Classical Dynamics of Anyons and the Quantum Spectrum

In this paper we show that (a) all the known exact solutions of the problem of N-anyons in oscillator potential precisely arise from the collective degrees of freedom, (b) the system is pseudo-integrable ala Richens and Berry. We conclude that the exact solutions are trivial thermodynamically as well as dynamically.Comment: 19 pages, ReVTeX, IMSc/93/0

Exactly solvable toy models of unconventional magnetic alloys: Bethe Ansatz versus Renormalization Group method

We propose toy models of unconventional magnetic alloys, in which the density of band states, $\rho(\epsilon)$, and hybridization, $t(\epsilon)$, are energy dependent; it is assumed, however, that $t^2(\epsilon)\propto\rho^{-1}(\epsilon)$, and hence an effective electron-impurity coupling $\Gamma(\epsilon)=\rho(\epsilon)t^2(\epsilon)$ is energy independent. In the renormalization group approach, the physics of the system is assumed to be governed by $\Gamma(\epsilon)$ only rather than by separate forms of $\rho(\epsilon)$ and $t(\epsilon)$. However, an exact Bethe Ansatz solution of the toy Anderson model demonstrates a crucial role of a form of inverse band dispersion $k(\epsilon)$.Comment: A final version. A previous one has been sent to Archive because of my technical mistake. Sorr

Magnetic phenomena at and near nu =1/2 and 1/4: theory, experiment and interpretation

I show that the hamiltonian theory of Composite Fermions (CF) is capable of yielding a unified description in fair agreement with recent experiments on polarization P and relaxation rate 1/T_1 in quantum Hall states at filling nu = p/(2ps+1), at and near nu = 1/2 and 1/4, at zero and nonzero temperatures. I show how rotational invariance and two dimensionality can make the underlying interacting theory behave like a free one in a limited context.Comment: Latex 4 pages, 2 figure

Magnetic anomalies of offshore Krishna-Godavari basin, eastern continental margin of India

The marine magnetic data acquired from offshore Krishna-Godavari (K-G) basin, eastern continental margin of India (ECMI), brought out a prominent NE-SW trending feature, which could be explained by a buried structural high formed by volcanic activity. The magnetic anomaly feature is also associated with a distinct negative gravity anomaly similar to the one associated with 85°E Ridge. The gravity low could be attributed to a flexure at the Moho boundary, which could in turn be filled with the volcanic material. Inversion of the magnetic and gravity anomalies was also carried out to establish the similarity of anomalies of the two geological features (structural high on the margin and the 85°E Ridge) and their interpretations. In both cases, the magnetic anomalies were caused dominantly by the magnetization contrast between the volcanic material and the surrounding oceanic crust, whereas the low gravity anomalies are by the flexures of the order of 3-4 km at Moho boundary beneath them. The analysis suggests that both structural high present in offshore Krishna-Godavari basin and the 85°E Ridge have been emplaced on relatively older oceanic crust by a common volcanic process, but at discrete times, and that several of the gravity lows in the Bay of Bengal can be attributed to flexures on the Moho, each created due to the load of volcanic material

Effective mass of composite fermion: a phenomenological fit in with anomalous propagation of surface acoustic wave

We calculate the conductivity associated with the anomalous propagation of a surface acoustic wave above a two-dimensional electron gas at $\nu=1/2$. Murthy-Shankar's middle representation is adopted and a contribution to the response functions beyond the random phase approximation has been taken into account. We give a phenomenological fit for the effective mass of composite fermion in with the experimental data of the anomalous propagation of surface acoustic wave at $\nu=1/2$ and find the phenomenological value of the effective mass is several times larger than the theoretical value $m_{th}^*=6\epsilon/e^2l_{1/2}$ derived from the Hartree-Fock approximation. We compare our phenomenologically fitting composite fermion effective mass with those appeared in the measurements of the activation energy and the Shubnikov-de Haas effect and find that our result is fairly reasonable.Comment: 8 pages, 5 figures, the longer version of cond-mat/9801131 with crucial corrections, accepted for publication by PR

Hamiltonian Description of Composite Fermions: Aftermath

The Lowest Landau Level (LLL), long distance theory of Composite Fermions (CF) developed by Murthy and myself is minimally extended to all distances, guided by very general principles. The resulting theory is mathematically consistent, and physically appealing: we clearly see the electron and the vortices binding to form the CF. The meaning of the constraints, their role in ensuring compressibility of dipolar objects at $\nu =1/2$, and the observability of dipoles are clarified.Comment: Revised for publication in PRL, 4 - epsilon page

Novel Phases of Planar Fermionic Systems

We discuss a {\em family} of planar (two-dimensional) systems with the following phase strucure: a Fermi liquid, which goes by a second order transition (with non classical exponent even in mean-field) to an intermediate, inhomogeneous state (with nonstandard ordering momentum) , which in turn goes by a first order transition to a state with canonical order parameter. We analyze two examples: (i) a superconductor in a parallel magnetic field (which was discussed independently by Bulaevskii)for which the inhomogeneous state is obtained for $1.86 T_c \stackrel{\sim}{<} B \stackrel{\sim}{<} 1.86 \sqrt{2} T_c$ where $T_c$ is the critical temperature (in Kelvin) of the superconductor without a field and $B$ is measured in Tesla, and (ii) spinless (or, as is explained, spin polarized) fermions near half-filling where a similar, sizeable window (which grows in size with anisotropy) exists for the intermediate CDW phase at an ordering momentum different from $(\pi , \pi )$. We discuss the experimental conditions for realizing and observing these phases and the Renormalization Group approach to the transitions.Comment: ([email protected],[email protected]) 29 p Latex 4 figs uuencoded separatel

A Composite Fermion Hofstader Problem: Partially Polarized Density Wave States in the 2/5 FQHE

It is well-known that the 2/5 state is unpolarized at zero Zeeman energy, while it is fully polarized at large Zeeman energies. A novel state with charge/spin density wave order for Composite Fermions is proposed to exist at intermediate values of the Zeeman coupling for 2/5. This state has half the maximum possible polarization, and can be extended to other incompressible fractions. A Hartree-Fock calculation based on the new approach for all fractional quantum Hall states developed by R.Shankar and the author is used to demonstrate the stability of this state to single-particle excitations, and compute gaps. We compare our results with a very recent experiment which shows direct evidence for the existence of such a state, and also with more indirect evidence from past experiments.Comment: One reference added, minor clarifying change

Scaling Relations for Gaps in Fractional Quantum Hall States

The microscopic approach of Murthy and Shankar, which has recently been used to calculate the transport gaps of quantum Hall states with fractions p/(2ps+1), also implies scaling relations between gaps within a single sequence (fixed s) as well as between gaps of corresponding states in different sequences. This work tests these relations for a system of electrons in the lowest Landau level interacting with a model potential cutoff at high momenta due to sample thickness

Hamiltonian Description of Composite Fermions: Calculation of Gaps

We analytically calculate gaps for the 1/3, 2/5, and 3/7 polarized and partially polarized Fractional Quantum Hall states based on the Hamiltonian Chern-Simons theory we have developed. For a class of potentials that are soft at high momenta (due to the finite thickness of the sample) we find good agreement with numerical and experimental results.Comment: 4 pages, 2 eps figures. One reference added, some typos (one in equation 7) corrected, and minor notational modification