Intermediate-field effects and electron motion in an axial plane in cadmium

1976 ◽  
Vol 54 (18) ◽  
pp. 1866-1879 ◽  
Author(s):  
J. E. A. Alderson ◽  
C. M. Hurd ◽  
S. P. McAlister
Keyword(s):  
Saddle Point ◽  
Path Integral ◽  
Field Condition ◽  
Basal Plane ◽  
Axial Plane ◽  
Electron Motion ◽  
Hall Resistivity ◽  
Magnetic Breakdown ◽  
Intermediate Field ◽  
Closed Electron

The Hall resistivity ρ21(B,T) observed in Cd when B lies in the basal plane has been measured in fields B = 0.1–2.4 T and at temperatures T = 1.7–560 K. The behaviour of ρ21(B,T) in the intermediate-field condition is analysed first qualitatively in terms of contributions arising from features such as intersheet scattering, magnetic breakdown, open and saddle-point orbits, as well as closed electron and hole orbits. These qualitative conclusions are supported by a path integral calculation of the magnetoresistive tensor that is produced by model orbits chosen to imitate the principal contributors to conduction in an axial plane. The results provide an explanation of the origins of the principal features seen in the behaviour of ρ21(B,T) when [Formula: see text].

Electron motion and the Hall effect in monocrystalline zinc

1977 ◽  
Vol 55 (7-8) ◽  
pp. 620-628 ◽  
Author(s):  
C. M. Hurd ◽  
J. E. A. Alderson ◽  
S. P. McAlister
Keyword(s):  
Qualitative Analysis ◽  
Hall Effect ◽  
Path Integral ◽  
Basal Plane ◽  
Electron Motion ◽  
Cyclotron Motion ◽  
Transverse Magnetoresistance ◽  
Hall Resistivity ◽  
Magnetic Breakdown

The Hall resistivity ρ21(B, T) observed in Zn when [Formula: see text] and [Formula: see text] has been measured in fields B = 0.1–2.0 T and at temperatures T = 1.7–680 K. Supporting measurements of the transverse magnetoresistance have also been made at 1.7 K. A qualitative analysis of ρ21(B, T) is given separately for the cases when the cyclotron motion is confined to an axial or to the basal plane. In the latter case, the discussion is supported by path integral calculations based upon model orbits chosen to imitate all the geometrical possibilities arising from magnetic breakdown between the monster and needle sheets. The results provide an explanation of the principal features shown by ρ21(B, T).

Temperature dependence of the Hall effect in monocrystalline magnesium

1977 ◽  
Vol 55 (18) ◽  
pp. 1621-1627 ◽  
Author(s):  
S. P. McAlister ◽  
J. E. A. Alderson ◽  
C. M. Hurd
Keyword(s):  
Fermi Surface ◽  
Temperature Dependence ◽  
Hall Effect ◽  
Path Integral ◽  
Basal Plane ◽  
Quantitative Interpretation ◽  
Cyclotron Motion ◽  
Temperature Range ◽  
Hall Resistivity ◽  
Magnetic Breakdown

The Hall resistivity ρ21(B,T) observed when [Formula: see text] and [Formula: see text] has been measured in monocrystals of Mg in the temperature range 1.7–300 K and in an applied flux up to 2 T. A quantitative interpretation when [Formula: see text] is made using a path integral calculation of the magnetoresistive tensor produced by representative orbits on a model Fermi surface. The results explain the origins of the principal features in the behaviour of ρ21(B,T), and show the importance of magnetic breakdown in cyclotron motion in the basal plane.

Intermediate-field effects and the Hall resistivity in the basal plane of cadmium

1976 ◽  
Vol 14 (2) ◽  
pp. 395-408 ◽  
Author(s):  
C. M. Hurd ◽  
J. E. A. Alderson ◽  
S. P. McAlister
Keyword(s):  
Basal Plane ◽  
Hall Resistivity ◽  
Field Effects ◽  
Intermediate Field

The physics of meron pairs. I. Introduction, motivation, and formalism

1980 ◽  
Vol 58 (6) ◽  
pp. 845-858 ◽  
Author(s):  
David G. Laughton
Keyword(s):  
Saddle Point ◽  
Path Integral ◽  
Path Integrals ◽  
Field Configuration ◽  
Degree Of Freedom ◽  
Leading Order ◽  
Local Minima ◽  
Yang Mills ◽  
Ordinary Integral

The physics of meron pairs is considered in this series of papers. The first paper presents the motivation for focussing on this particular type of field configuration as an important degree of freedom in the SU(N) Yang–Mills theory. It also outlines the formalism for doing a saddle point expansion of path integrals about configurations which are constrained minima of the action (such as meron pairs) as opposed to local minima (such as instantons). The formalism is illustrated by the treatment of an ordinary integral which is analogous to the meron pair region of the Yang–Mills path integral. It is found that the expansion about constrained minima depends to leading order on the constraints chosen to partition the integral. This means that some criteria must be found for the choice of constraints. This problem is discussed. The actual meron pair calculations are partially described here and done in the second and third papers. Applications are to be considered in any subsequent papers.

scholarly journals Gravitational and gravitoscalar thermodynamics

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Shoichiro Miyashita
Keyword(s):  
Scalar Field ◽  
Partition Function ◽  
Cosmological Constant ◽  
Saddle Point ◽  
Path Integral ◽  
Thermodynamical Properties ◽  
Entropy Bound ◽  
New Type ◽  
Universal Properties ◽  
Gravitational Thermodynamics

Abstract Gravitational thermodynamics and gravitoscalar thermodynamics with S2 × ℝ boundary geometry are investigated through the partition function, assuming that all Euclidean saddle point geometries contribute to the path integral and dominant ones are in the B3 × S1 or S2 × Disc topology sector. In the first part, I concentrate on the purely gravitational case with or without a cosmological constant and show there exists a new type of saddle point geometry, which I call the “bag of gold(BG) instanton,” only for the Λ > 0 case. Because of this existence, thermodynamical stability of the system and the entropy bound are absent for Λ > 0, these being universal properties for Λ ≤ 0. In the second part, I investigate the thermodynamical properties of a gravity-scalar system with a φ2 potential. I show that when Λ ≤ 0 and the boundary value of scalar field Jφ is below some value, then the entropy bound and thermodynamical stability do exist. When either condition on the parameters does not hold, however, thermodynamical stability is (partially) broken. The properties of the system and the relation between BG instantons and the breakdown are discussed in detail.

SPIN AND CHARGE FLUCTUATION IN CUPRATE OXIDE SUPERCONDUCTORS

1996 ◽  
Vol 10 (15) ◽  
pp. 705-716
Author(s):  
MING-LIANG ZHANG ◽  
ZHONG-XIAN ZHAO
Keyword(s):  
Saddle Point ◽  
Path Integral ◽  
Integral Form ◽  
Band Model ◽  
Oxide Superconductors ◽  
Charge Fluctuation ◽  
Saddle Point Approximation ◽  
Point Approximation ◽  
Cuprate Oxide ◽  
Two Band Model

Spin and charge fluctuation are obtained from a two-band model making use of saddle point approximation in path-integral form.

Activation instanton in real-time formalism

2014 ◽  
Vol 28 (16) ◽  
pp. 1450128
Author(s):  
I. V. Kolokolov ◽  
Nguyen Thanh Trung
Keyword(s):  
Saddle Point ◽  
Real Time ◽  
Path Integral ◽  
Soft Mode ◽  
Brownian Particle ◽  
Integral Formalism ◽  
Path Integral Formalism ◽  
Time Formalism ◽  
Probability Flux ◽  
Real Time Formalism

In this paper, we study the dynamics of the activation of a Brownian particle using the path integral formalism in real time. Along with the construction of the saddle-point (instanton) solutions, we develop the formalism allowing to calculate the effect of the fluctuations near this solution in detail. In particular, it is shown that there is a soft mode for which the integration is not Gaussian and just this mode is responsible for the finite probability flux.

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.

Sign in / Sign up

Export Citation Format

Share Document