Measurement of Small One-Bond Proton–Carbon Residual Dipolar Coupling Constants in Partially Oriented C Natural Abundance Oligosaccharide Samples: Analysis of Heteronuclear JCH-Modulated Spectra with the BIRD Inversion Pulse

Two 2D J-modulated HSQC-based experiments were designed for precise determination of small residual dipolar one-bond carbon–proton coupling constants in ¹³C natural abundance carbohydrates. Crucial to the precision of a few hundredths of Hz achieved by these methods was the use of long modulation intervals and BIRD pulses, which acted as semiselective inversion pulses. The BIRD pulses eliminated effective evolution of all but ¹J_CH couplings, resulting in signal modulation that can be described by simple modulation functions. A thorough analysis of such modulation functions for a typical four-spin carbohydrate spin system was performed for both experiments. The results showed that the evolution of the ¹H–¹H and long-range ¹H–¹³C couplings during the BIRD pulses did not necessitate the introduction of more complicated modulation functions. The effects of pulse imperfections were also inspected. While weakly coupled spin systems can be analyzed by simple fitting of cross peak intensities, in strongly coupled spin systems the evolution of the density matrix needs to be considered in order to analyse data accurately. However, if strong coupling effects are modest the errors in coupling constants determined by the “weak coupling” analysis are of similar magnitudes in oriented and isotropic samples and are partially cancelled during dipolar coupling calculation. Simple criteria have been established as to when the strong coupling treatment needs to be invoked.     

Phase modulation in dipolar-coupled A2 spin systems: effect of maximum state mixing in 1H NMR in vivo

Coupling constants of nuclear spin systems can be determined from phase modulation of multiplet resonances. Strongly coupled systems such as citrate in prostatic tissue exhibit a more complex modulation than AX connectivities, because of substantial mixing of quantum states. An extreme limit is the coupling of n isochronous spins (An system). It is observable only for directly connected spins like the methylene protons of creatine and phosphocreatine which experience residual dipolar coupling in intact muscle tissue in vivo. We will demonstrate that phase modulation of this "pseudo-strong" system is quite simple compared to those of AB systems. Theory predicts that the spin-echo experiment yields conditions as in the case of weak interactions, in particular, the phase modulation depends linearly on the line splitting and the echo time.     

Model glasses coupled to two different heat baths

In a p-spin interaction spherical spin-glass model both the spins and the couplings are allowed to change with time. The spins are coupled to a heat bath with temperature T, while the coupling constants are coupled to a bath having temperature T_J. In an adiabatic limit (where relaxation time of the couplings is much larger that of the spins) we construct a generalized two-temperature thermodynamics. It involves entropies of the spins and the coupling constants. The application for spin-glass systems leads to a standard replica theory with a non-vanishing number of replicas, n=T/T _J . For p>2 there occur at low temperatures two different glassy phases, depending on the value of n. The obtained first-order transitions have positive latent heat, and positive discontinuity of the total entropy. This is an essentially non-equilibrium effect. The dynamical phase transition exists only for n<1. For p=2 correlation of the disorder (leading to a non-zero n) removes the known marginal stability of the spin glass phase. If the observation time is very large there occurs no finite-temperature spin glass phase. In this case there are analogies with the non-equilibrium (aging) dynamics. A generalized fluctuation-dissipation relation is derived. Received 12 July 1999 and Received in final form 8 December 1999     

Improved quantification of alite and belite in anhydrous Portland cements by Si MAS NMR: Effects of paramagnetic ions

The applicability, reliability, and repeatability of ²⁹Si MAS NMR for determination of the quantities of alite (Ca₃SiO₅) and belite (Ca₂SiO₄) in anhydrous Portland cement was investigated in detail for 11 commercial Portland cements and the results compared with phase quantifications based on powder X-ray diffraction combined with Rietveld analysis and with Taylor–Bogue calculations. The effects from paramagnetic ions (Fe³⁺) on the spinning sideband intensities, originating from dipolar couplings between ²⁹Si and the spins of the paramagnetic electrons, were considered and analyzed in spectra recorded at four magnetic fields (4.7–14.1 T) and this has led to an improved quantification of alite and belite from ²⁹Si MAS NMR spectra recorded at “high” spinning speeds of ν_R=12.0–13.0 kHz using 4 or 5 mm rotors. Furthermore, the impact of Fe³⁺ ions on the spin-lattice relaxation was studied by inversion-recovery experiments and it was found that the relaxation is overwhelmingly dominated by the Fe³⁺ ions incorporated as guest-ions in alite and belite rather than the Fe³⁺ sites present in the intimately mixed ferrite phase (Ca₂Al_xFe_2−xO₅).     

Clustering in neural networks with heterogeneous and asymmetrical coupling strengths

The existence and stability of phase-clustered states have been studied previously in networks of weakly coupled oscillators with uniform coupling strengths [Physica D 63 (1993) 424]. However, several studies have shown that if the coupling is uniform and repulsive, it is hard to obtain stable phase-clustered states in networks of realistic neural oscillators when noise is present [Neural Comput. 7 (1995) 307; Phys. Rev. E 57 (1998) 2150]. This problem was avoided by introducing heterogeneity in the distribution of coupling strengths [J. Phys. Soc. Jpn. 72 (2003) 443]. It has been shown that heterogeneous coupling strengths make the occurrence of stable clustered states possible in small networks of repulsively coupled neural oscillators of all kinds [J. Comput. Neurosci. 14 (2003) 139; SIAM J. Appl. Math., submitted for publication]. The present work extends these results to large networks of N identical neurons that are globally coupled with heterogeneous and asymmetrical coupling strengths. Conditions for the existence and stability of a state of n synchronized clusters at evenly distributed phases, called the state of n splay-phase clusters, are derived. Clusters of different sizes, i.e. containing different numbers of neurons, are studied. The existence of such a state is guaranteed if the strength of the coupling originating from one neuron to other neurons is inversely proportional to the size of the cluster to which it belongs. This condition is called the rule of inverse cluster-size. At the state of n splay-phase clusters, the N-neuron network behaves like a network of n “big neurons”. Stability of this state is determined by n eigenvalues of which only one determines the stability of intra-cluster phase differences. The remaining n−1 conditions determine the stability of inter-cluster phase differences, but only n_h=(n− mod (n,2))/2 of them have distinct real parts due to symmetry. Heterogeneous coupling makes the stability conditions depend on coupling strengths. This analysis not only reveals how clustered states occur in more general kinds of networks, but also illustrates how the stability of clustered states can be achieved in networks of repulsively coupled neural oscillators. Results on clustered states with phases that are not evenly distributed in the phase space are also presented. Potential applications of these results are discussed.     

Theoretical study of the magnetism in the incommensurate phase of TiOCl

Going beyond a recently proposed microscopic model [D. Mastrogiuseppe, A. Dobry, arXiv:0810.3018v1] for the incommensurate transition in the spin-Peierls TiOX (X=Cl, Br) compounds, in the present work we start by studying the thermodynamics of the model with XY spins and adiabatic phonons. We find that the system enters an incommensurate phase by a first order transition at a low temperature T_c1. At a higher temperature T_c2 a continuous transition to a uniform phase is found. Furthermore, we study the magnetism in the incommensurate phase by density matrix renormalization group (DMRG) calculations on a one-dimensional Heisenberg model where the exchange is modulated by the incommensurate atomic position pattern. When the wave vector q of the modulation is near π, we find local magnetized zones (LMZ) in which spins abandon their singlets as a result of the domain walls induced by the modulated distortion. When q moves far away enough from π, the LMZ disappear and the system develops incommensurate magnetic correlations induced by the structure. We discuss the relevance of this result regarding previous and future experiments in TiOCl.     

Randomized Acquisition for the Suppression of Systematic F1 Artifacts in Two-Dimensional NMR Spectroscopy

2D spectra, particularly for homonuclear correlation, can show a variety of artifactual signals in the F₁ domain. Common sources include carry-over of signal modulation from one transient to the next (“rapid pulsing artifacts”) and systematic variations in room temperature (“parallel diagonals”). In both cases there is one very simple expedient which can greatly reduce the impact of these sources of error. Multidimensional data sets are almost invariably recorded by simply incrementing or decrementing evolution periods, largely for reasons of convenience and historical precedent. If instead the sampling of the evolution periods is carried out in random order, the perturbations responsible for the sharp F₁ signals in the conventional experiment manifest themselves as t₁ noise. Since the randomized acquisition redistributes coherent artifactual signals randomly in F₁, the maximum artifactual signal is substantially reduced in the randomized experiment and no longer appears in the form of misleading distinct peaks.     

Generic phase diagram of “electron-doped” T′ cuprates

We investigated the generic phase diagram of the electron doped superconductor, Nd_2−xCe_xCuO₄, using films prepared by metal organic decomposition. After careful oxygen reduction treatment to remove interstitial O_ap atoms, we found that the T_c increases monotonically from 24 K to 29 K with decreasing x from 0.15 to 0.00, demonstrating a quite different phase diagram from the previous bulk one. The implication of our results is discussed on the basis of tremendous influence of O_ap “impurities” on superconductivity and also magnetism in T′ cuprates. Then we conclude that our result represents the generic phase diagram for oxygen-stoichiometric Nd_2−xCe_xCuO₄.     

A New Two-Dimensional Pulse Sequence for T2* Measurements of Protons in C Isotopomers

A new two-dimensional pulse sequence for T₂* measurement of protons directly coupled to ¹³C spins is proposed. The sequence measures the tranverse relaxation time of heteronuclear proton single-quantum coherence under conditions of free precession and is therefore well suited to evaluate relaxation losses of proton magnetization during preparation delays of heteronuclear pulse experiments in analytical NMR. The relevant part of the pulse sequence can be inserted as a “building block” into any direct or inverse detecting H,C correlation pulse sequence if proton spin–spin relaxation is to be investigated. In this contribution, the building block is inserted into a HETCOR as well as into a HMQC pulse sequence. Experimental results for the HETCOR-based sequence are given.     

Wave Node Dynamics and Revival Symmetry in Quantum Rotors

Symmetries and dynamics of wave nodes in space and time expose principles of quantum theory and its relativistic underpinning. Among these are key principles behind recently discovered dephasing and rephasing phenomena known as revivals. A reexamination of basic Eberly revivals, Berry “quantum fractal” landscapes, and the “quantum carpets” of Schleich and co-workers reveals a simple Farey arithmetic and C_n-group revival structure in one of the earliest quantum wave models, the Bohr rotor. These principles may be useful for interpreting modern time-dependent rovibrational spectra. The nodal dynamics of the Bohr rotor is seen to have a quasi-fractal structure similar to that of earlier systems involving chaotic circle maps. The fractal structure is an overlay of discrete versions of Bohr's rotor model. Each N-point Bohr rotor acts like a base-N quantum “odometer” which performs rational fraction arithmetic. Such systems may have applications for optical information technology and quantum computing.     

Complex temperature plane zeros in the mean-field approximation

We derive asymptotic expressions for the complex temperature plane zeros of the infinite-range Ising model in the scaling regime. The results also apply to high-dimensional, short-range Ising systems. For thenth zero in a system ofN spins, the leading asymptotic result ist _n (n/N)^1/2(–1 ±i).     

Multiple-Photon Dynamics in Molecules: A New Approach to High Resolution Spectroscopy of Highly Excited Vibrational States

Multi-photon transitions with two simultaneously interacting IR laser fields lead to final excited states with frequenciesnν = n₁ν₁+ n₂ν₂, withnthe total number of photons absorbed and (n,n₁,n₂) = (2, 1, 1), (3, 2, 1), (4, 1, 3), etc. The nature of the actual transition is determined by shift measurements, where the lasers are frequency-tuned by δν_iin opposite directions keeping the sum frequency,nν, resonant with the molecular transition. This technique opens a new spectral range for multi-photon transitions and a unique identification of the observed features. Forn₁andn₂both positive the excitation will lead to a “normal” up–up multi-photon transition. Many three- and four-photon transitions in the ν₃vibrational ladder of SF₆could be resolved with a resolution of 1 MHz, as well as four new two-photon transitions. As long asn₁+ n₂≥ 0, one of the twon_imay be negative resulting in an, e.g., up–down excitation pathway with its particular selection rules. The up–down excitations are demonstrated both for one- and two-photon transitions using the frequency shift technique. The different possible excitation schemes which meet the resonance condition for these transitions lead to interference effects and local couplings to highly excited states. Changes in resonance frequency for a one-photon transition (n= 1), due to these effects, are demonstrated. Evidently, the radiative coupling of participating levels to high-lying or quasi-continuum states may drastically change for different δν_ileading both to ac Stark shift and transition probability variations.     

Vortex dynamics in single crystal Hg-1201

Anisotropic superconducting materials often show an enhanced pinning along their crystallographic ab-planes. To obtain information about such a behavior of the high-T_c system Hg-1201 (HgBa₂CuO₄) magnetic investigations on a single crystal are performed for the two field orientations, parallel to the c-axis and parallel to the ab-planes. The dependence of the ac magnetization on temperature, magnetic field and frequency is determined. Compared to former results on powder samples of this system no indication of a second peak in the imaginary part of the susceptibility χ′′ is found. It seems to be shifted to higher temperatures overlapping now with the first peak. The corresponding irreversibility lines for both orientations, parallel to c and parallel to ab, are determined and discussed within the framework of a “diffusion” model.     

Role of the coupling between strains and order parameter gradient in crystals

The manifestation and the role of coupling between order parameter gradient and strains, or equivalently between order parameter and gradient of strains, is reviewed. Dynamical phenomena occurring in perovskites, and in particular in quantum paraelectric phases, evidenced as a coupling between phonon branches at q≠0, and also in several other systems (quartz, Sn₂P₂Se₆, Cs₂HgBr₄, and other systems satisfying the Lifshitz criterion) in relation with the formation of an incommensurate phase, are presented. Besides, the consequences in relation with domain walls, structure of incommensurate phases, and defects are also discussed.     

Observation of record flux pinning in melt-textured NEG-123 superconductor doped by Nb, Mo, and Ti nanoparticles

Flux pinning in melt-processed (Nd_0.33Eu_0.33Gd_0.33)Ba₂Cu₃O_y “NEG-123” + 35 mol% Gd₂BaCuO₅ “NEG-211” (70 nm in size) composite doped by TiO₃, MoO₃ and Nb₂O₅ achieved record values. The optimum values of all three dopands were found to be around 0.1 mol%. Transmission electron microscope (TEM) analysis found clouds of <10 nm sized particles in the NEG-123 matrix, shifting the pinning particle size distribution to significantly lower values. TEM by energy dispersive X-ray spectroscopy (EDX) analysis clarified that these nanoparticles contained a significant amount of Nb, Mo, and Ti. Appearance of nanometer-sized defects correlated with a significantly improved flux pining at low and medium magnetic fields, which was particularly significant at high temperatures. In the Nb-doped sample, a record J_c value of 925 kA/cm² at the secondary peak field (4.5 T) was achieved at 65 K, 640 kA/cm² at zero field at 77 K, and 100 kA/cm² at 90.2 K, the last value having been up to now considered as a good standard for REBa₂Cu₃O_y “RE-123” materials at 77 K. The greatly improved J_c–B performance in Nb/Mo/Ti doped samples can be easily translated to large-scale LRE-123 (LRE = light rare earths, Nd, Eu, Gd, Sm) blocks intended for real superconducting super-magnets applications.     

$\mathsf{La_{0.5}Sr_{0.5}CoO_{3}}$: A ferromagnet with strong irreversibility

Large spin systems as given by magnetic macromolecules or two-dimensional spin arrays rule out an exact diagonalization of the Hamiltonian. Nevertheless, it is possible to derive upper and lower bounds of the minimal energies, i.e. the smallest energies for a given total spin S. The energy bounds are derived under additional assumptions on the topology of the coupling between the spins. The upper bound follows from “n-cyclicity", which roughly means that the graph of interactions can be wrapped round a ring with n vertices. The lower bound improves earlier results and follows from “n-homogeneity", i.e. from the assumption that the set of spins can be decomposed into n subsets where the interactions inside and between spins of different subsets fulfill certain homogeneity conditions. Many Heisenberg spin systems comply with both concepts such that both bounds are available. By investigating small systems which can be numerically diagonalized we find that the upper bounds are considerably closer to the true minimal energies than the lower ones. Received 22 October 2002 / Received in final form 4 April 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: jschnack@uos.de