Integral Kernel Operators on Fock Space – Generalizations and Applications to Quantum Dynamics

A general theory of operators on Boson Fock space is discussed in terms of the white noise distribution theory on Gaussian space (white noise calculus). An integral kernel operator is generalized from two aspects: (i) The use of an operator-valued distribution as an integral kernel leads us to the Fubini type theorem which allows an iterated integration in an integral kernel operator. As an application a white noise approach to quantum stochastic integrals is discussed and a quantum Hitsuda–Skorokhod integral is introduced. (ii) The use of pointwise derivatives of annihilation and creation operators assures the partial integration in an integral kernel operator. In particular, the particle flux density becomes a distribution with values in continuous operators on white noise functions and yields a representation of a Lie algebra of vector fields by means of such operators.     

抽指加权宽带扇形叉指声表面波滤波器的等效电路分析

扇形换能器可以看成若干个沿孔径方向划分的均匀孔径换能器电端并联而成，根据梅森(Mason)等效电路模型以及由其延伸的混合场等效电路模型，推导出整个扇形换能器的导纳矩阵和频率响应，其中采用复阻抗模型考虑了叉指电极与自由表面的阻抗不连续的因素。本方法能够模拟指间反射、三次行程、指条寄生阻抗以及外围电路等对器件性能的影响；理论模拟与实验结果吻合。     

Optical current transducer with bulk type Bi12SiO20 faraday sensor for power systems

Two types of optical current transducers (OCTs) have a bulk Faraday sensor inserted into the gap of an iron core and a porcelain insulator with optical fiber. The sensor consists of Bi₁₂SiO₂₀ (BSO) single crystal, a polarizer, and an analyzer. The OCTs satisfied the target performance requirement for fault location and metering and demonstrated maintained performance at some power utilities in Japan and the US. We have developed a fault location system that immediately detects the fault current with the OCTs, there by locating the fault section. The OCT can easily replace the existing support insulators for the disconnecting switch without any modifications to structure height or bus-bar. For metering requiring 0.3% class accuracy, use of a BSO with right optical rotatory power combined with BSO with left optical rotatory power results in a Faraday sensor with improved temperature characteristics. The OCT demonstrated 0.3% class accuracy for metering described in the current transformer Specifications of IEEE C57–13, 1993.     

A new formula for the saddle-to-scission time

We propose a new formula for the saddle-to-scission time that is more general that the one based on Kramers' approach. Its validity and applicability is then studied in detail. Such a formula is useful for the evaluation of the fission time of very heavy nuclei.     

Polarizability effect in metallic clusters

Langevin approach implemented in the inelastic cross-sections measured for the low-energy electrons colliding with metallic clusters points out that statical form of the polarizability dominate at energies less than 1.25 eV. The dynamical form comes into play at energies around 1.3 eV. The form of the polarizabilities indicates that polarizability of the metallic clusters is energy-dependent.     

Optical current transducers using flint glass fiber as the faraday sensor element

This paper describes development of the optical current transducers using flint glass fiber as the Faraday effect sensing element. Excellent polarization properties of the fiber with low birefringence are described, and the design and test data of a current transducer using the fiber manufactured for use in electric power facilities are reviewed. Experimental results on flexible characteristics of a scheme with round trip light transmission in the fiber is also reported.     

Velocity spectrum for non-Markovian Brownian motion in a periodic potential

Non-Markovian Brownian motion in a periodic potential is studied by means of an electronic analogue simulator. Velocity spectra, the Fourier transforms of velocity autocorrelation functions, are obtained for three types of random force, that is, a white noise, an Ornstein—Uhlenbeck process, and a quasimonochromatic noise. The analogue results are in good agreement both with theoretical ones calculated with the use of a matrix-continued-fraction method, and with the results of digital simulations. An unexpected extra peak in the velocity spectrum is observed for Ornstein-Uhlenbeck noise with large correlation time. The peak is attributed to a slow oscillatory motion of the Brownian particle as it moves back and forth over several lattice spaces. Its relationship to an approximate Langevin equation is discussed.     

Projector formalism of generalized Brownian motion theory applied to dissipative and noisy systems

The projector formalism of Zwanzig-Mori type is extended to obtain generalized Fokker-Planck and generalized nonlinear Langevin equations for coarse-grained variables when the underlying microscopic dynamics is dissipative and noisy (stochastic).     

Frequency fine-tuning in Class IV flextensional transducers

Class IV flextensional transducers (FTs) are the best-known FTs in literature. These are light-weight projectors (compared to the conventional Tonpilz designs) with capability for high power delivery at low frequencies. The resonance frequencies of this type of transducers are known to be dominantly dependent on the characteristics of the outer shell than on the driver stack. Consequently, the method of achieving fine-tuning of the transducer by modifying the characteristics of the stack, as practiced in the case of Tonpilz designs, is not very effective. This paper describes a method for fine-tuning of the frequency of a Class IV FT, which involves only a modification of a pair of small components used for coupling the stack to the transducer. The effectiveness of the method is examined by finite element modelling using the package ATILA, in the case of a 3 kHz aluminium shell transducer. Experimental results are also presented.     

Langevin dynamic simulation of hysteresis in a field-swept Landau potential

Numerical simulations are done of Langevin dynamics for a uniform-orderparameter, field-swept Landau model,= –|a/2|m ²+|b/4|m ⁴–mh(t) , to study hysteresis effects. The field is swept at a constant rateh(t)=h(0)+ht. The stochastic jump values of the field {h_J from an initially prepared metastable minimumm(0) are recorded, on passage to a global minimum m(). The results are: (a) The mean jump¯h _J(h) increases (hysteresis loop widens) with h, confirming a previous theoretical criterion based on rate competition between field-sweep and inverse mean first-passage time (FPT); (b) The broad jump distribution(h _J,h) is related to intrinsically large FPT fluctuations ( ²–²)/ ² O(1), and can be quantitatively understood. Possible experimental tests of the ideas are indicated.