Validity of the Conservation Rule of Nodal Surface Numbers in the Wave Function of Hydrogenic Exciton in Magnetic Field

1982 ◽  
Vol 48 (17) ◽  
pp. 1215-1219 ◽  
Author(s):  
Noritaka Kuroda ◽  
Yuichiro Nishina ◽  
Hidenobu Hori ◽  
Muneyuki Date
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Nodal Surface ◽  
Conservation Rule

Superfluidity and Superconductivity

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Wave Packet ◽  
Long Range ◽  
Cooper Pair ◽  
Bose Condensation ◽  
Range Order ◽  
Condensed State ◽  
Long Range Order ◽  
Coherent Wave

Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.

scholarly journals Gutzwiller wave function under magnetic field

1997 ◽  
Vol 230-232 ◽  
pp. 418-420 ◽  
Author(s):  
Hisatoshi Yokoyama ◽  
Shinya Tokizaki
Keyword(s):  
Magnetic Field ◽  
Wave Function

scholarly journals DISSIPATIVE 2D ELECTRON ON A TORUS IN EXTERNAL MAGNETIC FIELD: TRANSPORT PROPERTIES AND MAGNETIC TRANSLATIONS

1995 ◽  
Vol 09 (24) ◽  
pp. 3229-3240 ◽  
Author(s):  
G. CRISTOFANO ◽  
D. GIULIANO ◽  
G. MAIELLA ◽  
L. VALENTE
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Transport Properties ◽  
Ground State ◽  
Large Time ◽  
Transverse Magnetic ◽  
The Novel ◽  
Translation Operators ◽  
Magnetic Translation ◽  
Electron Ground State

The effect of dissipation on the electron ground state wave function on a torus in the presence of an external transverse magnetic field is analyzed on large time scales [Formula: see text]. Its extension to the multiparticle center of the mass wave function is also given. The novel transport properties of the system are then studied by applying Laughlin gauge argument with the use of the magnetic translation operators.

THE SUPERFLUID PHASES OF LIQUID 3He: BCS THEORY

2010 ◽  
Vol 24 (25) ◽  
pp. 2525-2539 ◽  
Author(s):  
A. J. LEGGETT
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Weak Interactions ◽  
Spin Fluctuation ◽  
Zero Magnetic Field ◽  
Bcs Theory ◽  
Neutral System ◽  
Cooper Pairing ◽  
Pair Wave Function

Following the success of the original BCS theory as applied to superconductivity in metals, it was suggested that the phenomenon of Cooper pairing might also occur in liquid 3- He , though unlike the metallic case the pairs would most likely form in an anisotropic state, and would then lead in this neutral system to superfluidity. However, what had not been anticipated was the richness of the phenomena which would be revealed by the experiments of 1972. In the first place, even in a zero magnetic field there is not one but two superfluid phases, and the explanation of this involves ideas concerning "spin fluctuation feedback" which have no obvious analog in metals. Secondly, the anisotropic nature of the pair wave function, which in the case of the B phase is quite subtle, and the fact that the orientation must be the same for all the pairs, leads to a number of qualitatively new effects, in particular to a spectacular amplification of ultra-weak interactions seen most dramatically in the NMR behavior. In this chapter I review the application of BCS theory to superfluid 3- He with emphasis on these novel features.

scholarly journals Magnetic-field reentrant wave function hybridization in stacked one-dimensional electron systems

2010 ◽  
Author(s):  
S. S. Buchholz ◽  
P. S. Zapp ◽  
S. F. Fischer ◽  
U. Kunze ◽  
D. Schuh ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Electron Systems ◽  
Dimensional Electron ◽  
One Dimensional

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.

Wave Mechanics

2019 ◽  
pp. 91-174
Author(s):  
P.J.E. Peebles
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Angular Momentum ◽  
Hydrogen Atom ◽  
Physical System ◽  
Adjoint Operator ◽  
Physical Application ◽  
Wave Mechanics ◽  
Definite Form ◽  
Quantum Wave

This chapter develops the wave mechanics formalism. The emphasis here is on symmetries and conservation laws: parity, linear and angular momentum, and the electromagnetic interaction. The only specific physical application is the completion of the study of an isolated hydrogen atom, with some discussion of the motion of a particle in a magnetic field. The chapter also outlines the general assumptions of quantum wave mechanics, which may be summarized as follows: the state of a physical system is represented by a wave function and each measurable attribute of the system is represented by a linear self-adjoint operator in the space of functions. To apply these general assumptions to a given physical system, one must give a specific prescription for the observables and their algebra, and one must adopt a definite form for the Hamiltonians as a function of the observables.

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