Local Lagrangian Formalism and Discretization of the Heisenberg Magnet Model

In this paper we develop the Lagrangian and multisymplectic structures of the Heisenberg magnet (HM) model which are then used as the basis for geometric discretizations of HM. Despite a topological obstruction to the existence of a global Lagrangian density, a local variational formulation allows one to derive local conservation laws using a version of N\"other's theorem from the formal variational calculus of Gelfand-Dikii. Using the local Lagrangian form we extend the method of Marsden, Patrick and Schkoller to derive local multisymplectic discretizations directly from the variational principle. We employ a version of the finite element method to discretize the space of sections of the trivial magnetic spin bundle $N = M\times S^2$ over an appropriate space-time $M$. Since sections do not form a vector space, the usual FEM bases can be used only locally with coordinate transformations intervening on element boundaries, and conservation properties are guaranteed only within an element. We discuss possible ways of circumventing this problem, including the use of a local version of the method of characteristics, non-polynomial FEM bases and Lie-group discretization methods.Comment: 12 pages, accepted Math. and Comp. Simul., May 200

Ab initio lattice dynamics simulations and inelastic neutron scattering spectra for studying phonons in BaFe2As2: Effect of structural phase transition, structural relaxation and magnetic ordering

We have performed extensive ab initio calculations to investigate phonon dynamics and their possible role in superconductivity in BaFe2As2 and related systems. The calculations are compared to inelastic neutron scattering data that offer improved resolution over published data [Mittal et al., PRB 78 104514 (2008)], in particular at low frequencies. Effects of structural phase transition and full/partial structural relaxation, with and without magnetic ordering, on the calculated vibrational density of states are reported. Phonons are best reproduced using either the relaxed magnetic structures or the experimental cell. Several phonon branches are affected by the subtle structural changes associated with the transition from the tetragonal to the orthorhombic phase. Effects of phonon induced distortions on the electronic and spin structure have been investigated. It is found that for some vibrational modes, there is a significant change of the electronic distribution and spin populations around the Fermi level. A peak at 20 meV in the experimental data falls into the pseudo-gap region of the calculation. This was also the case reported in our recent work combined with an empirical parametric calculation [Mittal et al., PRB 78 104514 (2008)]. The combined evidence for the coupling of electronic and spin degrees of freedom with phonons is relevant to the current interest in superconductivity in BaFe2As2 and related systems

Diffusion and jump-length distribution in liquid and amorphous Cu33_{33}Zr67_{67}

Using molecular dynamics simulation, we calculate the distribution of atomic jum ps in Cu$_{33}$Zr$_{67}$ in the liquid and glassy states. In both states the distribution of jump lengths can be described by a temperature independent exponential of the length and an effective activation energy plus a contribution of elastic displacements at short distances. Upon cooling the contribution of shorter jumps dominates. No indication of an enhanced probability to jump over a nearest neighbor distance was found. We find a smooth transition from flow in the liquid to jumps in the g lass. The correlation factor of the diffusion constant decreases with decreasing temperature, causing a drop of diffusion below the Arrhenius value, despite an apparent Arrhenius law for the jump probability

Non-Orthogonal Multiple Access for FSO Backhauling

We consider a free space optical (FSO) backhauling system which consists of two base stations (BSs) and one central unit (CU). We propose to employ non-orthogonal multiple access (NOMA) for FSO backhauling where both BSs transmit at the same time and in the same frequency band to the same photodetector at the CU. We develop a dynamic NOMA scheme which determines the optimal decoding order as a function of the channel state information at the CU and the quality of service requirements of the BSs, such that the outage probabilities of both BSs are jointly minimized. Moreover, we analyze the performance of the proposed NOMA scheme in terms of the outage probability over Gamma-Gamma FSO turbulence channels. We further derive closed-form expressions for the outage probability for the high signal-to-noise ratio regime. Our simulation results confirm the analytical derivations and reveal that the proposed dynamic NOMA scheme significantly outperforms orthogonal transmission and existing NOMA schemes.Comment: This paper has been submitted to IEEE WCNC 201

Vibrational instability, two-level systems and Boson peak in glasses

We show that the same physical mechanism is fundamental for two seemingly different phenomena such as the formation of two-level systems in glasses and the Boson peak in the reduced density of low-frequency vibrational states g(w)/w^2. This mechanism is the vibrational instability of weakly interacting harmonic modes. Below some frequency w_c << w_0 (where w_0 is of the order of Debye frequency) the instability, controlled by the anharmonicity, creates a new stable universal spectrum of harmonic vibrations with a Boson peak feature as well as double-well potentials with a wide distribution of barrier heights. Both are determined by the strength of the interaction I ~ w_c between the oscillators. Our theory predicts in a natural way a small value for the important dimensionless parameter C ~ 10^{-4} for two-level systems in glasses. We show that C ~ I^{-3} and decreases with increasing of the interaction strength I. We show that the number of active two-level systems is very small, less than one per ten million of oscillators, in a good agreement with experiment. Within the unified approach developed in the present paper the density of the tunneling states and the density of vibrational states at the Boson peak frequency are interrelated.Comment: 28 pages, 3 figure

Field-induced structural aging in glasses at ultra low temperatures

In non-equilibrium experiments on the glasses Mylar and BK7, we measured the excess dielectric response after the temporary application of a strong electric bias field at mK--temperatures. A model recently developed describes the observed long time decays qualitatively for Mylar [PRL 90, 105501, S. Ludwig, P. Nalbach, D. Rosenberg, D. Osheroff], but fails for BK7. In contrast, our results on both samples can be described by including an additional mechanism to the mentioned model with temperature independent decay times of the excess dielectric response. As the origin of this novel process beyond the "tunneling model" we suggest bias field induced structural rearrangements of "tunneling states" that decay by quantum mechanical tunneling.Comment: 4 pages, 4 figures, accepted at PRL, corrected typos in version

Pressure dependence of diffusion in simple glasses and supercooled liquids

Using molecular dynamics simulation, we have calculated the pressure dependence of the diffusion constant in a binary Lennard-Jones Glass. We observe four temperature regimes. The apparent activation volume drops from high values in the hot liquid to a plateau value. Near the critical temperature of the mode coupling theory it rises steeply, but in the glassy state we find again small values, similar to the ones in the liquid. The peak of the activation volume at the critical temperature is in agreement with the prediction of mode coupling theory