Hiroshi Ezawa

Phonons in a half space

Abstract Quantization of elastic waves in solid having a stress-free plane boundary and occupying a half space is carried out by constructing a complete orthonormal set of such waves. The quanta, which are called (generalized) surfons, should replace the ordinary bulk phonons when one deals with quantum physics of solid surfaces, e.g., the electron mobility in the inversion layer (thickness ∼ 10−6 cm, typically) of field-effect transistors.

Effect of inelastic scattering on resonant tunneling studied by the optical potential and path integrals

An analytical expression is obtained for the peak and valley currents of a resonant tunneling diode by using the optical potential to represent the effect of inelastic scattering. The assumption is made that scattered electrons in the well tunnel through both the left‐ and right‐hand‐side barriers in proportion to the transmission coefficient of each barrier. The result for peak current showing that scattering has little influence on it is in good agreement with microscopic theory. In contrast, the valley current increases in proportion to the scattering rate. It is pointed out that the controversy regarding sequential tunneling arises from the ambiguity of its definition. It is also pointed out that the Fabry–Perot effect still plays a significant role in producing resonance even when scattering is strong.

Characterization of thermal coherent and thermal squeezed states

Abstract Characterization of thermal coherent and thermal squeezed states are given in terms of the characteristic function. Previous characterizations of coherent state are analyzed and shown to involve a special stiplation for zero temperature. Relaxation of this stipulation characterizes the thermal coherent state. Further relaxation of the attributes leading to a thermal coherent state characterizes a general thermal squeezed state. Gedanken-experiment that allows the delineation of thermal coherent state from thermal squeezed state is outlined.

THEORY OF THE KAPITZA--DIRAC EFFECT.

The Kapitza-Dirac effect is the scattering of electrons by a standing wave of very intense light, which can nowadays be realized by using laser beam. A theory is presented, in which no assumptions are necessary as to the strength of the field and to the length of the interaction time. Basic is the assumption that the laser beam should have a gentle cross-sectional profile. It allows one to separate the electron motion into two components: The one parallel to the beam is the motion in the periodic field of light, which generates “adiabatic potential” for the motion transverse to the beam. This picture can be compared to that of hydrogen molecule in which electron motion generates the adiabatic potential for nuclear vibration. In this way, it is shown that the problem can be reduced to that of one-dimensional scattering. The present theory is shown to embrace the predecessor theories of Bartell and of Fedorov.

Difference in elastic scattering effects on resonant tunneling in one dimension and three dimensions

Abstract By use of the scattering matrix method which is equivalent to Feynmans path integrals, it is shown that elastic scattering influences resonant tunneling in quite a different manner in the one-dimensional and three-dimensional cases. In one dimensional resonant tunneling, the scattered waves interfere constructively with each other and, as a result, elastic scattering only shifts the resonance energy. On the contrary, in three dimensions, the scattered waves do not interfere with each other. Then, elastic scattering reduces the peak transmission and broadens the resonance width just as in the case of inelastic scattering.

Can Milne's method work well for the Coulomb-like potentials ?

We extend the improved Milnes (Milne-spline) method for obtaining eigenvalues and eigenfunctions to the cases of long-range and singular potentials, for which we have conjectured that it is difficult to apply the method. Contrary to our conjecture it turned out that the method is valid also for Coulomb potential and repulsive 1/xn(n = 2,3,...) type potential. Further we applied the method for two cases, for which the solutions are not known, in order to investigate the stability of the multi-dimensional universe. It has been shown that the extra-dimensional (internal) space of our universe is not stable in classical Einstein gravity as well as canonically quantized one. Two possibilities for stabilization were investigated: (i) noncanonically quantized Einstein gravity and (ii) canonically quantized higher curvature gravity. It has been suggested that the space is stable by qualitative and approximate methods. Exact analytical treatment is very difficult, so that numerical investigation is highly desirable. Numerical investigation shows that the space is stable with sufficient reliability.

Ornstein–Uhlenbeck Path Integral and Its Application

Introducing a path integral for the Ornstein–Uhlenbeck process distorted by a potential V(x), we find out the T→∞ limit of the probability distributions of X[ω]:=1/Tν∫0TV(ω(t)) dt for Ornstein–Uhlenbeck process ω(t), with appropriate values of the exponent ν that depend on V. The results are compared with those for the Wiener process.

Many-body effects in the subband structure of Si-MOS inversion layer

Abstract Exchange and correlation energies for the electron system in the (100) inversion layer in the Si-MOS at room temperature are calculated to determine the shifts of the subband bottoms. These shifts are expected to reduce the discrepancies between theory and experiments on electron mobility in the inversion layer.

Long-time average of field measured by a two-dimensional Brownian wanderer

For a 2-dimensional Brownian motion ω ( t ) starting from x 0 at t = 0 and for a given function V ( x ), x ∈ R 2 , we determine (i) a normalization factor ν( T ) such that the random variable, \(X[\mathbf{\omega}] = \lim_{T \to \infty} \nu(T)^{-1}\int_0^T V(\mathbf{\omega}(t))\text{d}t\), converges in law to have a nontrivial statistical distribution and (ii) the distribution itself. Assuming that \(\int_{\mathbb{R}^2}V(\mathbf{x})\text{d}^2x \ne 0\), we use a perturbation theory approach and obtain the complete sum of the series to find out that ν( T ) is log T and the probability distribution is one-sided exponential, independent of the starting point of the Brownian motion and the shape of V ( x ) under the condition that V ( x )∈ L 1 ( R 2 ) ∩ L p ( R 2 ) for some p >1 and its Fourier transform be Lipschitz continuous (order arbitrary) at the origin. This condition is slightly different from that of Kallianpur and Robbins who obtained the same result using a different method. We give an estimate, impo...

Long-time average of field values measured by a Brownian wanderer

For a given field V ( x ) on the x -axis, we shall find out the exponent ν such that \(X[\omega] = \frac{1}{T^{\nu}}\int_{0}^{T}V (\omega(t))\text{d}t\) has, in the limit T →∞, a non-trivial statis...