Nonlinear ac stationary response and dynamic magnetic hysteresis of quantum uniaxial superparamagnets

The nonlinear ac stationary response of uniaxial paramagnets and superparamagnets - nanoscale solids or clasters with spin number S ~ 10^0 - 10^4 - in superimposed uniform ac and dc bias magnetic fields of arbitrary strength, each applied along the easy axis of magnetization, is determined by solving the evolution equation for the reduced density matrix represented as a finite set of three-term differential-recurrence relations for its diagonal matrix elements. The various harmonic components of the magnetization, dynamic magnetic hysteresis loops, etc. are then evaluated via matrix continued fractions indicating a pronounced dependence of the nonlinear response on S arising from the quantum spin dynamics. In the linear response approximation, the results concur with existing solutions.Comment: 28 pages, 10 figures, 33 refererence

Magnetization dynamics of two interacting spins in an external magnetic field

The longitudinal relaxation time of the magnetization of a system of two exchange coupled spins subjected to a strong magnetic field is calculated exactly by averaging the stochastic Gilbert-Landau-Lifshitz equation for the magnetization, i.e., the Langevin equation of the process, over its realizations so reducing the problem to a system of linear differential-recurrence relations for the statistical moments (averaged spherical harmonics). The system is solved in the frequency domain by matrix continued fractions yielding the complete solution of the two-spin problem in external fields for all values of the damping and barrier height parameters. The magnetization relaxation time extracted from the exact solution is compared with the inverse relaxation rate from Langer's theory of the decay of metastable states, which yields in the high barrier and intermediate-to-high damping limits the asymptotic behaviour of the greatest relaxation time.Comment: 32 pages, 5 figures. The paper has been revised and new results added (e.g., Fig. 5

Specific heat anomalies of open quantum systems

The evaluation of the specific heat of an open, damped quantum system is a subtle issue. One possible route is based on the thermodynamic partition function which is the ratio of the partition functions of system plus bath and of the bath alone. For the free damped particle it has been shown, however, that the ensuing specific heat may become negative for appropriately chosen environments. Being an open system this quantity then naturally must be interpreted as the change of the specific heat obtained as the difference between the specific heat of the heat bath coupled to the system degrees of freedom and the specific heat of the bath alone. While this difference may become negative, the involved specific heats themselves are always positive; thus, the known thermodynamic stability criteria are perfectly guaranteed. For a damped quantum harmonic oscillator, instead of negative values, under appropriate conditions one can observe a dip in the difference of specific heats as a function of temperature. Stylized minimal models containing a single oscillator heat bath are employed to elucidate the occurrence of the anomalous temperature dependence of the corresponding specific heat values. Moreover, we comment on the consequences for the interpretation of the density of states based on the thermal partitionfunction.Comment: 7 pages, 6 figures, new title and some modifications of the main tex

Physical properties of the jet from DG Tauri on sub-arcsecond scales with HST/STIS

We derive the physical properties at the base of the jet from DG Tau both along and across the flow and as a function of velocity. We analysed seven optical spectra of the DG Tau jet, taken with the Hubble Space Telescope Imaging Spectrograph. The spectra were obtained by placing a long-slit parallel to the jet axis and stepping it across the jet width. The resulting position-velocity diagrams in optical forbidden emission lines allowed access to plasma conditions via calculation of emission line ratios. We find at the base of the jet high electron density, $n_e \sim$ 10$^5$, and very low ionisation, $x_e \sim 0.02-0.05$, which combine to give a total density up to $n_H \sim$ 3 10$^6$. This analysis confirms previous reports of variations in plasma parameters along the jet, (i.e. decrease in density by several orders of magnitude, increase of $x_e$ from 0.05 to a plateau at 0.7 downstream at 2$''$ from the star). Furthermore, a spatial coincidence is revealed between sharp gradients in the total density and supersonic velocity jumps. This strongly suggests that the emission is caused by shock excitation. The position-velocity diagrams indicate the presence of both fast accelerating gas and slower, less collimated material. We derive the mass outflow rate, $\dot{M}_j$, in the blue-shifted lobe in different velocity channels, that contribute to a total of $\dot{M}_j \sim$ 8 $\pm$ 4 10$^{-9}$ M$_\odot$ yr$^{-1}$. We estimate that a symmetric bipolar jet would transport at the low and intermediate velocities probed by rotation measurements, an angular momentum flux of $\dot{L}_j \sim$ 2.9 $\pm$ 1.5 10$^{-6}$ M$_\odot$ yr$^{-1}$ AU km s$^{-1}$. The derived properties of the DG Tau jet are demonstrated to be consistent with magneto-centrifugal theory. However, non-stationary modelling is required in order to explain all of the features revealed at high resolution.Comment: 16 pages, 18 figure

Role of interactions in ferrofluid thermal ratchets

Orientational fluctuations of colloidal particles with magnetic moments may be rectified with the help of external magnetic fields with suitably chosen time dependence. As a result a noise-driven rotation of particles occurs giving rise to a macroscopic torque per volume of the carrier liquid. We investigate the influence of mutual interactions between the particles on this ratchet effect by studying a model system with mean-field interactions. The stochastic dynamics may be described by a nonlinear Fokker-Planck equation for the collective orientation of the particles which we solve approximately by using the effective field method. We determine an interval for the ratio between coupling strength and noise intensity for which a self-sustained rectification of fluctuations becomes possible. The ratchet effect then operates under conditions for which it were impossible in the absence of interactions.Comment: 18 pages, 10 figure

Calcium and magnesium absorption and retention by growing goats offered diets with different calcium sources

Calcium addition is necessary in order to balance the high phosphorus concentrations that are characteristic of high-concentrate ruminant diets. However, calcium sources differ in their bioavailability. Our objective was to determine apparent calcium and magnesium absorption and retention in goats offered diets containing different sources of calcium. Spanish-Boer goats (n = 18; 19.6 ± 1.88 kg) were stratified by body weight (BW) and sex and randomized to dietary treatments consisting of Purina Antlermax 16 containing either calcium carbonate (CC), Calmin (CM) or Milk Cal (MC). Goats were adapted to a control, corn-based high-concentrate diet on pasture and then moved to individual 1.0 × 1.5-m pens with plastic coated expanded metal floors, and adjusted to their respective diets along with removal of hay from the diet over a 7-d period. Goats were then offered their respective diets at a total of 2% of BW in equal feedings at 8:30 AM and 5:00 PM for an additional 14-d adaption period to diet and facilities followed by a 7-d collection of total urine and feces. Data were analyzed using PROC MIXED of SAS. Calcium and magnesium intake were not different (P ≥ 0.12) among diets. Calcium and magnesium apparent absorption and retention (g/d and % of intake) were greatest (P \u3c 0.05) in goats offered CC and did not differ (P ≥ 0.20) between goats offered the CM and MC diets. Therefore, calcium and magnesium were more available for goats from the diet containing calcium carbonate compared with diets containing Calmin and Milk Cal

Integral Relaxation Time of Single-Domain Ferromagnetic Particles

The integral relaxation time \tau_{int} of thermoactivating noninteracting single-domain ferromagnetic particles is calculated analytically in the geometry with a magnetic field H applied parallel to the easy axis. It is shown that the drastic deviation of \tau_{int}^{-1} from the lowest eigenvalue of the Fokker-Planck equation \Lambda_1 at low temperatures, starting from some critical value of H, is the consequence of the depletion of the upper potential well. In these conditions the integral relaxation time consists of two competing contributions corresponding to the overbarrier and intrawell relaxation processes.Comment: 8 pages, 3 figure

Reversal time of the magnetization of magnetic nanoparticles at very low damping

The magnetization reversal time of ferromagnetic nanoparticles is investigated in the very low damping regime. The energy-controlled diffusion equation rooted in a generalization of the Kramers escape rate theory for point Brownian particles in a potential to the magnetic relaxation of a macrospin, yields the reversal time in closed integral form. The latter is calculated for a nanomagnet with uniaxial anisotropy with a uniform field applied at an angle to the easy axis and for a nanomagnet with biaxial anisotropy with the field along the easy axis. The results completely agree with those yielded by independent numerical and asymptotic methods.Comment: An extended version: 28 pages; 5 figures; Mathematica Program