Coherence-decoherence transition in a spin-magnetoexcitonic ensemble in a quantum Hall system

Spin-flip excitations and Stoner ferromagnetism in a strongly correlated quantum Hall system

“…At the same time, it is important that the trivial case, when n max = m max = 1 (i.e. the basic set is reduced to the single state 3,6 ), results in an essentially different spin-flip dispersion curve. In particular, then the spin-flip energy is always positive -the gap does not vanish at any q.…”

“…Note also that Q ab q ≡ Q † ba−q . These Q-operators have a very important property: when acting on the state of the QH system they add value q/l B to total momentum of the system since there occurs commutator equality P , Q † abq = qQ † abq [wherê P describes the dimensionless (with = l B = 1) 'momentum' operator 6 ]. In particular, if |0 is the ground state, then the exciton state Q † ab q |0 , if not zero, is the eigenstate of momentum operator P with eigen quantum number q.…”

Damping via the hyperfine interaction of a spin-rotation mode in a two-dimensional strongly magnetized electron plasma

“…for P describing the dimensionless (with = l B = 1) 'momentum' operator. 8,10,11 In particular, if |0 is the ground state, then the exciton state Q † q |0 , if not zero, is the eigenstate of momentum operator P with eigen quantum number q. Thus, exciton states, in contrast to single electron states, possess a natural quantum number, namely, the 2D momentum whose existence is the consequence of the translational invariance of the system.…”

Stochastization of long living spin-cyclotron excitations in a spin-unpolarised quantum Hall system

“…We study CSFE at ν = 2, hence in our case a = (0, ↓) and b = (1, ↑). The Q † q |0 state (we omit the 'ab' index, besides, note that Q q |0 ≡ 0) represents an eigen state of our quantum Hall system yielding, in accordance with the solution of the many-electron Schrödinger equation, 2,6 the CSFE energy to the first order in terms of parameter r s with the q-dispersion part:…”

“…We consider the situation where the CSFE ensemble represents a rarefied gas, and thus we ignore any direct interaction among excitons originating from the e-e Coulomb coupling accounted ab initio. 6 This approach is certainly valid if the number of excitons N is much smaller than N φ (number of electrons = 2N φ ). However, there is an indirect interexcitonic coupling via the GaAs lattice, which enables us to study the two-exciton process of quantum transition from the initial state…”