Formation of an Edge Striped Phase in Fractional Quantum Hall Systems

We have performed an exact diagonalization study of up to N=12 interacting electrons on a disk at filling $\nu={1/3}$ for both Coulomb and $V_1$ short-range interaction for which Laughlin wave function is the exact solution. For Coulomb interaction and $N\geq 10$ we find persistent radial oscillations in electron density, which are not captured by the Laughlin wave function. Our results srongly suggest formation of a chiral edge striped phase in quantum Hall systems. The amplitude of the charge density oscillations decays slowly, perhaps as a square root of the distance from the edge; thus the spectrum of edge excitations is likely to be affected.Comment: 4 pages, 3 Figs. include

On the solutions of the Schrodinger equation with some molecular potentials: wave function ansatz

Making an ansatz to the wave function, the exact solutions of the $D$% -dimensional radial Schrodinger equation with some molecular potentials like pseudoharmonic and modified Kratzer potentials are obtained. The restriction on the parameters of the given potential, $\delta$ and $\eta$ are also given, where $\eta$ depends on a linear combination of the angular momentum quantum number $\ell$ and the spatial dimensions $D$ and $\delta$ is a parameter in the ansatz to the wave function. On inserting D=3, we find that the bound state eigensolutions recover their standard analytical forms in literature.Comment: 14 page

Invariance of Charge of Laughlin Quasiparticles

A Quantum Antidot electrometer has been used in the first direct observation of the fractionally quantized electric charge. In this paper we report experiments performed on the integer i = 1, 2 and fractional f = 1/3 quantum Hall plateaus extending over a filling factor range of at least 27%. We find the charge of the Laughlin quasiparticles to be invariantly e/3, with standard deviation of 1.2% and absolute accuracy of 4%, independent of filling, tunneling current, and temperature.Comment: 4 pages, 5 fig

Reply to ``Comment on `Magnetic field effects on neutron diffraction in the antiferromagnetic phase of UPt3UPt_3'''

Fak, van Dijk and Wills (FDW) question our interpretation of elastic neutron-scattering experiments in the antiferromagnetic phase of UPt_3. They state that our analysis is incorrect because we average over magnetic structures that are disallowed by symmetry. We disagree with FDW and reply to their criticism. FDW also point out that we have mistaken the magnetic field direction in the experiment reported by N. H. van Dijk et al. [Phys. Rev. B 58, 3186 (1998)]. We correct this error and note that our previous conclusion is also valid for the correct field orientation.Comment: 3 page

Hamiltonian Theory of the Composite Fermion Wigner Crystal

Experimental results indicating the existence of the high magnetic field Wigner Crystal have been available for a number of years. While variational wavefunctions have demonstrated the instability of the Laughlin liquid to a Wigner Crystal at sufficiently small filling, calculations of the excitation gaps have been hampered by the strong correlations. Recently a new Hamiltonian formulation of the fractional quantum Hall problem has been developed. In this work we extend the Hamiltonian approach to include states of nonuniform density, and use it to compute the excitation gaps of the Wigner Crystal states. We find that the Wigner Crystal states near $\nu=1/5$ are quantitatively well described as crystals of Composite Fermions with four vortices attached. Predictions for gaps and the shear modulus of the crystal are presented, and found to be in reasonable agreement with experiments.Comment: 41 page, 6 figures, 3 table

T-Odd Correlations in pi->e nu_e gamma and pi->mu nu_mu gamma Decays

The transverse lepton polarization asymmetry in pi_l2gamma decays may probe T-violating interactions beyond the Standard Model. Dalitz plot distributions of the expected effects are presented and compared to the contribution from the Standard Model final state interactions. We give an example of a phenomenologically viable model, where a considerable contribution to the transverse lepton polarization asymmetry arises.Comment: 19 pages, 5 figures. To be published in Phys.Rev.D. Fixed sign in FSI contribution figure, fixed formulas in K-bar{K} mixing analysis, added some minor comment

Time consistent discounting

A possibly immortal agent tries to maximise its summed discounted rewards over time, where discounting is used to avoid infinite utilities and encourage the agent to value current rewards more than future ones. Some commonly used discount functions lead to time-inconsistent behavior where the agent changes its plan over time. These inconsistencies can lead to very poor behavior. We generalise the usual discounted utility model to one where the discount function changes with the age of the agent. We then give a simple characterisation of time-(in)consistent discount functions and show the existence of a rational policy for an agent that knows its discount function is time-inconsistent

A General Approach for the Exact Solution of the Schrodinger Equation

The Schr\"{o}dinger equation is solved exactly for some well known potentials. Solutions are obtained reducing the Schr\"{o}dinger equation into a second order differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the corresponding wave functions.Comment: 20 page

Tritium Beta Decay, Neutrino Mass Matrices and Interactions Beyond the Standard Model

The interference of charge-changing interactions, weaker than the V-A Standard Model (SM) interaction and having a different Lorentz structure, with that SM interaction, can, in principle, produce effects near the end point of the Tritium beta decay spectrum which are of a different character from those produced by the purely kinematic effect of neutrino mass expected in the simplest extension of the SM. We show that the existence of more than one mass eigenstate can lead to interference effects at the end point that are stronger than those occurring over the entire spectrum. We discuss these effects both for the special case of Dirac neutrinos and the more general case of Majorana neutrinos and show that, for the present precision of the experiments, one formula should suffice to express the interference effects in all cases. Implications for "sterile" neutrinos are noted.Comment: 32 pages, LaTeX, 6 figures, PostScript; full discussion and changes in notation from Phys. Lett. B440 (1998) 89, nucl-th/9807057; submitted to Phys. Rev.

Early Life Characteristics and Neurodevelopmental Phenotypes in the Mount Sinai Children’s Environmental Health Center

Neurodevelopmental outcomes including behavior, executive functioning, and IQ exhibit complex correlational structures, although they are often treated as independent in etiologic studies. We performed a principal components analysis of the behavioral assessment system for children, the behavior rating inventory of executive functioning, and the Wechsler scales of intelligence in a prospective birth cohort, and estimated associations with early life characteristics. We identified seven factors: (1) impulsivity and externalizing, (2) executive functioning, (3) internalizing, (4) perceptual reasoning, (5) adaptability, (6) processing speed, and (7) verbal intelligence. Prenatal fish consumption, maternal education, preterm birth, and the home environment were important predictors of various neurodevelopmental factors. Although maternal smoking was associated with more adverse externalizing, executive functioning, and adaptive composite scores in our sample, of the orthogonally-rotated factors, smoking was only associated with the impulsivity and externalizing factor (β^ − 0.82, 95% CI − 1.42, − 0.23). These differences may be due to correlations among outcomes that were accounted for by using a phenotypic approach. Dimension reduction may improve upon traditional approaches by accounting for correlations among neurodevelopmental traits