Electromagnetic Interactions in the Quantum Hall Ferromagnet

The $\nu =1$ quantum Hall ground state in samples like GaAs is well known to be ferromagnetic. The global SU(2) spin symmetry of the microscopic action is broken down to a U(1) symmetry by the ground state. The Goldstone bosons corresponding to this spontaneous breaking of symmetry are the ferromagnetic magnons which are neutral spin waves. In addition, there are topologically nontrivial, electrically charged spin excitations known as spin skyrmions, which in these samples are the favoured charge carriers. In this letter, we look into the electromagnetic coupling of these spin excitations. The discrete symmetries P and T are also broken by the ground state and we find that to the leading order, the electromagnetic interaction of the spin waves occurs through a nonminimal coupling given by a Chern-Simons like term containing both the electromagnetic potentials and the two Euler angles that specify the coset SU(2)/U(1) and thereby, the Goldstone bosons.Comment: 13 pages, Plain TeX, no figure

Effective Interactions of Planar Fermions in a Strong Magnetic Field-the Effect of Landau Level Mixing

We obtain expressions for the current operator in the lowest Landau level (L.L.L.) field theory, where higher Landau level mixing due to various external and interparticle interactions is sytematically taken into account. We consider the current operators in the presence of electromagnetic interactions, both Coulomb and time-dependent, as well as local four-fermi interactions. The importance of Landau level mixing for long-range interactions is especially emphasized. We also calculate the edge-current for a finite sample.Comment: 15 pages, plain te

Bulk and Edge excitations in a ν=1\nu =1 quantum Hall ferromagnet

In this article, we shall focus on the collective dynamics of the fermions in a $\nu = 1$ quantum Hall droplet. Specifically, we propose to look at the quantum Hall ferromagnet. In this system, the electron spins are ordered in the ground state due to the exchange part of the Coulomb interaction and the Pauli exclusion principle. The low energy excitations are ferromagnetic magnons. To provide a means for describing these magnons, we shall discuss a method of introducing collective coordinates in the Hilbert space of many-fermion systems. These collective coordinates are bosonic in nature. They map a part of the fermionic Hilbert space into a bosonic Hilbert space. Using this technique, we shall interpret the magnons as bosonic collective ex citations in the Hilbert space of the many-electron Hall system. By considering a Hall droplet of finite extent, we shall also obtain the effective Lagrangian governing the spin collective excitations at the edge of the sample.Comment: Plain TeX 18 Pages Proceedings for the Y2K conference on strongly c orrelated fermionic systems, Calcutta, Indi

Fluids, Anomalies and the Chiral Magnetic Effect: A Group-theoretic Formulation

It is possible to formulate fluid dynamics in terms of group-valued variables. This is particularly suited to the cases where the fluid has nonabelian charges and is coupled to nonabelian gauge fields. We explore this formulation further in this paper. An action for a fluid of relativistic particles (with and without spin) is given in terms of the Lorentz and Poincare (or de Sitter) groups. Considering the case of particles with flavor symmetries, a general fluid action which also incorporates all flavor anomalies is given. The chiral magnetic and chiral vorticity effects as well as the consequences of the mixed gauge-gravity anomaly are discussed.Comment: 17 pages, version to be published in Phys Rev

Multiple edges of a quantum Hall system in a strong electric

In this paper we show that if the electrons in a quantum Hall sample are subjected to a constant electric field in the plane of the material, comparable in magnitude to the background magnetic field on the system of electrons, a multiplicity of edge states localized at different regions of space is produced in the sample. The actions governing the dynamics of these edge states are obtained starting from the well-known Schrödinger field theory for a system of nonrelativistic electrons, where on top of the constant background electric and magnetic fields, the electrons are further subject to slowly varying weak electromagnetic fields. In the regions between the edges, dubbed as the "bulk," the fermions can be integrated out entirely and the dynamics expressed in terms of a local effective action involving the slowly varying electromagnetic potentials. It is further shown how the bulk action is gauge noninvariant in a particular way, and how the edge states conspire to restore the U(1) electromagnetic gauge invariance of the system. In the edge action we obtain a heretofore unnoticed gauge-invariant term that depends on the particular edge. We argue that this term may be detected experimentally as different edges respond differently to a monochromatic probe due to this ter

Some topological issues for ferromagnets and fluids

We analyze the canonical structure of a continuum model of ferromagnets and clarify known difficulties in defining a momentum density. The moments of the momentum density corresponding to volume-preserving coordinate transformations can be defined, but a nonsingular definition of the other moments requires an enlargement of the phase space which illuminates a close relation to fluid mechanics. We also discuss the nontrivial connectivity of the phase space for two and three dimensions and show how this feature can be incorporated in the quantum theory, working out the two-dimensional case in some detail.Comment: LaTeX, 19 page

Quantum Hall Ferromagnets: Induced Topological term and electromagnetic interactions

The $\nu = 1$ quantum Hall ground state in materials like GaAs is well known to be ferromagnetic in nature. The exchange part of the Coulomb interaction provides the necessary attractive force to align the electron spins spontaneously. The gapless Goldstone modes are the angular deviations of the magnetisation vector from its fixed ground state orientation. Furthermore, the system is known to support electrically charged spin skyrmion configurations. It has been claimed in the literature that these skyrmions are fermionic owing to an induced topological Hopf term in the effective action governing the Goldstone modes. However, objections have been raised against the method by which this term has been obtained from the microscopics of the system. In this article, we use the technique of the derivative expansion to derive, in an unambiguous manner, the effective action of the angular degrees of freedom, including the Hopf term. Furthermore, we have coupled perturbative electromagnetic fields to the microscopic fermionic system in order to study their effect on the spin excitations. We have obtained an elegant expression for the electromagnetic coupling of the angular variables describing these spin excitations.Comment: 23 pages, Plain TeX, no figure

Antihypertensive and Antioxidant Action of Amlodipine and Vitamin C in Patients of Essential Hypertension

The etiology of essential hypertension includes increased oxidative stress. The role of antihypertensive drug amlodipine as an antioxidant and the benefit of addition of vitamin C, an antioxidant to antihypertensive therapy were studied. Forty male patients of essential hypertension were randomly divided into two groups and treated with 5 mg amlodipine. In addition one group also received 1000 mg vitamin C (as two 500 mg tablets) once daily for three months. Although blood pressure decreased in both groups, the systolic blood pressure in patients given vitamin C was less (126.4 ± 7.47) compared to the other group (130.9 ± 7.27). A decrease in malondialdehyde, an increase in erythrocyte sodium-potassium adenosine triphosphatase (Na+ K+ ATPase) and an increase in the superoxide dismutase levels were observed in both groups. The increase in SOD was statistically more in the patients given vitamin C in addition to amlodipine (0.1717 ± 0.0150 compared to 0.152 ± 0.0219 units/100 ml assay). In spite of the known antihypertensive, antioxidant activity, similarity in correcting endothelial dysfunction independently, giving the two drugs together and early introduction of vitamin C perhaps decreases oxidative stress and augments the antioxidant status. This may prevent further vascular damage due to oxidative stress, leading to a better prognosis in essential hypertension patients