Supersymmetric Approach to Heavy-Fermion Systems

We present a new supersymmetric approach to the Kondo lattice model in order to describe simultaneously the quasiparticle excitations and the low-energy magnetic fluctuations in heavy-Fermion systems. This approach mixes the fermionic and the bosonic representation of the spin following the standard rules of superalgebra. Our results show the formation of a bosonic band within the hybridization gap reflecting the spin collective modes. The density of states at the Fermi level is strongly renormalized while the Fermi surface sum rule includes $n_{c}+1$ states. The dynamical susceptibility is made of a Fermi liquid superimposed on a localized magnetism contribution.Comment: 5 pages, 2 figure

Quantum Boltzman equation study for the Kondo breakdown quantum critical point

We develop the quantum Boltzman equation approach for the Kondo breakdown quantum critical point, involved with two bands for conduction electrons and localized fermions. Particularly, the role of vertex corrections in transport is addressed, crucial for non-Fermi liquid transport of temperature linear dependence. Only one band of spinons may be considered for scattering with gauge fluctuations, and their associated vertex corrections are introduced in the usual way, where divergence of self-energy corrections is cancelled by that of vertex corrections, giving rise to the physically meaningful result in the gauge invariant expression for conductivity. On the other hand, two bands should be taken into account for scattering with hybridization excitations, giving rise to coupled quantum Boltzman equations. We find that vertex corrections associated with hybridization fluctuations turn out to be irrelevant due to heavy mass of spinons in the so called decoupling limit, consistent with the diagrammatic approach showing the non-Fermi liquid transport

Quasiparticle Formation and Optical Sum Rule Violation in Cuprate Superconductors

Using a simple model for the frequency dependent scattering rate, we evaluate the in-plane optical integral for cuprate superconductors in the normal and superconducting states. In the overdoped region, this integral is conserved. In the optimal and underdoped region, though, the optical integrals differ, implying a lowering of the in-plane kinetic energy in the superconducting state. This sum rule violation, due to the difference of the non Fermi liquid normal state and the superconducting Fermi liquid state, has a magnitude comparable to recent experimental results.Comment: 5 pages, revtex, 4 encapsulated postscript figure

Quantum Phase Transitions

We give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter $g$ like pressure, chemical composition or magnetic field is tuned to a critical value are characterized by a dynamic exponent $z$ related to the energy and length scales $\Delta$ and $\xi$. Simple arguments based on an expansion to first order in the effective interaction allow to define an upper-critical dimension $D_{C}=4$ (where $D=d+z$ and $d$ is the spatial dimension) below which mean-field description is no longer valid. We emphasize the role of pertubative renormalization group (RG) approaches and self-consistent renormalized spin fluctuation (SCR-SF) theories to understand the quantum-classical crossover in the vicinity of the quantum critical point with generalization to the Kondo effect in heavy-fermion systems. Finally we quote some recent inelastic neutron scattering experiments performed on heavy-fermions which lead to unusual scaling law in $\omega /T$ for the dynamical spin susceptibility revealing critical local modes beyond the itinerant magnetism scheme and mention new attempts to describe this local quantum critical point.Comment: 13 pages, 4 figure

Timing of maternal exposure and fetal sex determine the effects of low-level chemical mixture exposure on the fetal neuroendocrine system in sheep

We have shown that continuous maternal exposure to the complex mixture of environmental chemicals (ECs) found in human biosolids (sewage sludge), disrupts mRNA expression of genes crucial for development and long-term regulation of hypothalamo-pituitary gonadal (HPG) function in sheep. This study investigated whether exposure to ECs only during preconceptional period or only during pregnancy perturbed key regulatory genes within the hypothalamus and pituitary gland and whether these effects were different from chronic (life-long) exposure to biosolid ECs. The findings demonstrate that the timing and duration of maternal EC exposure influences the subsequent effects on the fetal neuroendocrine system in a sex-specific manner. Maternal exposure prior to conception or during pregnancy only, altered the expression of key fetal neuroendocrine regulatory systems such as GnRH and kisspeptin to a greater extent than when maternal exposure was ‘life-long’. Furthermore, hypothalamic gene expression was affected to a greater extent in males than in females, and following EC exposure, male fetuses expressed more “female-like” mRNA levels for some key neuroendocrine genes. This is the first study to show that “real-life” maternal exposure to low levels of a complex cocktail of chemicals prior to conception can subsequently affect the developing fetal neuroendocrine system. These findings demonstrate that the developing neuroendocrine system is sensitive to EC mixtures in a sex-dimorphic manner likely to predispose to reproductive dysfunction in later life