30 years of ecopedagogy: Origin and reinvention

The question of a pedagogy that promotes the development of sustainability responsible students is at the centre of education for sustainability. Ecopedagogy incorporates socio-environmental concerns and promotes reflection on the multiple and complex relationship society-nature, engendering a criticism of the current unsustainable socioeconomic model, modern thought and the various forms of exploitation of life. We suggest that Ecopedagogy may provide the theoretical and practical approaches to foster sustainability teaching and inspire educators and students in a higher education context. Our presentation is an introduction to Ecopedagogy and the ongoing process of reinvention and establishment of new theoretical and practical bases, with its new challenges in the current time we live. We offer a review of the 30 years of Ecopedagogy from its Latin American origins; paths travelled along these years; and the process of reinvention of Ecopedagogy based on the three pillars of criticism: patriarchy, modernity and capitalism. We conclude with a set of propositions for a collective journey in view of the principles of Ecopedagogy as a field of academic investigation and social praxis

Goldstone Mode Relaxation in a Quantum Hall Ferromagnet due to Hyperfine Interaction with Nuclei

Spin relaxation in quantum Hall ferromagnet regimes is studied. As the initial non-equilibrium state, a coherent deviation of the spin system from the ${\vec B}$ direction is considered and the breakdown of this Goldstone-mode state due to hyperfine coupling to nuclei is analyzed. The relaxation occurring non-exponentially with time is studied in terms of annihilation processes in the "Goldstone condensate" formed by "zero spin excitons". The relaxation rate is calculated analytically even if the initial deviation is not small. This relaxation channel competes with the relaxation mechanisms due to spin-orbit coupling, and at strong magnetic fields it becomes dominating.Comment: 8 page

Comment on "Spin relaxation in quantum Hall systems"

W. Apel and Yu.A. Bychkov have recently considered the spin relaxation in a 2D quantum Hall system for the filling factor close to unity [PRL v.82, 3324 (1999)]. The authors considered only one spin flip mechanism (direct spin-phonon coupling) among several possible spin-orbit related ones and came to the conclusion that the spin relaxation time due to this mechanism is quite short: around $10^{-10}$ s at B=10 T (for GaAs). This time is much shorter than the typical time ($10^{-5}$ s) obtained earlier by D. Frenkel while considering the spin relaxation of 2D electrons in a quantizing magnetic field without the Coulomb interaction and for the same spin-phonon coupling. I show that the authors' conclusion about the value of the spin-flip time is wrong and have deduced the correct time which is by several orders of magnitude longer. I also discuss the admixture mechanism of the spin-orbit interaction.Comment: 1 pag

Activation Energy in a Quantum Hall Ferromagnet and Non-Hartree-Fock Skyrmions

The energy of Skyrmions is calculated with the help of a technique based on the excitonic representation: the basic set of one-exciton states is used for the perturbation-theory formalism instead of the basic set of one-particle states. We use the approach, at which a skyrmion-type excitation (at zero Lande factor) is considered as a smooth non-uniform rotation in the 3D spin space. The result within the framework of an excitonically diagonalized part of the Coulomb Hamiltonian can be obtained by any ratio $r_{\tiny C}=(e^2/\epsilon {}l_B)/\hbar \omega_c$ [where $e^2/\epsilon {}l_B$ is the typical Coulomb energy (${}l_B$ being the magnetic length); $\omega_c$ is the cyclotron frequency], and the Landau-level mixing is thereby taken into account. In parallel with this, the result is also found exactly, to second order in terms of the $r_{\tiny C}$ (if supposing $r_{\tiny C}$ to be small) with use of the total Hamiltonian. When extrapolated to the region $r_{\tiny C}\sim 1$, our calculations show that the skyrmion gap becomes substantially reduced in comparison with the Hartree-Fock calculations. This fact brings the theory essentially closer to the available experimental data.Comment: 14 pages, 1 figure. to appear in Phys. Rev. B, Vol. 65 (Numbers ~ 19-22), 200

Spin relaxation in a two-electron quantum dot

We discuss the rate of relaxation of the total spin in the two-electron droplet in the vicinity of the magnetic field driven singlet-triplet transition. The total spin relaxation is attributed to spin-orbit and electron-phonon interactions. The relaxation process is found to depend on the spin of ground and excited states. This asymmetry is used to explain puzzles in recent high source-drain transport experiments.Comment: 9 pages in the PDF format, 1 figur