Determining the long living quasi-normal modes of relativistic stars

Methods of finding quasi-normal modes of non-rotating relativistic stars have been well established,however,none of the existing treatments which take spacetime and fluid oscillations fully into account can determine modes of long decay time,e.g.,the p and g mode series,or the f modes for stars with low compactness ratio (M/R). In this paper we show how the quasi-normal modes of long lifetime can be determined through refinements of a treatment originally due to Detweiler and Lindblom. The determination of the p mode series has been argued in the literature to have implication on the life time of gravitational wave sources and stellar stability. In this paper we 1) provide detailed steps in our treatment to facilitate future effort in this direction; 2) correct mistakes in the literature on the formulation; and 3) analyse the accuracy of the quasi-normal mode frequencies obtained and the limitations of the treatment.     

Study of intrinsic localized vibrational modes in micromechanical oscillator arrays

Intrinsic localized modes (ILMs) have been observed in micromechanical cantilever arrays, and their creation, locking, interaction, and relaxation dynamics in the presence of a driver have been studied. The micromechanical array is fabricated in a 300 nm thick silicon-nitride film on a silicon substrate, and consists of up to 248 cantilevers of two alternating lengths. To observe the ILMs in this experimental system a line-shaped laser beam is focused on the 1D cantilever array, and the reflected beam is captured with a fast charge coupled device camera. The array is driven near its highest frequency mode with a piezoelectric transducer. Numerical simulations of the nonlinear Klein-Gordon lattice have been carried out to assist with the detailed interpretation of the experimental results. These include pinning and locking of the ILMs when the driver is on, collisions between ILMs, low frequency excitation modes of the locked ILMs and their relaxation behavior after the driver is turned off.     

Controlled generation of intrinsic localized modes in microelectromechanical cantilever arrays

We propose a scheme to induce intrinsic localized modes (ILMs) at an arbitrary site in microelectromechanical cantilever arrays. The idea is to locate the particular cantilever beam in the array that one wishes to drive to an oscillating state with significantly higher amplitude than the average and then apply small adjustments to the electrical signal that drives the whole array system. Our scheme is thus a global closed-loop control strategy. We argue that the dynamical mechanism on which our global driving scheme relies is spatiotemporal chaos and we develop a detailed analysis based on the standard averaging method in nonlinear dynamics to understand the working of our control scheme. We also develop a Markov model to characterize the transient time required for inducing ILMs.     

Quantization of intrinsic localized modes: Effective linear lattice method

A working method is proposed to quantize intrinsic localized modes (ILMs) in lattices with hard quartic anharmonicity in the framework of the rotating-wave approximation. This is done by reducing a nonlinear eigenvalue problem to a linear one by averaging slowly varying reduced effective force constants over frequencies, enabling us to quantize the ILM in a straightforward manner. Such an effective linear lattice (ELL) method is first applied to an analytically tractable d-dimensional cubic lattice to show that the concept of the ELL holds exactly in the strong localization limit. Next, general lattice models are investigated to achieve quantization of the ILM in an approximate manner. The obtained analytical results are tested by solving numerically a model one-dimensional lattice to show that phase-space trajectory of an ILM-bearing atom is of elliptic type with finite but small width. The numerical result confirms the validity of the ELL leading to its semi-classical quantization. On the other hand, orbits of all the remaining atoms exhibits complex non-periodic trajectory to which a direct application of the semi-classical quantization rule appears impossible.     

Controlled switching of intrinsic localized modes in a one-dimensional antiferromagnet

Nearly-steady-state locked intrinsic localized modes (ILMs) in the quasi-1D antiferromagnet (C(2)H(5)NH(3))(2)CuCl(4) are detected via four-wave mixing emission or the uniform mode absorption. Exploiting the long-time stability of these locked ILMs, repeatable nonlinear switching is observed by varying the sample temperature, and localized modes with various amplitudes are created by modulation of the microwave driver power. This steady-state ILM locking technique could be used to produce energy localization in other atomic lattices.     

Vertical transport of subwavelength localized surface electromagnetic modes

Transport of subwavelength electromagnetic (EM) energy has been achieved through near‐field coupling of highly confined surface EM modes supported by plasmonic nanoparticles, in a configuration usually on a two‐dimensional (2D) substrate. Vertical transport of similar modes along the third dimension, on the other hand, can bring more flexibility in designs of functional photonic devices, but this phenomenon has not been observed in reality. In this paper, designer (or spoof) surface plasmon resonators (‘plasmonic meta‐atoms’) are stacked in the direction vertical to their individual planes in demonstrating vertical transport of subwavelength localized surface EM modes. The dispersion relation of this vertical transport is determined from coupled‐mode theory and is verified with a near‐field transmission spectrum and field mapping with a microwave near‐field scanning stage. This work extends the near‐field coupled resonator optical waveguide (CROW) theory into the vertical direction, and may find applications in novel three‐dimensional slow‐light structures, filters, and photonic circuits.

     

Solitons and intrinsic localized modes in a one-dimensional antiferromagnetic chain

By use of the Hartree approximation and the method of multiple scales, we investigate quantum solitons and intrinsic localized modes in a one-dimensional antiferromagnetic chain. It is shown that there exist solitons of two different quantum frequency bands: i.e., magnetic optical solitons and acoustic solitons. At the boundary of the Brillouin zone, these solitons become quantum intrinsic localized modes: their quantum eigenfrequencies are below the bottom of the harmonic optical frequency band and above the top of the harmonic acoustic frequency band.     

Observation of locked intrinsic localized vibrational modes in a micromechanical oscillator array

The nonlinear vibrational properties of a periodic micromechanical oscillator array have been measured. For sufficiently large amplitude of the driver, the optic mode of the di-element cantilever array becomes unstable and breaks up into excitations ranging over only a few cells. A driver-induced locking effect is observed to eternalize some of these intrinsic localized modes so that their amplitudes become fixed and the modes become spatially pinned.     

On the possibility of a phonon mediated transport anomaly in MgB2 under compression

Results of electrical resistance measurements on MgB₂ at ambient temperature up to 25 GPa are presented. An abrupt reduction of nearly 30% in resistance around 18 GPa is observed. Band structure calculations in the presence of a frozen-in distortion of the E_2g phonon mode reveal that one of the closed Fermi sheets corresponding to the σ-band opens along the Γ-A direction at this pressure. It is suggested that the anomaly observed in the resistance is due to this phonon mediated electronic topological transition (ETT).     

On a possibility for observing the neutron electric polarizability

A new method is proposed for setting a lower or upper limit a α _n * on the neutron electric polarizability α _an . It is based on the fact that the real part of the s-wave scattering amplitude changes sign near the s-wave neutron resonance at E=E*. The methods consist of the observation of the energy behavior of the forward-backward scattering asymmetry ω ₁ which experiences a jump at E=E*. If the jump is such that dω ₁/dE>0, then α _n >α _n *, while if dω ₁/dE<0, then α _n <α _n *, and if dω ₁/dE∼0, then α _n ∼α _n *. Seven even-even nuclei are found with α _n * from 0.5 to 3.1 in 10⁻³ fm³. Some details of a possible experiment with ¹⁸²W are described. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 3, 171–174 (10 August 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

On the possibility of a thermal spectrum of particles produced by an electric field

The exponentially damped electric field is shown to produce particles with a thermal spectrum from vacuum if the residual action of the field on the particles produced may be neglected.     

Influence of nonlinear atomic interaction on excitation of intrinsic localized modes in carbon nanotubes

Excitation of intrinsic localized modes (ILMs) in carbon nanotubes (CNTs) with different chiral structures was investigated by molecular dynamics simulations. For CNTs with a chiral angle less than or equal to 30^°, energy concentration that continued for more than 200 fs was found in a localized area, where a pair of neighboring atoms strongly oscillated with a higher vibrational frequency than the upper bound of phonon bands. This evidently indicates excitation of the ILM. On the other hand, the ILM was not excited in CNTs with a chiral angle greater than or equal to 41^°. Analyzing the nonlinearity of the interaction between excited atoms in the ILM vibration mode, we elucidated that nonlinearity predominates the selective ILM excitation. Furthermore, stronger nonlinearity excites ILMs with both higher frequency and longer lifetime.     

具有格点各向异性的一维铁磁链中的量子孤子和内禀局域模(英文)

基于Hartree-Fock方法和多标度方法,我们考察了具有格点各向异性的一维铁磁链中的量子孤子和内禀局域模,量子磁振子的波函数由量子包络孤子来描述.在布里渊区边界,量子包络孤子变成了量子内禀局域模,它的量子本征频率在简谐波带的顶部上方,量子磁振子主要集中在中心位置j=j0的附近.     

On the intrinsic quadrupole electric field of a centrosymmetric dielectric

In agreement with a prediction of the theory, we have observed experimentally the intrinsic quadrupole electric field of a centrosymmetric crystal. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 1, 15–20 (10 January 1998)     

On the possibility of a new electric effect in ultrathin superfluid films

Two integrable cases of two-dimensional Schrödinger equation with a magnetic field are proposed. Using the polar coordinates and the symmetrical gauge, we will obtain solutions of these equations through biconfluent and confluent Heun functions. The quantization rules will be derived for both systems under consideration.