Multiple Quantum NMR Dynamics in Dipolar Ordered Spin Systems

We investigate analytically and numerically the Multiple Quantum (MQ) NMR dynamics in systems of nuclear spins 1/2 coupled by the dipole-dipole interactions in the case of the dipolar ordered initial state. We suggest two different methods of MQ NMR. One of them is based on the measurement of the dipolar temperature in the quasi-equilibrium state which establishes after the time of order T2 after the MQ NMR experiment. The other method uses an additional resonance 45^0 -pulse after the preparation period of the standard MQ NMR experiment in solids. Many-spin clusters and correlations are created faster in such experiments than in the usual MQ NMR experiments and can be used for the investigation of many-spin dynamics of nuclear spins in solids.Comment: 11 pages, 3 figures. accepted for publication in Physical Review

Variability of the soft X-ray excess in IRAS 13224-3809

We study the soft excess variability of the narrow line Seyfert 1 galaxy IRAS 13224-3809. We considered all five archival XMM-Newton observations, and we applied the 'flux-flux plot' (FFP) method. We found that the flux-flux plots were highly affected by the choice of the light curves' time bin size, most probably because of the fast and large amplitude variations, and the intrinsic non-linear flux--flux relations in this source. Therefore, we recommend that the smallest bin-size should be used in such cases. Hence, We constructed FFPs in 11 energy bands below 1.7 keV, and we considered the 1.7-3 keV band, as being representative of the primary emission. The FFPs are reasonably well fitted by a 'power-law plus a constant' model. We detected significant positive constants in three out of five observations. The best-fit slopes are flatter than unity at energies below $\sim 0.9$ keV, where the soft excess is strongest. This suggests the presence of intrinsic spectral variability. A power-law-like primary component, which is variable in flux and spectral slope (as $\Gamma\propto N_{\rm PL}^{0.1}$) and a soft-excess component, which varies with the primary continuum (as $F_{\rm excess}\propto F_{\rm primary}^{0.46}$), can broadly explain the FFPs. In fact, this can create positive `constants', even when a stable spectral component does not exist. Nevertheless, the possibility of a stable, soft--band constant component cannot be ruled out, but its contribution to the observed 0.2-1 keV band flux should be less than $\sim 15$ %. The model constants in the FFPs were consistent with zero in one observation, and negative at energies below 1 keV in another. It is hard to explain these results in the context of any spectral variability scenario, but they may signify the presence of a variable, warm absorber in the source.Comment: Accepted for publication in A&A, 10 pages, 7 figure

The multiple quantum NMR dynamics in systems of equivalent spins with the dipolar ordered initial state

The multiple quantum (MQ) NMR dynamics in the system of equivalent spins with the dipolar ordered initial state is considered. The high symmetry of the MQ Hamiltonian is used in order to develop the analytical and numerical methods for an investigation of the MQ NMR dynamics in the systems consisting of hundreds of spins from "the first principles". We obtain the dependence of the intensities of the MQ NMR coherences on their orders (profiles of the MQ NMR coherences) for the systems of $200 - 600$ spins. It is shown that these profiles may be well approximated by the exponential distribution functions. We also compare the MQ NMR dynamics in the systems of equivalent spins having two different initial states, namely the dipolar ordered state and the thermal equilibrium state in the strong external magnetic field.Comment: 11 pages 4 figure

Fine Tuning Free Paradigm of Two Measures Theory: K-Essence, Absence of Initial Singularity of the Curvature and Inflation with Graceful Exit to Zero Cosmological Constant State

The dilaton-gravity sector of the Two Measures Field Theory (TMT)is explored in detail in the context of cosmology. The model possesses scale invariance which is spontaneously broken due to the intrinsic features of the TMT dynamics. The effective model represents an explicit example of the effective k-essence resulting from first principles without any exotic term in the fundamental action. Depending of the choice of regions in the parameter space, TMT exhibits different possible outputs for cosmological dynamics: a) Absence of initial singularity of the curvature while its time derivative is singular. This is a sort of "sudden" singularities studied by Barrow on purely kinematic grounds. b) Power law inflation in the subsequent stage of evolution. Depending on the region in the parameter space (but without fine tuning) the inflation ends with a graceful exit either into the state with zero cosmological constant (CC) or into the state driven by both a small CC and the field phi with a quintessence-like potential. c) Possibility of resolution of the old CC problem. From the point of view of TMT, it becomes clear why the old CC problem cannot be solved (without fine tuning) in conventional field theories. d) TMT enables two ways for achieving small CC without fine tuning of dimensionfull parameters: either by a seesaw type mechanism or due to a correspondence principle between TMT and conventional field theories (i.e theories with only the measure of integration sqrt{-g} in the action. e) There is a wide range of the parameters such that in the late time universe: the equation-of-state w=p/\rho <-1; w asymptotically (as t\to\infty) approaches -1 from below; \rho approaches a constant, the smallness of which does not require fine tuning of dimensionfull parameters.Comment: 37 pages, 20 figures. Minor misprints corrected, reference added. The final version published in Phys. Rev.

Relationship between probabilities of the state transfers and entanglements in spin systems with simple geometrical configurations

In this paper we derive analytical relations between probabilities of the excited state transfers and entanglements calculated by both the Wootters and positive partial transpose (PPT) criteria for the arbitrary spin system with single excited spin in the external magnetic field and Hamiltonian commuting with $I_z$. We apply these relations to study the arbitrary state transfers and entanglements in the simple systems of nuclear spins having two- and three-dimensional geometrical configurations with $XXZ$ Hamiltonian. It is shown that High-Probability State Transfers (HPSTs) are possible among all four nodes placed in the corners of the rectangle with the proper ratio of sides as well as among all eight nodes placed in the corners of the parallelepiped with the proper ratio of sides. Entanglements responsible for these HPSTs have been identified.Comment: 27pages, 10 figure