Effect of Magnetic Breakdown on the Magnetoconductivity of Cadmium

1975 ◽  
Vol 53 (11) ◽  
pp. 1060-1070 ◽  
Author(s):  
R. J. Douglas ◽  
W. R. Datars
Keyword(s):  
Relaxation Time ◽  
Path Integral ◽  
Integral Method ◽  
Energy Gap ◽  
Relaxation Times ◽  
Breakdown Field ◽  
Fermi Velocity ◽  
Spin Orbit ◽  
Magnetic Breakdown ◽  
Path Integral Method

The magnetoconductivity and magnetoresistivity tensors of cadmium have been calculated by the path integral method for magnetic fields in the [Formula: see text] and [Formula: see text] directions. A uniform relaxation time and a modified nearly free electron Fermi surface were used. Magnetic breakdown across the HAL spin–orbit energy gap vitiated Kohler's rule and necessitated separate calculations for different relaxation times. Even with open orbits, cadmium was found to be a 'compensated' metal in that the Hall terms never dominated the conductivity tensor determinant. A single breakdown field was found to be inadequate to describe magnetic breakdown on the sheaf of orbits which touch the HAL plane. A range of breakdown fields was calculated across the sheaf of open orbits. From an explanation of induced torque data, it was found that the ratio of the spin–orbit energy gap in the HAL plane to the Fermi velocity is 1.4 × 10−8 eV s cm−1. The resulting field dependences of the magnetoconductivity and magnetoresistivity tensor components are presented and discussed. The use of the path integral technique when there is magnetic breakdown is also presented.

Magnetoconductivity of Aluminum Computed by the Path-Integral Method

1973 ◽  
Vol 51 (16) ◽  
pp. 1770-1785 ◽  
Author(s):  
R. J. Douglas ◽  
W. R. Datars
Keyword(s):  
Field Dependence ◽  
Path Integral ◽  
Integral Method ◽  
Relaxation Times ◽  
Longitudinal Component ◽  
Zero Field ◽  
Temperature Dependent ◽  
The Mean ◽  
Carrier Velocity ◽  
Path Integral Method

The components of the electrical magnetoconductivity and magnetoresistivity tensors of aluminum were calculated by the path-integral method using a nearly-free-electron Fermi surface and a uniform relaxation time. Results are presented for longitudinal and transverse magnetoresistance, the longitudinal–transverse components, and the Hall term. The induced torque calculated from the computed magnetoresistivity components is in excellent agreement with measured anisotropy and field dependence of the induced torque. The torque anisotropy results primarily from the longitudinal magnetoresistance anisotropy which arises from variations with crystal orientation of the mean of the orbitally averaged longitudinal component of carrier velocity. The observed magnetic field dependence of the Hall coefficient is reproduced using a temperature-dependent ratio of the relaxation times for the electron and hole bands. The irreducible even-field Hall terms, which are calculated for field directions in the (112) plane, are discussed. The longitudinal–transverse components of magnetoresistivity can saturate at values as high as 0.16 of the zero-field resistivity, but the effects of the longitudinal–transverse magnetoconductivity on the magnetoresistance and Hall coefficients are small. Reported linear high-field magnetoresistance is discussed.

Theoretical study on second hyperpolarizability of H3+ system by path integral method

1997 ◽  
Vol 85 (1-3) ◽  
pp. 1159-1160 ◽  
Author(s):  
H. Nagao ◽  
M. Nakano ◽  
S. Yamada ◽  
K. Ohta ◽  
K. Yamaguchi
Keyword(s):  
Path Integral ◽  
Integral Method ◽  
Theoretical Study ◽  
Second Hyperpolarizability ◽  
Path Integral Method

An analysis of quantum effects on the thermodynamic properties of cryogenic hydrogen using the path integral method

2014 ◽  
Vol 140 (13) ◽  
pp. 134506 ◽  
Author(s):  
H. Nagashima ◽  
S. Tsuda ◽  
N. Tsuboi ◽  
M. Koshi ◽  
K. A. Hayashi ◽  
...  
Keyword(s):  
Thermodynamic Properties ◽  
Path Integral ◽  
Integral Method ◽  
Quantum Effects ◽  
Path Integral Method

The quantum bouncer by the path integral method

1991 ◽  
Vol 59 (10) ◽  
pp. 924-930 ◽  
Author(s):  
D. A. Goodings ◽  
T. Szeredi
Keyword(s):  
Path Integral ◽  
Integral Method ◽  
Path Integral Method

PATH INTEGRAL METHOD FOR LIMITING DISTRIBUTION OF AN ESTIMATOR ARISING FROM AN AR(1)-PROCESS WITH A UNIT ROOT

2013 ◽  
Vol 16 (04) ◽  
pp. 1350029
Author(s):  
SHIH-FENG HUANG ◽  
YUH-JIA LEE ◽  
HSIN-HUNG SHIH
Keyword(s):  
Characteristic Function ◽  
Path Integral ◽  
Unit Root ◽  
Autoregressive Model ◽  
Integral Method ◽  
Unit Root Test ◽  
Random Variable ◽  
Limiting Distribution ◽  
First Order ◽  
Path Integral Method

We propose the path-integral technique to derive the characteristic function of the limiting distribution of the unit root test in a first order autoregressive model. Our results provide a new and useful approach to obtain the closed form of the characteristic function of a random variable associated with the limiting distribution, which is realized as a ratio of Brownian functionals on the classical Wiener space.

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