LANDAU LEVELS AND VERTEX OPERATIONS FOR ANYONS

1991 ◽  
Vol 06 (30) ◽  
pp. 2819-2826 ◽  
Author(s):  
GERALD V. DUNNE ◽  
ALBERTO LERDA ◽  
CARLO A. TRUGENBERGER
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
External Magnetic Field ◽  
String Theory ◽  
Ground State ◽  
Correlation Functions ◽  
Landau Levels ◽  
Vertex Operators ◽  
Many Body

We construct exact many-body eigenstates of both energy and angular momentum for the N-anyon problem in an external magnetic field. We show that such states span the full ground state eigenspace and arise as correlation functions of Fubini-Veneziano vertex operators of string theory.

scholarly journals ANYONS IN A MAGNETIC FIELD: LANDAU LEVELS AND VERTEX OPERATOR REPRESENTATION

1991 ◽  
Vol 05 (10) ◽  
pp. 1675-1684 ◽  
Author(s):  
Gerald V. Dunne ◽  
Alberto Lerda ◽  
Carlo A. Trugenberger
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
External Magnetic Field ◽  
Vertex Operator ◽  
Ground State ◽  
Landau Levels ◽  
Vertex Operators ◽  
Many Body ◽  
Natural Representation ◽  
Operator Representation

We construct exact many-body eigenstates of both energy and angular momentum for the N-anyon problem in an external magnetic field. Such states span the full ground-state eigenspace and have a natural representation in terms of the Fubini-Veneziano vertex operators of string theory.

THE GROUND STATE OF QUANTUM RINGS IN A MAGNETIC FIELD

2006 ◽  
Vol 20 (23) ◽  
pp. 1443-1451
Author(s):  
YI-MIN LIU ◽  
GANG-MING HUANG ◽  
TING-YUN SHI
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
External Magnetic Field ◽  
Effective Mass ◽  
Ground State ◽  
Geometric Configuration ◽  
Density Functions ◽  
Specific Group ◽  
Quantum Rings

The ground state of semiconductor quantum rings (QRs) in the presence of an external magnetic field B is theoretically analyzed. By numerically diagonalizing the effective-mass Hamiltonian of the QRs, the energy and wavefunction of the ground state are obtained. It is found that the energy oscillates as B increases. The evolution of the angular momentum L0 and the spin S0 of the ground state in accord with B is revealed. We depict the geometric configuration of the ground state via density functions. Based on an analysis of the wavefunction, it is shown that each configuration is accessible only to a specific group of states having specific L0 and S0.

Energy Spectra of the Low-Lying State in N-Layer Quantum Dots

2013 ◽  
Vol 483 ◽  
pp. 170-173
Author(s):  
An Mei Wang
Keyword(s):  
Magnetic Field ◽  
Quantum Dots ◽  
Angular Momentum ◽  
External Magnetic Field ◽  
Quantum Dot ◽  
Applied Magnetic Field ◽  
Ground State ◽  
Weak Coupling ◽  
State Energy ◽  
Energy Spectra

A method is proposed to exactly diagonalize the Hamiltonian of a N-layer quantum dot containing a single electron in each dot in arbitrary magnetic fields. the energy spectra of the dot are calculated as a function of the applied magnetic field. We find disco-ntinuous ground-state energy transitions induced by an external magnetic field in the case of strong coupling. However, in the case of weak coupling, such a transition does not occur and the angular momentum remains zero.

scholarly journals Exact Analytic Results for Composite Fermions in a Rajaraman–Sondhi Like Formulation

1998 ◽  
Vol 12 (29n30) ◽  
pp. 1203-1208
Author(s):  
Sumathi Rao
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
External Magnetic Field ◽  
Ground State ◽  
Wave Functions ◽  
Composite Fermions ◽  
Energy Eigenvalues

We obtain the exact spectrum and the unique ground state of two composite fermions (in a Rajaraman–Sondhi like formulation) in an external magnetic field B. We show that the energy eigenvalues decrease with increasing angular momentum, thus making it energetically favourable for composite fermions to stay apart. Generalizing this result to a gas of composite fermions, we provide an energetic justification of the Laughlin and Jain wave-functions.

THE ANGULAR MOMENTUM DEPENDENT CALCULATION OF THE GROUND STATE ENERGY OF LIQUID 3He

2005 ◽  
Vol 19 (30) ◽  
pp. 1793-1802 ◽  
Author(s):  
M. MODARRES
Keyword(s):  
Angular Momentum ◽  
Ground State Energy ◽  
Ground State ◽  
Correlation Functions ◽  
State Energy ◽  
Interatomic Potentials ◽  
Channel Correlation ◽  
P Waves ◽  
Effective Interactions ◽  
Three Body

We investigate the possible angular momentum, l, dependence of the ground state energy of normal liquid 3 He . The method of lowest order constrained variational (LOCV) which includes the three-body cluster energy and normalization constraint (LOCVE) is used with angular momentum dependent two-body correlation functions. A functional minimization is performed with respect to each l-channel correlation function. It is shown that this dependence increases the binding energy of liquid 3 He by 8% with respect to calculations without angular momentum dependent correlation functions. The l=0 state has completely different behavior with respect to other l-channels. It is also found that the main contribution from potential energy comes from the l=1 state (p-waves) and the effect of l≥11 is less than about 0.1%. The effective interactions and two-body correlations in different channels are being discussed. Finally we conclude that this l-dependence can be verified experimentally by looking into the magnetization properties of liquid helium 3 and interatomic potentials.

Theory of ground-state switching in an array of magnetic nanodots by application of a short external magnetic field pulse

2013 ◽  
Vol 87 (13) ◽  
Author(s):  
Roman Verba ◽  
Vasil Tiberkevich ◽  
Konstantin Guslienko ◽  
Gennadiy Melkov ◽  
Andrei Slavin
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Ground State ◽  
Magnetic Field Pulse ◽  
Field Pulse ◽  
Magnetic Nanodots ◽  
State Switching

SPIN-SPLITTING OF THE BOUND POLARON'S GROUND STATE BINDING ENERGY INDUCED BY THE RASHBA SPIN–ORBIT INTERACTION UNDER THE PERPENDICULAR MAGNETIC FIELD

2008 ◽  
Vol 22 (12) ◽  
pp. 1923-1932
Author(s):  
JIA LIU ◽  
ZI-YU CHEN
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Binding Energy ◽  
Ground State ◽  
Spin Splitting ◽  
Perpendicular Magnetic Field ◽  
Spin Orbit ◽  
Ground State Binding Energy ◽  
Bound Polaron ◽  
Rashba Spin

The influence of a perpendicular magnetic field on a bound polaron near the interface of a polar–polar semiconductor with Rashba effect has been investigated. The material is based on a GaAs / Al x Ga 1-x As heterojunction and the Al concentration varying from 0.2 ≤ x ≤ 0.4 is the critical value below which the Al x Ga 1-x As is a direct band gap semiconductor.The external magnetic field strongly altered the ground state binding energy of the polaron and the Rashba spin–orbit (SO) interaction originating from the inversion asymmetry in the heterostructure splitting of the ground state binding energy of the bound polaron. How the ground state binding energy will be with the change of the external magnetic field, the location of a single impurity and the electron area density have been shown in this paper, taking into account the SO coupling. The contribution of the phonons are also considered. It is found that the spin-splitting states of the bound polaron are more stable, and, in the condition of weak magnetic field, the Zeeman effect can be neglected.

THE GROUND-STATE PHASE DIAGRAMS OF THE SPIN-2 ISING MODEL

2007 ◽  
Vol 21 (31) ◽  
pp. 5265-5274 ◽  
Author(s):  
AHMET ERDİNÇ
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
External Magnetic Field ◽  
Phase Diagrams ◽  
Crystal Field ◽  
Ground State ◽  
Exchange Interactions ◽  
Nearest Neighbors ◽  
Biquadratic Exchange ◽  
Model Hamiltonian

The ground-state phase diagrams are obtained for the spin-2 Ising model Hamiltonian with bilinear and biquadratic exchange interactions and a single-ion crystal field. The interactions are assumed to be only between nearest-neighbors. Obtained phase diagrams are presented in the (Δ,J), (K,J), (Δ/J,K/J), (Δ/|J|,K/|J|), (Δ/|K|,J/|K|), (H/J,Δ/J), (H/|J|,Δ/|J|), (H/J,K/J), and (H/|J|,K/|J|) planes where J, K, Δ, and H are the bilinear, biquadratic exchange interactions, the single-ion crystal field, and the external magnetic field, respectively. The influence of the external magnetic field on the spin configurations is investigated.

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