Frobenius theorem and invariants for Hamiltonian systems

We apply Frobenius integrability theorem in the search of invariants for one-dimensional Hamiltonian systems with a time-dependent potential. We obtain several classes of potential functions for which Frobenius theorem assures the existence of a two-dimensional foliation to which the motion is constrained. In particular, we derive a new infinite class of potentials for which the motion is assurately restricted to a two-dimensional foliation. In some cases, Frobenius theorem allows the explicit construction of an associated invariant. It is proven the inverse result that, if an invariant is known, then it always can be furnished by Frobenius theorem

Quantum kinetic theory of the filamentation instability

The quantum electromagnetic dielectric tensor for a multi species plasma is re-derived from the gauge invariant Wigner-Maxwell system and presented under a form very similar to the classical one. The resulting expression is then applied to a quantum kinetic theory of the electromagnetic filamentation instability. Comparison is made with the quantum fluid theory including a Bohm pressure term, and with the cold classical plasma result. A number of analytical expressions are derived for the cutoff wave vector, the largest growth rate and the most unstable wave vector

Order by disorder from non-magnetic impurities in a two-dimensional quantum spin liquid

We consider doping of non-magnetic impurities in the spin-1/2, 1/5-depleted square lattice. This structure, whose undoped phase diagram offers both magnetically ordered and spin-liquid ground states, is realized physically in CaV_4O_9. Doping into the ordered phase results in a progressive loss of order, which becomes complete at the percolation threshold. By contrast, non-magnetic impurities introduced in the spin liquids create a phase of weak but long-ranged antiferromagnetic order coexisting with the gapped state. The latter may be viewed as a true order-by-disorder phenomenon. We study the phase diagram of the doped system by computing the static susceptibility and staggered magnetization using a stochastic series-expansion quantum Monte Carlo technique.Comment: 4 pages, 5 figure

Shadow features and shadow bands in the paramagnetic state of cuprate superconductors

The conditions for the precursors of antiferromagnetic bands in cuprate superconductors are studied using weak-to-intermediate coupling approach. It is shown that there are, in fact, three different precursor effects due to the proximity to antiferromagnetic instability: i) the shadow band which associated with new pole in the Green's function ii) the dispersive shadow feature due to the thermal enhancement of the scattering rate and iii) the non-dispersive shadow feature due to quantum spin fluctuation that exist only in $\vec{k}-$scan of the spectral function $A(\omega _{Fixed},\vec{k})$. I found that dispersive shadow peaks in $A(\omega,\vec{k})$ can exist at finite temperature T in the renormalized classical regime, when $T\gg \omega _{sf}$, $\xi_{AFM} >\xi_{th}=v_F/T$ ($\omega _{sf}$ is the characteristic energy of spin fluctuations, $\xi_{th}$ is the thermal wave length of electron). In contrast at zero temperature, only non-dispersive shadow feature in $A(\omega_{Fixed},\vec{k})$ has been found. I found, however, that the latter effect is always very small. The theory predict no shadow effects in the optimally doped materials. The conditions for which shadow peaks can be observed in photoemission are discussed.Comment: 6 pages, REVTEX, 2 ps figures, version to be published in PR

Quasiparticle spectrum of a type-II superconductor in a high magnetic field with randomly pinned vortices

We show that gapless superconductivity of a strongly type-II superconductor in a high magnetic field prevails in the presence of disorder, suggesting a topological nature. We calculate the density of states of the Bogoliubov-de Gennes quasiparticles for a two-dimensional inhomogeneous system in both cases of weak and strong disorder. In the limit of very weak disorder, the effect is very small and the density of states is not appreciably changed. As the disorder increases, the density of states at low energies increases and the ratio of the low-energy density of states to its maximum increases significantly

Static and Dynamical Properties of the Ferromagnetic Kondo Model with Direct Antiferromagnetic Coupling Between the localized t2gt_{2g} Electrons

The phase diagram of the Kondo lattice Hamiltonian with ferromagnetic Hund's coupling in the limit where the spin of the localized $t_{2g}$ electrons is classical is analyzed in one dimension as a function of temperature, electronic density, and a direct antiferromagnetic coupling $J'$ between the localized spins. Studying static and dynamical properties, a behavior that qualitatively resembles experimental results for manganites occurs for $J'$ smaller than 0.11 in units of the $e_g$ hopping amplitude. In particular a coexistence of ferromagnetic and antiferromagnetic excitations is observed at low-hole density in agreement with neutron scattering experiments on $\rm{La_{2-2x}Sr_{1+2x}Mn_2O_7}$ with$x=0.4$. This effect is caused by the recently reported tendency to phase separation between hole-rich ferromagnetic and hole-undoped antiferromagnetic domains in electronic models for manganites. As $J'$ increases metal-insulator transitions are detected by monitoring the optical conductivity and the density of states. The magnetic correlations reveal the existence of spiral phases without long-range order but with fairly large correlation lengths. Indications of charge ordering effects appear in the analysis of charge correlations.Comment: 14 pages with 25 eps figures embeded in the tex

Dynamical properties of the spin-Peierls compound \alpha'--NaV2O5

Dynamical properties of the novel inorganic spin-Peierls compound \alpha'--NaV2O5 are investigated using a one-dimensional dimerized Heisenberg model. By exact diagonalizations of chains with up to 28 sites, supplemented by a finite-size scaling analysis, the dimerization parameter \delta is determined by requiring that the model reproduces the experimentally observed spin gap \Delta. The dynamical and static spin structure factors are calculated. As for CuGeO3, the existence of a low energy magnon branch separated from the continuum is predicted. The present calculations also suggest that a large magnetic Raman scattering intensity should appear above an energy threshold of 1.9 \Delta. The predicted photoemission spectrum is qualitatively similar to results for an undimerized chain due to the presence of sizable short-range antiferromagnetic correlations.Comment: 4 pages, latex, minor misprints corrected and a few references adde

miR-155 regulates differentiation of brown and beige adipocytes via a bistable circuit

Brown adipocytes are a primary site of energy expenditure and reside not only in classical brown adipose tissue but can also be found in white adipose tissue. Here we show that microRNA 155 is enriched in brown adipose tissue and is highly expressed in proliferating brown preadipocytes but declines after induction of differentiation. Interestingly, microRNA 155 and its target, the adipogenic transcription factor CCAAT/enhancer-binding protein beta, form a bistable feedback loop integrating hormonal signals that regulate proliferation or differentiation. Inhibition of microRNA 155 enhances brown adipocyte differentiation and induces a brown adipocyte-like phenotype ('browning') in white adipocytes. Consequently, microRNA 155-deficient mice exhibit increased brown adipose tissue function and 'browning' of white fat tissue. In contrast, transgenic overexpression of microRNA 155 in mice causes a reduction of brown adipose tissue mass and impairment of brown adipose tissue function. These data demonstrate that the bistable loop involving microRNA 155 and CCAAT/enhancer-binding protein b regulates brown lineage commitment, thereby, controlling the development of brown and beige fat cells