The Stochastic Dynamics of Rectangular and V-shaped Atomic Force Microscope Cantilevers in a Viscous Fluid and Near a Solid Boundary

Using a thermodynamic approach based upon the fluctuation-dissipation theorem we quantify the stochastic dynamics of rectangular and V-shaped microscale cantilevers immersed in a viscous fluid. We show that the stochastic cantilever dynamics as measured by the displacement of the cantilever tip or by the angle of the cantilever tip are different. We trace this difference to contributions from the higher modes of the cantilever. We find that contributions from the higher modes are significant in the dynamics of the cantilever tip-angle. For the V-shaped cantilever the resulting flow field is three-dimensional and complex in contrast to what is found for a long and slender rectangular cantilever. Despite this complexity the stochastic dynamics can be predicted using a two-dimensional model with an appropriately chosen length scale. We also quantify the increased fluid dissipation that results as a V-shaped cantilever is brought near a solid planar boundary.Comment: 10 pages, 15 images, corrected equation (8

Break up of heavy fermions at an antiferromagnetic instability

We present results of high-resolution, low-temperature measurements of the Hall coefficient, thermopower, and specific heat on stoichiometric YbRh2Si2. They support earlier conclusions of an electronic (Kondo-breakdown) quantum critical point concurring with a field induced antiferromagnetic one. We also discuss the detachment of the two instabilities under chemical pressure. Volume compression/expansion (via substituting Rh by Co/Ir) results in a stabilization/weakening of magnetic order. Moderate Ir substitution leads to a non-Fermi-liquid phase, in which the magnetic moments are neither ordered nor screened by the Kondo effect. The so-derived zero-temperature global phase diagram promises future studies to explore the nature of the Kondo breakdown quantum critical point without any interfering magnetism.Comment: minor changes, accepted for publication in JPS

Fermi-surface collapse and dynamical scaling near a quantum critical point

Quantum criticality arises when a macroscopic phase of matter undergoes a continuous transformation at zero temperature. While the collective fluctuations at quantum-critical points are being increasingly recognized as playing an important role in a wide range of quantum materials, the nature of the underlying quantum-critical excitations remains poorly understood. Here we report in-depth measurements of the Hall effect in the heavy-fermion metal YbRh2Si2, a prototypical system for quantum criticality. We isolate a rapid crossover of the isothermal Hall coefficient clearly connected to the quantum-critical point from a smooth background contribution; the latter exists away from the quantum-critical point and is detectable through our studies only over a wide range of magnetic field. Importantly, the width of the critical crossover is proportional to temperature, which violates the predictions of conventional theory and is instead consistent with an energy over temperature, E/T, scaling of the quantum-critical single-electron fluctuation spectrum. Our results provide evidence that the quantum-dynamical scaling and a critical Kondo breakdown simultaneously operate in the same material. Correspondingly, we infer that macroscopic scale-invariant fluctuations emerge from the microscopic many-body excitations associated with a collapsing Fermi-surface. This insight is expected to be relevant to the unconventional finite-temperature behavior in a broad range of strongly correlated quantum systems.Comment: 5 pages, plus supporting materia

First-Order Reorientation of the Flux-Line Lattice in CaAlSi

The flux line lattice in CaAlSi has been studied by small angle neutron scattering. A well defined hexagonal flux line lattice is seen just above Hc1 in an applied field of only 54 Oe. A 30 degree reorientation of this vortex lattice has been observed in a very low field of 200 Oe. This reorientation transition appears to be of first-order and could be explained by non-local effects. The magnetic field dependence of the form factor is well described by a single penetration depth of 1496(1) angstroms and a single coherence length of 307(1) angstroms at 2 K. At 1.5 K the penetration depth anisotropy is 2.7(1) with the field applied perpendicular to the c axis and agrees with the coherence length anisotropy determined from critical field measurements.Comment: 5 pages including 6 figures, to appear in Physical Review Letter

Chemical Species Spatial Distribution and Relationship to Elevation and Snow Accumulation Rate over the Greenland Ice Sheet

Major chemical species (Cl−, NO−3, SO2−4, Na+, K+, Mg2+, Ca2+) from 24 snowpits (sampled at a resolution of 3 cm, total 2995 samples) collected from northern, central, and southern Greenland were used for this investigation. The annual and seasonal (winter and summer) concentration of each chemical species was calculated and used to study the spatial distribution of chemical species over the central portion of the Greenland Ice Sheet. A two-sided t-distribution test (α=0.05) suggests that concentrations of major chemical species in snow do not vary significantly over this portion of central Greenland. The relationship between chemical concentration and snow accumulation rate was investigated using annual data from two groups of snowpits: those from coastal sites (northern and southern Greenland); and those from high-altitude inland sites (central Greenland). The snowpit data from a single group, when examined independently of the other group, show that chemical concentrations do not vary with snow accumulation rate. However, when data from the two groups are integrated into a single data set, pseudorelationships appear, with NO−3 concentration decreasing and Na+, K+, Mg2+, and Cl− increasing as snow accumulation rate increases. Therefore we suggest that it is improper to study the relationship between chemical concentration and snow accumulation rate by using data collected from different geographic sites. The relationship between elevation and chemical concentration was investigated using the same suite of annual data sets. We find that Cl−, Na+, and Mg2+ concentrations decrease, while NO−3 concentration increases, with increasing elevation on the Greenland Ice Sheet

Non-Fermi liquid behavior from two-dimensional antiferromagnetic fluctuations: a renormalization-group and large-N analysis

We analyze the Hertz-Moriya-Millis theory of an antiferromagnetic quantum critical point, in the marginal case of two dimensions (d=2,z=2). Up to next-to-leading order in the number of components (N) of the field, we find that logarithmic corrections do not lead to an enhancement of the Landau damping. This is in agreement with a renormalization-group analysis, for arbitrary N. Hence, the logarithmic effects are unable to account for the behavior reportedly observed in inelastic neutron scattering experiments on CeCu_{6-x}Au_x. We also examine the extended dynamical mean-field treatment (local approximation) of this theory, and find that only subdominant corrections to the Landau damping are obtained within this approximation, in contrast to recent claims.Comment: 15 pages, 8 figure

The structure of epitaxial V2O3 films and their surfaces : a medium energy ion scattering study

Medium energy ion scattering, using 100 keV H+ incident ions, has been used to investigate the growth of epitaxial films, up to thicknesses of ~200 Å, of V2O3 on both Pd(111) and Au(111). Scattered-ion energy spectra provide a measure of the average film thickness and the variations in this thickness, and show that, with suitable annealing, the crystalline quality is good. Plots of the scattering yield as a function of scattering angle, so-called blocking curves, have been measured for two different incidence directions and have been used to determine the surface structure. Specifically, scattering simulations for a range of different model structures show poor agreement with experiment for half-metal (….V’O3V) and vanadyl (….V’O3V=O) terminations, with and without surface interlayer relaxations. However, good agreement with experiment is found for the modified oxygen-termination structure, first proposed by Kresse et al., in which a subsurface V half-metal layer is moved up into the outermost V buckled metal layer to produce a VO2 overlayer on the underlying V2O3, with an associated layer structure of ….O3VV’’V’O3

Physical and magnetic properties of Ba(Fe1-xMnx)(2)As-2 single crystals

Single crystals of Ba(Fe1−xMnx)2As2, 00.1–0.2. Our measurements show that whereas the structural/magnetic phase transition found in pure BaFe2As2 at 134 K is initially suppressed by Mn substitution, superconductivity is not observed at any substitution level. Although the effect of hydrostatic pressure up to 20 kbar in the parent BaFe2As2 compound is to suppress the structural/magnetic transition at the approximate rate of 0.9 K/kbar, the effects of pressure and Mn substitution in the x=0.102 compound are not cumulative. Phase diagrams of transition temperature versus substitution concentration x based on electrical transport, magnetization, and thermopower measurements have been constructed and compared to those of the Ba(Fe1−xTMx)2As2 (TM= Co and Cr) series

Time evolution, cyclic solutions and geometric phases for the generalized time-dependent harmonic oscillator

The generalized time-dependent harmonic oscillator is studied. Though several approaches to the solution of this model have been available, yet a new approach is presented here, which is very suitable for the study of cyclic solutions and geometric phases. In this approach, finding the time evolution operator for the Schr\"odinger equation is reduced to solving an ordinary differential equation for a c-number vector which moves on a hyperboloid in a three-dimensional space. Cyclic solutions do not exist for all time intervals. A necessary and sufficient condition for the existence of cyclic solutions is given. There may exist some particular time interval in which all solutions with definite parity, or even all solutions, are cyclic. Criterions for the appearance of such cases are given. The known relation that the nonadiabatic geometric phase for a cyclic solution is proportional to the classical Hannay angle is reestablished. However, this is valid only for special cyclic solutions. For more general ones, the nonadiabatic geometric phase may contain an extra term. Several cases with relatively simple Hamiltonians are solved and discussed in detail. Cyclic solutions exist in most cases. The pattern of the motion, say, finite or infinite, can not be simply determined by the nature of the Hamiltonian (elliptic or hyperbolic, etc.). For a Hamiltonian with a definite nature, the motion can changes from one pattern to another, that is, some kind of phase transition may occur, if some parameter in the Hamiltonian goes through some critical value.Comment: revtex4, 28 pages, no figur

On Predicting the Solar Cycle using Mean-Field Models

We discuss the difficulties of predicting the solar cycle using mean-field models. Here we argue that these difficulties arise owing to the significant modulation of the solar activity cycle, and that this modulation arises owing to either stochastic or deterministic processes. We analyse the implications for predictability in both of these situations by considering two separate solar dynamo models. The first model represents a stochastically-perturbed flux transport dynamo. Here even very weak stochastic perturbations can give rise to significant modulation in the activity cycle. This modulation leads to a loss of predictability. In the second model, we neglect stochastic effects and assume that generation of magnetic field in the Sun can be described by a fully deterministic nonlinear mean-field model -- this is a best case scenario for prediction. We designate the output from this deterministic model (with parameters chosen to produce chaotically modulated cycles) as a target timeseries that subsequent deterministic mean-field models are required to predict. Long-term prediction is impossible even if a model that is correct in all details is utilised in the prediction. Furthermore, we show that even short-term prediction is impossible if there is a small discrepancy in the input parameters from the fiducial model. This is the case even if the predicting model has been tuned to reproduce the output of previous cycles. Given the inherent uncertainties in determining the transport coefficients and nonlinear responses for mean-field models, we argue that this makes predicting the solar cycle using the output from such models impossible.Comment: 22 Pages, 5 Figures, Preprint accepted for publication in Ap