Cratering Experiments on the Self Armoring of Coarse-Grained Granular Targets

Recently published crater statistics on the small asteroids 25143 Itokawa and 433 Eros show a significant depletion of craters below approx. 100 m in diameter. Possible mechanisms that were brought up to explain this lack of craters were seismic crater erasure and self armoring of a coarse, boulder covered asteroid surface. While seismic shaking has been studied in this context, the concept of armoring lacks a deeper inspection and an experimental ground truth. We therefore present cratering experiments of glass bead projectiles impacting into granular glass bead targets, where the grain sizes of projectile and target are in a similar range. The impact velocities are in the range of 200 to 300 m/s. We find that craters become fainter and irregular shaped as soon as the target grains are larger than the projectile sizes and that granular craters rarely form when the size ratio between projectile and target grain is around 1:10 or smaller. In that case, we observe a formation of a strength determined crater in the first struck target grain instead. We present a simple model based on the transfer of momentum from the projectile to this first target grain, which is capable to explain our results with only a single free parameter, which is moreover well determined by previous experiments. Based on estimates of typical projectile size and boulder size on Itokawa and Eros, given that our results are representative also for km/s impact velocities, armoring should play an important role for their evolution.Comment: accepted for publication in Icaur

Distribution of exchange energy in a bond-alternating S=1 quantum spin chain

The quasi-one-dimensional bond-alternating S=1 quantum antiferromagnet NTENP is studied by single crystal inelastic neutron scattering. Parameters of the measured dispersion relation for magnetic excitations are compared to existing numerical results and used to determine the magnitude of bond-strength alternation. The measured neutron scattering intensities are also analyzed using the 1st-moment sum rules for the magnetic dynamic structure factor, to directly determine the modulation of ground state exchange energies. These independently determined modulation parameters characterize the level of spin dimerization in NTENP. First-principle DMRG calculations are used to study the relation between these two quantities.Comment: 10 pages, 10 figure

Quantum Error Correction via Convex Optimization

We show that the problem of designing a quantum information error correcting procedure can be cast as a bi-convex optimization problem, iterating between encoding and recovery, each being a semidefinite program. For a given encoding operator the problem is convex in the recovery operator. For a given method of recovery, the problem is convex in the encoding scheme. This allows us to derive new codes that are locally optimal. We present examples of such codes that can handle errors which are too strong for codes derived by analogy to classical error correction techniques.Comment: 16 page

Chiral Magnetic Effect on the Lattice

We review recent progress on the lattice simulations of the chiral magnetic effect. There are two different approaches to analyze the chiral magnetic effect on the lattice. In one approach, the charge density distribution or the current fluctuation is measured under a topological background of the gluon field. In the other approach, the topological effect is mimicked by the chiral chemical potential, and the induced current is directly measured. Both approaches are now developing toward the exact analysis of the chiral magnetic effect.Comment: to appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye

Efficiency of free energy calculations of spin lattices by spectral quantum algorithms

Quantum algorithms are well-suited to calculate estimates of the energy spectra for spin lattice systems. These algorithms are based on the efficient calculation of the discrete Fourier components of the density of states. The efficiency of these algorithms in calculating the free energy per spin of general spin lattices to bounded error is examined. We find that the number of Fourier components required to bound the error in the free energy due to the broadening of the density of states scales polynomially with the number of spins in the lattice. However, the precision with which the Fourier components must be calculated is found to be an exponential function of the system size.Comment: 9 pages, 4 figures; corrected typographical and minor mathematical error

Finite Size Scaling for Low Energy Excitations in Integer Heisenberg Spin Chains

In this paper we study the finite size scaling for low energy excitations of $S=1$ and $S=2$ Heisenberg chains, using the density matrix renormalization group technique. A crossover from $1/L$ behavior (with $L$ as the chain length) for medium chain length to $1/L^2$ scaling for long chain length is found for excitations in the continuum band as the length of the open chain increases. Topological spin $S=1/2$ excitations are shown to give rise to the two lowest energy states for both open and periodic $S=1$ chains. In periodic chains these two excitations are ``confined'' next to each other, while for open chains they are two free edge 1/2 spins. The finite size scaling of the two lowest energy excitations of open $S=2$ chains is determined by coupling the two free edge $S=1$ spins. The gap and correlation length for $S=2$ open Heisenberg chains are shown to be 0.082 (in units of the exchange $J$) and 47, respectively.Comment: 4 pages (two column), PS file, to be appear as a PRB Brief Repor

Global Phase Diagram of the Kondo Lattice: From Heavy Fermion Metals to Kondo Insulators

We discuss the general theoretical arguments advanced earlier for the T=0 global phase diagram of antiferromagnetic Kondo lattice systems, distinguishing between the established and the conjectured. In addition to the well-known phase of a paramagnetic metal with a "large" Fermi surface (P_L), there is also an antiferromagnetic phase with a "small" Fermi surface (AF_S). We provide the details of the derivation of a quantum non-linear sigma-model (QNLsM) representation of the Kondo lattice Hamiltonian, which leads to an effective field theory containing both low-energy fermions in the vicinity of a Fermi surface and low-energy bosons near zero momentum. An asymptotically exact analysis of this effective field theory is made possible through the development of a renormalization group procedure for mixed fermion-boson systems. Considerations on how to connect the AF_S and P_L phases lead to a global phase diagram, which not only puts into perspective the theory of local quantum criticality for antiferromagnetic heavy fermion metals, but also provides the basis to understand the surprising recent experiments in chemically-doped as well as pressurized YbRh2Si2. We point out that the AF_S phase still occurs for the case of an equal number of spin-1/2 local moments and conduction electrons. This observation raises the prospect for a global phase diagram of heavy fermion systems in the Kondo-insulator regime. Finally, we discuss the connection between the Kondo breakdown physics discussed here for the Kondo lattice systems and the non-Fermi liquid behavior recently studied from a holographic perspective.Comment: (v3) leftover typos corrected. (v2) Published version. 32 pages, 4 figures. Section 7, on the connection between the Kondo lattice systems and the holographic models of non-Fermi liquid, is expanded. (v1) special issue of JLTP on quantum criticalit

Squeezing based on nondegenerate frequency doubling internal to a realistic laser

We investigate theoretically the quantum fluctuations of the fundamental field in the output of a nondegenerate second harmonic generation process occuring inside a laser cavity. Due to the nondegenerate character of the nonlinear medium, a field orthogonal to the laser field is for some operating conditions indepedent of the fluctuations produced by the laser medium. We show that this fact may lead to perfect squeezing for a certain polarization mode of the fundamental field. The experimental feasibility of the system is also discussed.Comment: 6 pages, 5 figure

On the Application of the Non Linear Sigma Model to Spin Chains and Spin Ladders

We review the non linear sigma model approach (NLSM) to spin chains and spin ladders, presenting new results. The generalization of the Haldane's map to ladders in the Hamiltonian approach, give rise to different values of the $\theta$ parameter depending on the spin S, the number of legs $n_{\ell}$ and the choice of blocks needed to built up the NLSM fields. For rectangular blocks we obtain $\theta = 0$ or $2 \pi S$ depending on wether $n_{\ell}$, is even or odd, while for diagonal blocks we obtain $\theta = 2 \pi S n_{\ell}$. Both results agree modulo $2 \pi$, and yield the same prediction, namely that even ( resp. odd) ladders are gapped (resp. gapless). For even legged ladders we show that the spin gap collapses exponentially with $n_{\ell}$ and we propose a finite size correction to the gap formula recently derived by Chakravarty using the 2+1 NSLM, which gives a good fit of numerical results. We show the existence of a Haldane phase in the two legged ladder using diagonal blocks and finally we consider the phase diagram of dimerized ladders.Comment: 25 pages, Latex, 7 figures in postscript files, Proc. of the 1996 El Escorial Summer School on "Strongly Correlated Magnetic and Superconducting Systems". Some more references are adde

Quantum error rejection code with spontaneous parametric conversion

We propose a linear optics scheme with SPDC process to test the fault tolerance property of quantum error correction code. To transmit an unknown qubit robustly through the noisy channel, one may first encode it into a certain quantum error correction code and then transmit it. The remote party decodes it and stores it. Sending a qubit in such a way can significantly reduces the error rate compared with directly sending the qubit itself. Here we show how to realize such a scheme by linear optics.Comment: To appear in Phys. Rev. A. 18 pages, 2 figure, minor erros corrected and more explanations added to increase the readabilit