Triple, quintuple and higher order multiple quantum MAS NMR of quadrupolar nuclei

The optimization of the coherence transfers involved in five, seven and nine-quantum versions of the recently discovered MQMAS technique, is analysed numerically. Data reported in this paper may serve as starting parameters for the experiment set up. An analysis of the intensity and resolution given by each type of experiment is performed, which confirms the need to use very high rf fields for MQ transfers. It follows that five-quantum is achievable rather easily but the use of seven and nine-quantum MAS experiments becomes increasingly difficult due to the demand for high rf power and decreasing sensitivity. The advantages of using the z-filter MQMAS method with respect to a two-pulse sequence are analysed. The method for qualitatively and quantitatively interpret the MQMAS spectra is described. The nature of the spinning side bands along the multiple quantum dimension is explained. It is shown that the rotor synchronization can be conveniently used to eliminate these side bands, but only for 3QMAS experiments. The use of the multiple-quantum method in combination with static samples and VAS, DAS and DOR techniques is finally discussed.     

On the incorporation of cubic and hexagonal interfacial energy anisotropy in phase field models using higher order tensor terms

In this paper, we show how to incorporate cubic and hexagonal anisotropies in interfacial energies in phase field models; this incorporation is achieved by including up to sixth rank tensor terms in the free energy expansion, assuming that the free energy is only a function of coarse-grained composition, its gradient, curvature and aberration. We derive the number of non-zero and independent components of these tensors. Further, by demanding that the resultant interfacial energy is positive definite for inclusion of each of the tensor terms individually, we identify the constraints imposed on the independent components of these tensors. The existing results in the invariant group theory literature can be used to simplify the process of construction of some (but not all) of the higher order tensors. Finally, we derive the relevant phase field evolution equations and describe some preliminary results from our 1D simulations.     

A density expansion of the pion-nucleus optical potential. II. Second order terms

The second order terms in a density expansion of the pion optical potential V_opt are evaluated quantitatively. The coefficients of these terms are proportional to various combinations of on- and off-shell nucleon-nucleon T-matrices, averaged over the distribution of two nucleon relative momenta in the Fermi sea. The on-shell contributions can be obtained directly from experimental phase shifts, but the calculation of the off-shell-parts requires a model for the nucleon-nucleon potential. We consider a number of realistic local and nonlocal, separable potentials which fit nucleon-nucleon phase shifts, in order to study the variations in V_opt which arise from differences in the off-shell behavior of T. We find absorptive (imaginary) and dispersive (real) contributions to V_opt which are of comparable magnitude. The dispersive part, which leads to a real energy shift associated with the two nucleon absorptive process, has not been previously estimated quantitatively. We compare our results to empirical potentials obtained by fitting energy level shifts and widths in pi-mesic atoms, as well as theoretical estimates based on threshold cross sections for the processes π + N + N ? N + N.     

Multiple bursts, multiple looks, and stream coherence in the release from informational masking

In the simultaneous multitone masking paradigm introduced by Neff and Green [Percept. Psychophys. 41, 409-415 (1987)] the masker typically is a small number of tones having frequencies and levels that are randomly drawn on every presentation. Large amounts of masking for a pure-tone signal often occur that are thought to reflect central, rather than peripheral, limitations on processing. Previous work from this laboratory has indicated that playing a rapid succession of randomly drawn multitone maskers in each observation interval dramatically reduces the amount of masking that is observed relative to a single burst (SB). In this multiple-bursts-different (MBD) procedure, the signal tone is the only constant frequency component during the sequence of bursts and tends to perceptually segregate from the masker. In this study, the number of masker bursts and the interburst interval (IBI) were varied. The goals were to determine how the release from masking relative to the SB condition depends on the number of bursts and to examine whether increasing the IBI would cause each burst to be processed independently. If the latter were true, it might disrupt the perception of signal stream coherence, thereby diminishing the MBD advantage. However, multiple independent looks could also lead to an improvement in performance. For those subjects showing large amounts of informational masking in the SB condition, substantial reduction in masked thresholds occurred as the number of masker bursts increased, while masking increased as IBI lengthened. The results were not consistent with a simple version of a multiple-look model in which the information from each burst was combined optimally, but instead appear to be attributable to mechanisms involved in the perceptual organization of sounds.     

Chaos in the perturbed Korteweg-de Vries equation with nonlinear terms of higher order

The dynamical behaviour of the generalized Korteweg-de Vries (KdV) equation under a periodic perturbation is investigated numerically. The bifurcation and chaos in the system are observed by applying bifurcation diagrams, phase portraits and Poincaré maps. To characterise the chaotic behaviour of this system, the spectra of the Lyapunov exponent and Lyapunov dimension of the attractor are also employed.     

Phase representations of the density matrix and quantum distribution functions

A broad class of representations for the density matrix of phase-space functions is proposed. It is shown that all the known quantum distribution functions are particular cases of this representation. The corresponding equations are found. An examination is made of the conditions under which the phase representation may be a quantum distribution function.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol. 12, No. 4, pp. 111–115, April, 1969.The author thanks Professor Ya. P. Terletskii for valuable advice.     

Role of interfaces in higher order angular terms of magnetic anisotropies: ultrathin film structures

The role of interface inhomogeneities on macroscopic magnetic anisotropy terms was investigated using simple mathematical modeling. It is shown that the intrinsic anisotropies caused by the spin–orbit interaction in the presence of lateral inhomogeneities can create additional magnetic anisotropies with higher order angular terms. The lateral inhomogeneous distribution of the uniaxial anisotropy can result in the presence of a fourth order angular term. These anisotropies decrease the total energy, and their strength is affected by the exchange averaging effect. Large atomic terraces allow the local magnetic moment to deviate from the mean orientation resulting in negative higher order angular terms in magnetic anisotropies satisfying the sample symmetry. The negative sign results in the magnetic easy axes being oriented 45° with respect to the intrinsic uniaxial axis. It is shown that the additional higher order terms do not always have to satisfy the time inversion symmetry. Odd powers in directional cosines can arise when the exchange restoring torque becomes comparable to or weaker than torques from the internal fields. The additional higher order angular terms in magnetic anisotropies decrease usually more rapidly with the sample thickness than the intrinsic interface anisotropies. Their rapid decrease in strength with an increasing sample thickness allows one to distinguish them from the intrinsic interface anisotropies. It will be shown that the magnetic anisotropies originating in interface inhomogeneities can play an important role in the magnetic phase transitions of ultrathin film structures.     

On the existence of equilibrium states in local quantum field theory

It is shown that any local quantum field theory admits thermodynamical equilibrium states (KMS-states) for all positive temperatures provided it satisfies a nuclearity condition, proposed by Wichmann and one of the authors, which restricts the admissible number of local degrees of freedom.Dedicated to E. H. Wichmann on the occasion of his 60th birthday     

Off-diagonal long-range order coherence,quantum chaos and nonself-averaging of the excitation function oscillations in dissipative heavy-ion collisions

We support a recent suggestion that the exit microchannel correlation in dissipative heavy-ion collisions indicates the off-diagonal long-range order coherence and quantum chaos. Such a correlation is revealed in the nonself-averaging of the excitation function oscillations observed in dissipative heavy-ion collisions. We present the results of an analysis of the data to demonstrate this correlation, and discuss a possible interconnection between quantum coherent motion and macroscopic phenomena.     

Theoretical investigations of the vapour-liquid equilibrium and dielectric properties of dipolar Yukawa fluids in an external field

In a low field approximation, using the dipolar Yukawa fluid model (in mean spherical approximation as a reference system) a consistent field-dependent free energy expression is proposed for the calculation of the vapour-liquid equilibrium of polar fluids in an applied electric field. A perturbation theory high field approximation expression of the free energy is also proposed to study the field-dependent properties of fluids. In the high field approximation, equations for the field-dependent polarization and for the nonlinear dielectric constant (or Piekara constant) are also predicted. It has been discussed that our approximations are appropriate to describe the vapour-liquid-like phase equilibria and the magnetization curves of magnetic fluids.     

Local properties of equilibrium states and the particle spectrum in quantum field theory

It is shown that in a quantum field theory describing free, scalar particles with masses m _i , i there exist locally normal equilibrium states with finite energy density for all temperature >0 if and only if . This result lends support to the conjecture that the nuclearity criterion proposed by Buchholz and Wichmann is sensitive to the thermodynamical properties of field-theoretic models.     

Propagation and coherence properties of higher order partially coherent dark hollow beams in turbulence

We formulate and evaluate in terms of graphical outputs, source and receiver plane expressions, the complex degree of coherence, beam size variation and power in bucket performance for higher order partially coherent dark hollow beams propagating in turbulent atmosphere. Our formulation is able to cover square, rectangular, circular, elliptical geometries for dark hollow and flat-topped beams in one single expression. From the graphical outputs of the receiver plane, it is observed that higher order partially coherent dark hollow beams will initially develop an outer ring around a central lobe, but will eventually evolve towards a Gaussian shape as the propagation distance is extended. It is further observed that stronger turbulence levels and greater partial coherence have similar effects on beam profile. During propagation, modulus of complex degree of coherence of partially coherent dark hollow beams appears to rise above that of the source plane values, reaching as high as near unity. Beam size analysis shows that, among the types examined, (nearly) flat-topped beam experiences the least beam expansion. Power in bucket analysis indicates that lowest order square fully coherent dark beam offers the best power capturing.     

On the characterization of relativistic quantum field theories in terms of finitely many vacuum expectation values. II

The problem of uniqueness of monotone continuous linear extensions of $$T_{(2N)} = \{ 1,T_1 ,...,T_{2N} \} \in E'_{(2N)} = \prod\limits_{n = 0}^{2N} {E'_n } $$ is solved. A characterization of a relativistic QFT in terms of finitely many VEV's is derived. All results are illustrated by an explicit discussion of the extension problem for special cases ofT ₍₄₎={1,0,T ₂,T ₃,T ₄}. This discussion contains explicitly necessary and sufficient conditions onT ₍₄₎ for the existence of minimal extensions and some convenient sufficient conditions.     

Causal independence and the energy-level density of states in local quantum field theory

Within the general framework of local quantum field theory a physically motivated condition on the energy-level density of well-localized states is proposed and discussed. It is shown that any model satisfying this condition obeys a strong form of the principle of causal (statistical) independence, which manifests itself in a specific algebraic structure of the local algebras (split property). It is also shown that the proposed condition holds in a free field theory.Dedicated to H. J. Borchers on the occasion of his 60th birthday     

NMR dipolar constants of motion in liquid crystals: Jeener–Broekaert, double quantum coherence experiments and numerical calculation on a 10-spin cluster

Two proton quasi-equilibrium states were previously observed in nematic liquid crystals, namely the and quasi-invariants. Even though the experimental evidence suggested that they originate in a partition of the spin dipolar energy into a strong and a weak part, respectively, from a theoretical viewpoint, the existence of an appropriate energy scale which allows such energy separation remains to be confirmed and a representation of the quasi-invariants is still to be given. We compare the dipolar NMR signals yielded both by the Jeener–Broekaert (JB) experiment as a function of the preparation time and the free evolution of the double quantum coherence (DQC) spectra excited from the state, with numerical calculations carried out from first principles under different models for the dipolar quasi-invariants, in a 10-spin cluster which represents the 5CB (4^′-pentyl-4-biphenyl-carbonitrile) molecule. The calculated signals qualitatively agree with the experiments and the DQC spectra as a function of the single-quantum detection time are sensible enough to the different models to allow both to probe the physical nature of the initial dipolar-ordered state and to assign a subset of dipolar interactions to each constant of motion, which are compatible with the experiments. As a criterion for selecting a suitable quasi-equilibrium model of the 5CB molecule, we impose on the time evolution operator consistency with the occurrence of two dipolar quasi-invariants, that is, the calculated spectra must be unaffected by truncation of non-secular terms of the weaker dipolar energy. We find that defining the quasi-invariant as the subset of the dipolar interactions of each proton with its two nearest neighbours yields a realistic characterization of the dipolar constants of motion in 5CB. We conclude that the proton-spin system of the 5CB molecule admits a partition of the dipolar energy into a bilinear strong and a multiple-spin weak contributions therefore providing two orthogonal constants of motion, which can be prepared and observed by means of the JB experiment. This feature, which implies the existence of two timescales of very different nature in the proton-spin dynamics, is ultimately dictated by the topology of the spin distribution in the dipole network and can be expected in other liquid crystals. Knowledge of the nature of the dipolar quasi-invariants will be useful in studies of dipolar-order relaxation, decoherence and multiple quantum NMR experiments where the initial state is a dipolar-ordered one.     

Stability and coherence of strong-coupling magneto-bipolaron in asymmetric quantum dot under laser field effect

On the fundamental basis of the modified Lee Low Pines theoretical method, we study analytically the stability and coherence of magneto-bipolaron in asymmetric quantum dot (QD) under the laser field. It is observed that, the bipolaron stability strongly depends on the electron–phonon coupling constant, magnetic field, laser frequency and high laser field strength. It is shown that, the laser field can trap and cool the magneto-bipolaron under certain conditions. The laser and magnetic field strongly affect the coherence time of bipolaron. This study enables to construct superconducting materials.