Functional approach to nuclear field theory: A schematic model with pairing and particle-hole forces

Path integral techniques in collective variables are applied to a schematic model with monopole pairing and particle-hole forces. The single-particle and collective excitation modes of the system for various kinds of phase transitions are discussed. We formulate a modified perturbation theory (loop expansion) from which, finally, nuclear field theory (NFT) is obtained. The NFT Lagrangian is strictly derived. The graphical rules of the NFT expansion come out automatically.     

Nuclear effective interactions and spin excitations

In view of the one-boson-exchange model for the nucleon-nucleon interaction and the Hartree-Fock (HF) interaction, we formulate the effective interactions for particle-hole states in terms of the exchange of the fields which are confined in the nucleus. This theory, as an extension to the nuclear field theory (NFT), takes into account the propagation of the fields which is neglected in NFT. The effective interactions thus obtained reproduce the energies of a sequence of electric giant resonances and the core polarizabilities associated with the resonances. It is found that the coupling constants of the σ- and ω-fields are suppressed for the particle-hole interaction by 60% with respect to the HF interaction. As for the effective interactions involving nucleon spins, we consider the fields coupled to nucleon spins. The effective interactions obtained, essentially different from those in NFT, have a tensor component. We analyse the energies and cross sections for excitation of stretched spin particle-hole states which are the most sensitive to the tensor force. The effective interaction responsible for the stretched spin states is shown to be consistent with that for the magnetic resonances observed in the (p, n) reactions.     

The boson-fermion hybrid representation formulation,I

A boson-fermion hybrid representation is presented. In this framework, a fermion system is described concurrently by the bosonic and the fermionic degrees of freedom. A fermion pair in this representation can be treated as a boson without violating the Pauli principle. Furthermore the “bosonic interactions” are shown to originate from the exchange processes of the fermions and can be calculated from the original fermion interactions. Both the formulation of the BFH representations for the even and odd nuclear systems are given. We find that the basic equation of the nuclear field theory (NFT) is just the usual Schrödinger equation in such a representation with the empirical NFT diagrammatic rules emerging naturally. This theory was numerically checked in the case of four nucleons moving in a single-j shell and the exactness of the theory was established.     

Application of the nuclear field theory to superfluid nuclei: The quasiparticle-phonon multiplet

The quasiparticle-phonon multiplet of superfluid spherical nuclei is investigated in the framework of the nuclear field theory (NFT), using the pairing plus quadrupole force. In leading order of the NFT expansion there exists a simple relation between the energy splitting of the multiplet and the ground state B(Eλ) transitions from the multiplet. This relation states that the reduced matrix elements for the B(Eλ) transition decrease linearly with increasing energies of the multiplet states. The extent to which this relation is fulfilled by available experimental data is checked.The influence of the spurious correlations involved in the NFT treatment due to the BCS approximation is estimated. The numerical calculations are performed for ⁹³Nb where the ground state B(Eλ) transitions are measured for all multiplet states.     

Neurofeedback Training Based on Motor Imagery Strategies Increases EEG Complexity in Elderly Population

Neurofeedback training (NFT) has shown promising results in recent years as a tool to address the effects of age-related cognitive decline in the elderly. Since previous studies have linked reduced complexity of electroencephalography (EEG) signal to the process of cognitive decline, we propose the use of non-linear methods to characterise changes in EEG complexity induced by NFT. In this study, we analyse the pre- and post-training EEG from 11 elderly subjects who performed an NFT based on motor imagery (MI–NFT). Spectral changes were studied using relative power (RP) from classical frequency bands (delta, theta, alpha, and beta), whilst multiscale entropy (MSE) was applied to assess EEG-induced complexity changes. Furthermore, we analysed the subject’s scores from Luria tests performed before and after MI–NFT. We found that MI–NFT induced a power shift towards rapid frequencies, as well as an increase of EEG complexity in all channels, except for C3. These improvements were most evident in frontal channels. Moreover, results from cognitive tests showed significant enhancement in intellectual and memory functions. Therefore, our findings suggest the usefulness of MI–NFT to improve cognitive functions in the elderly and encourage future studies to use MSE as a metric to characterise EEG changes induced by MI–NFT.     

Electromagnetic decay of the giant quadrupole resonances: (II). Nuclear structure aspects

We analyze experiments on the electromagnetic decay of the GQR from the point of view of the microscopic theory of the nuclear structure. The calculations are made systematically in the lowest contributing order of perturbation theory within the NFT formalism. Care is taken in order to prevent spurious mixing of the isoscalar and isovector parts of dipole operators. As in previous theoretical calculations, the results are consistent with the experimental limit of the ratio between the transition populating the 2.62 MeV 3⁻ state and the g.s. However they fail to reproduce the strong dipole transition to the 4.97 MeV 3⁻ state.     

Simulation on double-ring-resonator-type device considering gain for heat-assisted magnetic recording

Optical Review - Heat-assisted magnetic recording (HAMR) is a promising technology for improving the recording density of hard disk drives. A near-field transducer (NFT), which forms a small light...     

Simulation on near-field light on recording medium generated by semiconductor ring resonator with metal nano-antenna for heat-assisted magnetic recording

Optical Review - Heat-assisted magnetic recording (HAMR) is a promising technology for achieving more than 10 Tbit/inch2 recording density. A near-field transducer (NFT), which forms a small light...     

An all-scale anelastic model for geophysical flows: dynamic grid deformation

We have developed an adaptive grid-refinement approach for simulating geophysical flows on scales from micro to planetary. Our model is nonoscillatory forward-in-time (NFT), nonhydrostatic, and anelastic. The major focus in this effort to date has been the design of a generalized mathematical framework for the implementation of deformable coordinates and its efficient numerical coding in a generic Eulerian/semi-Lagrangian NFT format. The key prerequisite of the adaptive grid is a time-dependent coordinate transformation, implemented rigorously throughout the governing equations of the model. The transformation enables mesh refinement indirectly via dynamic change of the metric coefficients, while retaining advantages of Cartesian mesh calculations (speed, low memory requirements, and accuracy) conducted fully in the computational domain. Diverse test results presented in this paper – simulations of a traveling stratospheric inertio-gravity-wave packet (with numerically advected dense-mesh region) and an idealized climate of the Earth (with analytically prescribed adaptive transformations) – demonstrate the potential and the efficacy of the new deformable grid model for tracing targeted flow features and dynamically adjusting to prescribed undulations of model boundaries.     

The exactness of the GCM description of the j3 and j4 systems

Under the single-j shell assumption, some typical cases of j³ and j⁴ are introduced as examples of the way in which the validity and exactness of the GCM (generator coordinate method) can be demonstrated. The exact solutions, equivalent to those from the shell model and exact NFT (nuclear field theory), are obtained within the actual procedure of effective GCM hamiltonian derivation, while the unphysical states are identified and discarded in this procedure naturally through performing diagonalization of the N-operator matrix.     

The renormalization of collective states and the improper initial or final states in NFT

The collective lines in a given diagram are renormalized by including higher order processes. The problem is cast into the form of a conventional linear algebraic matrix equation that allows a simple treatment of the normalization conditions. It is shown that the states entering in the renormalization of the phonons become improper initial or final states, if dressed phonons are used in the intermediate states. A simple extension of this argument allows one to justify one of the rules given in the formulation of the NFT.     

Simulation on near-field light generated by metal nano-dot on GaAs substrate for heat source of heat-assisted magnetic recording

Heat-assisted magnetic recording (HAMR) is promising for achieving more than 1 Tb/inch² recording density. A near-field transducer (NFT), which forms a hot spot of 10–100 nm in diameter on a recording medium, is necessary in HAMR. In this study, localized surface plasmons generated by a metal nano-dot in a novel device for a heat source of heat-assisted magnetic recording were analyzed using a simple model in which a metal hemisphere was formed on a GaAs substrate and a quasi-electrostatic approximation. The scattering and absorption efficiencies as well as the enhancement factor were investigated for several kinds of metal. As a result, their dependence on the wavelength and the polarization direction of the incident light was clarified.     

Non local effects induced by the particle-vibration coupling

Dynamical corrections to the single particle potential are (perturbatively) evaluated. The corrections tom ^*/m resulting from the coupling of independent (effective) fermions to collective vibrations (low energy modes) are analyzed within the NFT formalism. The results for the²⁰⁸Pb are discussed.     

The applicability of nuclear field theory to shell-model calculations

Previous NFT calculations of the four-particle spectrum reached different conclusions concerning the applicability of the lowest-order Rayleigh-Schroedinger perturbation expansion. In the present paper, we show that the inclusion of second-order diagrams and/or diagonalization procedures yields satisfactory results both for the energies and for the transfer matrix elements even for j-shells as small as the $\text{j =}\text{7}\text{2}$ and $\text{j =}\text{11}\text{2}$ shells.     

Building resolving large-eddy simulations and comparison with wind tunnel experiments

We perform large-eddy simulations (LES) of the flow past a scale model of a complex building. Calculations are accomplished using two different methods to represent the edifice. The first method employs the standard Gal-Chen and Somerville terrain-following coordinate transformation, common in mesoscale atmospheric simulations. The second method uses an immersed boundary approach, in which fictitious body forces in the equations of motion are used to represent the building by attenuating the flow to stagnation within a time comparable to the time step of the model. Both methods are implemented in the same hydrodynamical code (EULAG) using the same nonoscillatory forward-in-time (NFT) incompressible flow solver based on the multidimensional positive definite advection transport algorithms (MPDATA). The two solution methods are compared to wind tunnel data collected for neutral stratification. Profiles of the first- and second-order moments at various locations around the model building show good agreement with the wind tunnel data. Although both methods appear to be viable tools for LES of urban flows, the immersed boundary approach is computationally more efficient. The results of these simulations demonstrate that, contrary to popular opinion, continuous mappings such as the Gal-Chen and Somerville transformation are not inherently limited to gentle slopes. Calculations for a strongly stratified case are also presented to point out the substantial differences from the neutral boundary layer flows.     

Eigenvalue spectrum analysis for temporal signals of Kerr optical frequency combs based on nonlinear Fourier transform

Based on the nonlinear Schr?dinger equation(NLSE) with damping, detuning, and driving terms describing the evolution of signals in a Kerr microresonator, we apply periodic nonlinear Fourier transform(NFT) to the study of signals during the generation of the Kerr optical frequency combs(OFCs). We find that the signals in different states, including the Turing pattern, the chaos, the single soliton state, and the multi-solitons state, can be distinguished according to different distributions of the eigenvalue spectrum. Specially, the eigenvalue spectrum of the single soliton pulse is composed of a pair of conjugate symmetric discrete eigenvalues and the quasi-continuous eigenvalue spectrum with eye-like structure.Moreover, we have successfully demonstrated that the number of discrete eigenvalue pairs in the eigenvalue spectrum corresponds to the number of solitons formed in a round-trip time inside the Kerr microresonator. This work shows that some characteristics of the time-domain signal can be well reflected in the nonlinear domain.     

Dual origin of pairing in nuclei

The pairing correlations of the nucleus ¹²⁰Sn are calculated by solving the Nambu–Gor’kov equations, including medium polarization effects resulting from the interweaving of quasiparticles, spin and density vibrations, taking into account, within the framework of nuclear field theory (NFT), processes leading to self-energy and vertex corrections and to the induced pairing interaction. From these results one can not only demonstrate the inevitability of the dual origin of pairing in nuclei, but also extract information which can be used at profit to quantitatively disentangle the contributions to the pairing gap Δ arising from the bare and from the induced pairing interaction. The first is the strong ¹ S ₀ short-range NN potential resulting from meson exchange between nucleons moving in time reversal states within an energy range of hundreds of MeV from the Fermi energy. The second results from the exchange of vibrational modes between nucleons moving within few MeV from the Fermi energy. Short- (v _p ^bare) and long-range (v _p ^ind) pairing interactions contribute essentially equally to nuclear Cooper pair stability. That is to the breaking of gauge invariance in open-shell superfluid nuclei and thus to the order parameter, namely to the ground state expectation value of the pair creation operator. In other words, to the emergent property of generalized rigidity in gauge space, and associated rotational bands and Cooper pair tunneling between members of these bands.     

Dynamic non-linear response of beams subjected to impact loads

A non-linear theory is presented for plane deformation of beams which allows for longitudinal stretching as well as for cross-sectional stretching and shearing. The exact strain measures for this theory are also deduced. The longitudinal and flexural motions are coupled in the theory. If the cross section is constrained from stretching, the resulting theory may be classified as a non-linear Timoshenko beam theory. The equations of the latter theory are used to study the motion of beams under impact loads.     

On the Foundations of Superstring Theory

Superstring theory is an extension of conventional quantum field theory that allows for stringlike and branelike material objects besides pointlike particles. The basic foundations on which the theory is built are amazingly shaky, and, equally amazingly, it seems to be this lack of solid foundations to which the theory owes its strength. We emphasize that such a situation is legitimate only in the development phases of a new doctrine. Eventually, a more solidly founded structure must be sought. Although it is advertised as a “candidate theory of quantum gravity”, we claim that string theory may not be exactly that. Rather, just like quantum field theory itself, it is a general mathematical framework for a class of theories. Its major flaw could be that it still embraces a Copenhagen view on the relation between quantum mechanics and reality, while any “theory of everything”, that is, a theory for the entire cosmos, should do better than that.