Narrow Results

Radio frequency (RF) magnetoplasmic waves known as helicons will propagate in solid-state plasmas when a strong magnetic field is applied. In our device the helicons were excited by RFs (the range 100-2000 MHz) much higher than the helicon generation frequency (the main peak at 20 MHz). The excitation of helicons in this case may be described by the effect similar to the Combination Scattering (Raman effect) when a part of the high RF wave energy that passes through the active material is absorbed and re-emitted by the magnetized solid-state plasma. It is expedient to call this experimental device a Helicon Maser (HRM) and the higher frequency e/m field - a pumping field. In full analogy with the usual Raman maser (or laser) the magnetized semiconductor sample plays the role of active material and the connecting cable - the role of high quality external resonator.

We develop a semiclassical theory of the nondegenerate parametric amplification in a single miniband of superlattice. We present the formulas describing absorption and gain of signal and idler fields in superlattice and analyze the limiting cases of strong and weak dissipation. We show how the well-known Manley-Rowe relations arise in the tight-binding lattice in the weak dissipation limit. Our results can be applied to an amplification of THz signals in semiconductor superlattices and a control of nonlinear transport of cold atoms in optical lattices.

We solve various master equations to obtain density operators' infinite operator-sum representation via a new approach, i.e., by virtue of the thermo-entangled state representation that has a fictitious mode as a counterpart mode of the system mode. The corresponding Kraus operators from the point of view of quantum channel are derived, whose normalization conditions are proved. Miscellaneous characters possessed by different quantum channels, such as decoherence, phase diffusion, damping, and amplification, can be shown explicitly in the entangled state representation of the density operators. Squeezing transformation is applied to the density operator for decoherence to generate a master equation for describing the phase sensitive process. Partial trace method for deriving new density operators is also introduced. Throughout our discussion, the technique of integration within an ordered product (IWOP) of operators is fully used.

The scattering properties of one-dimensional potential with gain are studied by using a Schrödinger-like equation. The corresponding Hamiltonian is non-Hermitian with a real energy spectrum. The amplification-absorption duality previously observed is interpreted in terms of the transmission and reflection phases. For a rectangular barrier, the transmission phase oscillates with the barrier width as for passive systems, but the oscillations period is significantly reduced in the absorption region. In this region the reflection phase vanishes and the multiple scattering and interferences dominate. The gain effect is also investigated for double barrier structures as well as superlattices with active potentials. It is found that resonant tunneling energy and the mini-band width are not influenced by the gain, but the transmission is enhanced for small values of the potential imaginary part. For large values, the resonant transmission significantly decreases and the mini-bands disappear.

Two “amplified” quantum states, that is, amplified coherent state (ACS) and amplified squeezed vacuum (ASV), are considered in this paper by applying operator $(g-1)a^{†}a+1$ on coherent state (CS) and squeezed vacuum (SV), respectively. Here $g$$(\ge 1)$ denotes a amplification factor and $a^{†}(a$) denote the creation (annihilation) operator. Along these two lines, we make a comparative analysis of properties for ACS and ASV. The considered properties include density matrix elements, Wigner function, mean photon number, second-order autocorrelation function, and quadrature squeezing. We derive analytical expressions and make numerical simulations for all the properties. The noteworthy results include: (1) the ACS has antibunching and squeezing characters; (2) the ASV will have the bunching and antibunching effect in small initial squeezing.

In this paper, we introduce the amplified thermal state (ATS) by operating $(g-1)\widehat{n}+1$ on the thermal state (TS). Here, $g>1$ is the amplification factor and $\widehat{n}$ is the photon number operator. We study its properties, such as light intensity, signal-to-noise ratio (SNR), Fock matrix elements and Wigner function. In addition, we study its decoherence in photon-loss channel by analyzing evolution of all above properties. All considered properties are derived analytically and simulated numerically. Compared with the original TS, the amplification can enhance light intensity and SNR, remain the mixed character, and exhibit non-Gaussianity. While the decoherence will weaken light intensity and SNR, remain the mixed character, and return to Gaussian state.

This paper aims to study the transfer laws of vibration signals in the free field near a high-speed train line by conducting a field test. The characteristics of ground vibration acceleration were analyzed in the time and frequency domains, and a prediction method in the frequency domain was proposed. The results show: (1) there is a vibration amplification area away from the bottom of the pier under the influence of high-speed trains running over the bridge due to the fluctuation attenuation of the vibration waves; (2) the dominant peak frequency points in the frequency spectrum of the acceleration can be regarded as the resonance frequency induced by periodic loading; and (3) the soil vibration can be effectively predicted by the proposed method with a strong capability to defend the interference of environmental vibrations according to the comparison between the predicted value and the experimental data.

Two schemes of amplification of two-mode squeezed light in the continuous variable EPR-state are considered. They are based on the integrals of motion, which allow conserving quantum correlations whereas the power of each mode may increase. One of these schemes involves a three-photon parametric process in a nonlinear transparent medium and the other is a Raman type interaction of light with atomic ensemble. A generalization to multimode squeezed light is discussed.

We prove energy estimates for exact solutions to a class of linear, weakly stable, first-order hyperbolic boundary problems with “large”, oscillatory, zeroth-order coefficients, that is, coefficients whose amplitude is large, $O(1)$, compared to the wavelength of the oscillations, $O(𝜖)$. The methods that have been used previously to prove useful energy estimates for weakly stable problems with oscillatory coefficients (e.g. simultaneous diagonalization of first-order and zeroth-order parts) all appear to fail in the presence of such large coefficients. We show that our estimates provide a way to “justify geometric optics”, that is, a way to decide whether or not approximate solutions, constructed for example by geometric optics, are close to the exact solutions on a time interval independent of $𝜖$. Systems of this general type arise in some classical problems of “strongly nonlinear geometric optics” coming from fluid mechanics. Special assumptions that we make here do not yet allow us to treat the latter problems, but we believe the present analysis will provide some guidance on how to attack more general cases.

An analytical model is used to investigate the resonant behavior in a semi-closed channel. The main integral quantities of the tidal wave are obtained by means of a linearized one-dimensional model as a function of three dimensionless parameters, representing cross-section convergence, friction and distance to the closed boundary. Arbitrary along-channel variations of width and depth are accounted for by using a multi-reach approach, whereby the main tidal dynamics are reconstructed by solving a set of linear equations satisfying the continuity conditions of water level and discharge at the junctions of the sub-reaches. We highlight the importance of depth variation in the momentum equation, which is not considered in the classical tidal theory. The model allows for a direct characterization of the resonant response and for the understanding of the relative importance of the controlling parameters, highlighting the role of convergence and friction. Subsequently, the analytical model is applied to the Bristol Channel and the Guadalquivir estuary. The proposed analytical relations provide direct insights into the tidal resonance in terms of tidal forcing, geometry and friction, which will be useful for the study of semi-closed tidal channels that experience relatively large tidal ranges at the closed end.

Earthquakes and microtremor records are used for estimating the site response of hard rock sites comprising four three-component seismic stations which operate as part of the Israel Seismic Network. The response functions are determined by implementing the horizontal-to-vertical component spectral ratio of earthquake shear-waves (receiver function estimates) and microtremors (Nakamura's estimate) observed simultaneously at the site. The sites of seismic stations ATZ (Mt. Atzmon), MBH (Mt. Berech) and MRNI (Mt. Meron) exhibit amplification attributed to topography effects. At ATZ, within the 1.3–2.0 Hz range, the amplification is in the order of factor 4. At MBH amplification levels of 3.0–3.5 are observed in the frequency range 1.5–4.0 Hz. Station MRNI exhibits a relatively strong amplification effect (up to 4) in the frequency range of about 2.5 to 3.5 Hz. Slight amplification around 5 Hz is observed at ATR (the proposed site for a nuclear power plant). These effects were correlated with the thickness of the weathered layer above unweathered chalk. A comparison between the amplification factor observed during earthquakes and those inferred from microtremors shows that these are, in general, in agreement. However, details of the spectral ratios from different microtremor recordings are not exactly the same. Differences appear mainly in the frequency at which the maximum amplification occurs. These observations demonstrate the usefulness of non-reference technique in estimating the topographical effects of ground shaking. These methods may be used in the process of seismic hazard assessment for ridges and mountain tops, common sites for settlements, communication relay stations, bridges, rope-drive and power transmission towers.

A time-domain parametric study for the seismic response of a region located on the eastern bank of the Kifisos river canyon is performed to evaluate the significance of topography and soil effects on the seismic response of slopes. This region experienced unexpectedly heavy damage during the 7 September 1999 M_s 5.9 earthquake. Two-dimensional finite-element and spectral-element analyses are conducted using Ricker wavelets of various central frequencies as horizontal and vertical base excitation. The significance of a layered soil profile and the frequency content of the input motion, the emergence of "parasitic" acceleration components, and the effect of the angle of incidence on the amplification of the incoming waves are all discussed in detail. It is shown that the presence of a surface soil layer significantly affects the amplification pattern. The so-called Topographic Aggravation Factor (defined as the 2D/1D Fourier spectral ratio) achieves its maximum value very near the crest, in function of the frequency content of the excitation. For the particular soil conditions and geometry analysed, vertically propagating SV waves incite at about the critical angle, resulting in the highest topographic amplification.

Large modifications of seismic waves are produced by variations of material properties near the Earth's surface and by both surface and buried topography. These modifications, usually referred to as "site response", in general lead to larger motions on soil sites than on rock-like sites. Because the soil amplifications can be as large as a factor of ten, they are important in engineering applications that require the quantitative specification of ground motions. This has been recognised for years by both seismologists and engineers, and it is hard to open an earthquake journal these days without finding an article on site response. What is often missing in these studies, however, are discussions of the uncertainty of the predicted response. A number of purely observational studies demonstrate that ground motions have large site-to-site variability for a single earthquake and large earthquake-location-dependent variability for a single site. This variability makes site-specific, earthquake-specific predictions of site response quite uncertain, even if detailed geotechnical and geological information is available near the site. Predictions of site response for average classes of sites exposed to the motions from many earthquakes can be made with much greater certainty if sufficient empirical observations are available.

A summary of dynamic measurements are presented that illustrate relations between linear seismic demand and true nonlinear response of unreinforced masonry buildings with flexible diaphragms and rocking piers subjected to a series of simulated earthquake motions.

This paper examines the seismic response of clay pile-raft system with flexible and stiff piles using centrifuge and numerical studies. Centrifuge studies showed that interaction between pile-raft and clay will cause a significant softening in the clay adjacent to the pile-raft which produced a lengthening of resonance period in near-field soil compared to the far-field soil. The difference of response among the raft and the soil at both near- and far-field indicates that ground motion at both near- and far-field cannot be representative of raft motion. There is also significant difference between flexible and stiff pile response. It has been shown in a previous study that, for stiff pile, the soft clay acts as an inertial loading medium rather than a supporting medium. For this reasons, the bending moment diagram extends deep into the soft soil stratum. However, for flexible pile, the supporting effect of the surrounding clay is much more significant than in stiff pile. As a result, the bending moment envelope for flexible pile under earthquake shaking is very similar to the head-loaded test results, with an active length of pile below which no significant bending moment occurs.

One of the important factors in the amplification of seismic waves arriving the ground surface is site effects. Site effects, known as topographic irregularities, lead to seismic wave scattering, and this phenomenon can amplify or reduce the displacement recorded in different parts of a site. Therefore, it is necessary to investigate these effects for an accurate evaluation of the dynamic response of the structures built on these sites. One of the topics that has been given little attention is the interaction effects of topographic irregularities on each other’s dynamic responses. Using the three-dimensional boundary element method (3D-BEM) in the frequency domain, this study investigated the dynamic response of the site with canyons and hills adjacent to each other at different intervals and under SH seismic waves with different angles and dimensionless frequencies and with the hill in different geometries (semi-elliptical, triangular, semi-circular). The obtained results indicated that parts of the canyon that are adjacent to the hill underwent the greatest amplification, especially when the distance between the canyon and the hill is small. It was also found that the incident angle of the waves is one of the important parameters in the obtained displacement pattern on the site. Although the wave hit the canyon-hill site vertically, the results revealed that an asymmetric displacement pattern was experienced on the dynamic response of the site due to the phenomenon of amplification of seismic wave dispersion.

A systematic analysis of matched layers is undertaken with special attention to better understand the remarkable method of Bérenger. We prove that the Bérenger and closely related layers define well-posed transmission problems in great generality. When the Bérenger method or one of its close relatives is well-posed, perfect matching is proved. The proofs use the energy method, Fourier–Laplace transform, and real coordinate changes for Laplace transformed equations. It is proved that the loss of derivatives associated with the Bérenger method does not occur for elliptic generators. More generally, an essentially necessary and sufficient condition for loss of derivatives in Bérenger's method is proved. The sufficiency relies on the energy method with pseudodifferential multiplier. Amplifying and nonamplifying layers are identified by a geometric optics computation. Among the various flavors of Bérenger's algorithm for Maxwell's equations, our favorite choice leads to a strongly well-posed augmented system and is both perfect and nonamplifying in great generality. We construct by an extrapolation argument an alternative matched layer method which preserves the strong hyperbolicity of the original problem and though not perfectly matched has leading reflection coefficient equal to zero at all angles of incidence. Open problems are indicated throughout.

Radio frequency (RF) magnetoplasmic waves known as helicons will propagate in solid-state plasmas when a strong magnetic field is applied. In our device the helicons were excited by RFs (the range 100-2000 MHz) much higher than the helicon generation frequency (the main peak at 20 MHz). The excitation of helicons in this case may be described by the effect similar to the Combination Scattering (Raman effect) when a part of the high RF wave energy that passes through the active material is absorbed and re-emitted by the magnetized solid-state plasma. It is expedient to call this experimental device a Helicon Maser (HRM) and the higher frequency e/m field - a pumping field. In full analogy with the usual Raman maser (or laser) the magnetized semiconductor sample plays the role of active material and the connecting cable - the role of high quality external resonator.

We develop a semiclassical theory of the nondegenerate parametric amplification in a single miniband of superlattice. We present the formulas describing absorption and gain of signal and idler fields in superlattice and analyze the limiting cases of strong and weak dissipation. We show how the well-known Manley-Rowe relations arise in the tight-binding lattice in the weak dissipation limit. Our results can be applied to an amplification of THz signals in semiconductor superlattices and a control of nonlinear transport of cold atoms in optical lattices.

We naturally define the weak value on the basis of the probability theory in quantum mechanics. Furthermore, using this theory, we discuss the amplification process of a signal, and we have shown that there is no upper bound for the signal amplification.