Z(3) vortices obtained in the staggered dimer state. Unlike in the case of a columnar dimer state, disordering such vortices in the staggered dimer state does not naturally lead to magnetic order, suggesting that, in this model, the dimer and Neel order parameters should be thought of as independent fields as in conventional Landau theory.Comment: 13 pages, 10 fig

Permutation-Symmetric Multicritical Points in Random Antiferromagnetic Spin Chains

The low-energy properties of a system at a critical point may have additional symmetries not present in the microscopic Hamiltonian. This letter presents the theory of a class of multicritical points that provide an interesting example of this in the phase diagrams of random antiferromagnetic spin chains. One case provides an analytic theory of the quantum critical point in the random spin-3/2 chain, studied in recent work by Refael, Kehrein and Fisher (cond-mat/0111295).Comment: Revtex, 4 pages (2 column format), 2 eps figure

Multi-walled carbon nanotube electrodes for sodium borohydride fuel cell

Borohydride fuel cell has been constructed for the first time using multi-walled carbon nanotubes (MCNT), functionalized MWCNT, platinized MWCNT or polycarbzole (Pcz) as electrodes. The output characteristics of borohydride fuel cell with platinized MWCNT electrodes have been shown to be superior to the conventional graphite based borohydride fuel cells. The catalytic activity of platinized carbon nanotubes has also been established in this study. The MWCNTs have been functionalized by refluxing in 60-70% nitric acid for a period of 12 hours. The functionalized MWCNTs were characterized by FTIR and TGA. Platinization of MWCNTs was carried out electrochemically from chloroplatinic acid. Platinization of the tubes was demonstrated through SEM and XRD. Cyclic Voltammetry was used to characterize the platinum in MWCNT. Fuel cells were constructed using MWCNT of different forms as the anode and commercially available oxygen electrode as the cathode. The current values at different loads were measured and plotted to construct the load curves . From this data, the power density maps were generated. The power output of borohydride fuel cell has been shown to be higher than the graphite based fuel cell. The performance of borohydride fuel cells with Pcz electrode could not be decisive as the polymer deposited on platinum was used in the experiments. The polymer tends to peel off with time due to hydrogen bubbles generated in the medium. In the short time of the cell operation, it produced open circuit voltage of 1.369 V that is about 50% more than the commercially available borohydride fuel cell. However, it was noticed that it functions well as the cathode material in the borohydride fuel cells

Stable motions of high energy particles interacting via a repelling potential

The motion of N particles interacting by a smooth repelling potential and confined to a compact d-dimensional region is proved to be, under mild conditions, non-ergodic for all sufficiently large energies. Specifically, choreographic solutions, for which all particles follow approximately the same path close to an elliptic periodic orbit of the single-particle system, are proved to be KAM stable in the high energy limit. Finally, it is proved that the motion of N repelling particles in a rectangular box is non-ergodic at high energies for a generic choice of interacting potential: there exists a KAM-stable periodic motion by which the particles move fast only in one direction, each on its own path, yet in synchrony with all the other parallel moving particles. Thus, we prove that for smooth interaction potentials the Boltzmann ergodic hypothesis fails for a finite number of particles even in the high energy limit at which the smooth system appears to be very close to the Boltzmann hard-sphere gas

Soft billiards with corners

We develop a framework for dealing with smooth approximations to billiards with corners in the two-dimensional setting. Let a polygonal trajectory in a billiard start and end up at the same billiard's corner point. We prove that smooth Hamiltonian flows which limit to this billiard have a nearby periodic orbit if and only if the polygon angles at the corner are ''acceptable''. The criterion for a corner polygon to be acceptable depends on the smooth potential behavior at the corners, which is expressed in terms of a {scattering function}. We define such an asymptotic scattering function and prove the existence of it, explain how it can be calculated and predict some of its properties. In particular, we show that it is non-monotone for some potentials in some phase space regions. We prove that when the smooth system has a limiting periodic orbit it is hyperbolic provided the scattering function is not extremal there. We then prove that if the scattering function is extremal, the smooth system has elliptic periodic orbits limiting to the corner polygon, and, furthermore, that the return map near these periodic orbits is conjugate to a small perturbation of the Henon map and therefore has elliptic islands. We find from the scaling that the island size is typically algebraic in the smoothing parameter and exponentially small in the number of reflections of the polygon orbit

Memory Response of Magneto-Thermoelastic Problem Due to the Influence of Modified Ohm’s Law

In this article, in the form of the heat conduction equation with memory-dependent-derivative (MDD), a new model in magneto-thermoelasticity was developed with modified Ohm’s law. To obtain the solutions, normal mode analysis is used. The obtained solution is then exposed to time- dependent thermal shock and stress-free boundary conditions. The effect of the modified Ohm’s law coefficient, time-delay, and different kernel functions under the magnetic field effect on different quantities are evaluated and observed graphically on all field variables

Seismometer Detection of Dust Devil Vortices by Ground Tilt

We report seismic signals on a desert playa caused by convective vortices and dust devils. The long-period (10-100s) signatures, with tilts of ~10$^{-7}$ radians, are correlated with the presence of vortices, detected with nearby sensors as sharp temporary pressure drops (0.2-1 mbar) and solar obscuration by dust. We show that the shape and amplitude of the signals, manifesting primarily as horizontal accelerations, can be modeled approximately with a simple quasi-static point-load model of the negative pressure field associated with the vortices acting on the ground as an elastic half space. We suggest the load imposed by a dust devil of diameter D and core pressure {\Delta}Po is ~({\pi}/2){\Delta}PoD$^2$, or for a typical terrestrial devil of 5 m diameter and 2 mbar, about the weight of a small car. The tilt depends on the inverse square of distance, and on the elastic properties of the ground, and the large signals we observe are in part due to the relatively soft playa sediment and the shallow installation of the instrument. Ground tilt may be a particularly sensitive means of detecting dust devils. The simple point-load model fails for large dust devils at short ranges, but more elaborate models incorporating the work of Sorrells (1971) may explain some of the more complex features in such cases, taking the vortex winds and ground velocity into account. We discuss some implications for the InSight mission to Mars.Comment: Contributed Article for Bulletin of the Seismological Society of America, Accepted 29th August 201

Construction of mutually unbiased bases with cyclic symmetry for qubit systems

For the complete estimation of arbitrary unknown quantum states by measurements, the use of mutually unbiased bases has been well-established in theory and experiment for the past 20 years. However, most constructions of these bases make heavy use of abstract algebra and the mathematical theory of finite rings and fields, and no simple and generally accessible construction is available. This is particularly true in the case of a system composed of several qubits, which is arguably the most important case in quantum information science and quantum computation. In this paper, we close this gap by providing a simple and straightforward method for the construction of mutually unbiased bases in the case of a qubit register. We show that our construction is also accessible to experiments, since only Hadamard and controlled-phase gates are needed, which are available in most practical realizations of a quantum computer. Moreover, our scheme possesses the optimal scaling possible, i.e., the number of gates scales only linearly in the number of qubits.Comment: 4 pages, 1 figure, minor correction