A nodal determination of the Hall conductance

1991 ◽  
Vol 433 (1889) ◽  
pp. 547-571
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Uniform Magnetic Field ◽  
Periodic Potential ◽  
Electronic States ◽  
Simple Method ◽  
Hall Conductance ◽  
Nodal Structure ◽  
Nodal Pattern

We investigate the nodal structure of the electronic states which arise in the case of a uniform magnetic field and a weak periodic potential. By making use of the continuous motion of these zeros as the K -value labelling the state is varied, we introduce a simple method of obtaining the quantized value of the Hall conductance of a filled band from the nodal pattern of the band wave function. This method is demonstrated to give the correct results in the cases where the Hall conductances are known, given by the solutions of a Diophantine equation.

Calcul des éléments dipolaires et quadrupolaires de la matrice de transition moléculaire dans Na2

1990 ◽  
Vol 68 (4-5) ◽  
pp. 365-368 ◽  
Author(s):  
K. Hussein ◽  
O. Babaky
Keyword(s):  
Numerical Integration ◽  
Electronic States ◽  
Transition Elements ◽  
Simple Method ◽  
Selection Rules ◽  
Variable Formula ◽  
Method Of Calculation ◽  
Analytical Integration ◽  
Fifth Order

In this paper, we study a calculation of the transition elements [Formula: see text] between electronic states of the diatomic molecules Na2. We show the necessary selection rules for the determination of these operators by a method of analytical integration on the variable [Formula: see text], combined with a numerical integration to fifth order. The values found by this simple method of calculation are very reasonable and show that the important transitions [Formula: see text], [Formula: see text]; and [Formula: see text] of the dimer Na2 are dipolar. [Traduit par la revue]

STRING THEORY AND DUALITIES IN THE QUANTUM DISSIPATIVE HOFSTADTER SYSTEM

2009 ◽  
Vol 24 (32) ◽  
pp. 6141-6156 ◽  
Author(s):  
TAEJIN LEE
Keyword(s):  
Magnetic Field ◽  
String Theory ◽  
Uniform Magnetic Field ◽  
Periodic Potential ◽  
Open String ◽  
Coulomb Gas ◽  
Two Dimensions ◽  
Theory Formulation ◽  
Critical Regions ◽  
Gas Expansion

We study the dualities of the quantum dissipative Hofstadter system which describes particles moving in two dimensions, subject to a uniform magnetic field, a periodic potential and a dissipative force. Using the string theory formulation, we show that the system has two kinds of dualities. The duality, previously known as the exact duality in the literature is shown to correspond to a subgroup of the T-dual symmetry group unbroken by the periodic boundary potential in string theory. The other duality is a particle–kink duality in the noncommutative open string theory which is a generalized Schmid duality in the presence of the uniform magnetic field. The kinks of the dissipative Hofstadter model are found to be noncommutative objects. The particle–kink duality, which is called previously the approximate duality, is shown to be also exact. In contrast to the previous derivation, which is based on the Coulomb gas expansion of the partition function and asserts that the duality holds only approximately in the regime of strong magnetic field, the string theory formulation proves that duality holds always exactly in the off-critical regions where the periodic potential becomes strong, regardless of the strength of the magnetic field. The dualities of the DHM may also be useful for studying the rolling tachyon in string theory in the presence of the Neveu–Schwarz (NS) B-field, since both DHM and rolling tachyon in the presence of NS B-field are described by the same action.

Some magnetic properties of metals. V. Magnetic behaviour of a cylindrical system of electrons for all magnetic fields

1953 ◽  
Vol 216 (1124) ◽  
pp. 118-142 ◽  
Keyword(s):  
Magnetic Field ◽  
Magnetic Properties ◽  
Wave Function ◽  
Magnetic Susceptibility ◽  
Uniform Magnetic Field ◽  
Magnetic Behaviour ◽  
The Other ◽  
Cylindrical System ◽  
Different Types ◽  
Large Systems

The Wentzel-Kramers-Brillouin method is used to solve the Schrödinger equation for an electron moving in a uniform magnetic field H , the boundary of the system being a cylinder with its axis lying along the direction of the field. It is found that there are two entirely different types of wave-function possible, one type leading to the small Landau diamagnetism of large systems discussed in part I of this series, the other to the larger diamagnetism of small systems discussed in part IV. Taking into account the occupied states of both types, the steady (non-periodic) contributions to the magnetic susceptibility are derived for all fields in both the low- and high-temperature limits, and for most fields at intermediate temperatures.

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