Inhomogeneous Quasi-stationary States in a Mean-field Model with Repulsive Cosine Interactions

The system of N particles moving on a circle and interacting via a global repulsive cosine interaction is well known to display spatially inhomogeneous structures of extraordinary stability starting from certain low energy initial conditions. The object of this paper is to show in a detailed manner how these structures arise and to explain their stability. By a convenient canonical transformation we rewrite the Hamiltonian in such a way that fast and slow variables are singled out and the canonical coordinates of a collective mode are naturally introduced. If, initially, enough energy is put in this mode, its decay can be extremely slow. However, both analytical arguments and numerical simulations suggest that these structures eventually decay to the spatially uniform equilibrium state, although this can happen on impressively long time scales. Finally, we heuristically introduce a one-particle time dependent Hamiltonian that well reproduces most of the observed phenomenology.Comment: to be published in J. Phys.

Space-time evolution induced by spinor fields with canonical and non-canonical kinetic terms

We study spinor field theories as an origin to induce space-time evolution. Self-interacting spinor fields with canonical and non-canonical kinetic terms are considered in a Friedman-Robertson-Walker universe. The deceleration parameter is calculated by solving the equation of motion and the Friedman equation, simultaneously. It is shown that the spinor fields can accelerate and decelerate the universe expansion. To construct realistic models we discuss the contributions from the dynamical symmetry breaking.Comment: 16 pages, 19 figure

A Quantum Monte Carlo Method and Its Applications to Multi-Orbital Hubbard Models

We present a framework of an auxiliary field quantum Monte Carlo (QMC) method for multi-orbital Hubbard models. Our formulation can be applied to a Hamiltonian which includes terms for on-site Coulomb interaction for both intra- and inter-orbitals, intra-site exchange interaction and energy differences between orbitals. Based on our framework, we point out possible ways to investigate various phase transitions such as metal-insulator, magnetic and orbital order-disorder transitions without the minus sign problem. As an application, a two-band model is investigated by the projection QMC method and the ground state properties of this model are presented.Comment: 10 pages LaTeX including 2 PS figures, to appear in J.Phys.Soc.Jp

Formation of fractal structure in many-body systems with attractive power-law potentials

We study the formation of fractal structure in one-dimensional many-body systems with attractive power-law potentials. Numerical analysis shows that the range of the index of the power for which fractal structure emerges is limited. Dependence of the growth rate on wavenumber and power-index is obtained by linear analysis of the collisionless Boltzmann equation, which supports the numerical results.Comment: accepted by PR

Superconducting Fluctuations in a Multi-Band 1D Hubbard Model

A renormalization-group and bosonization approach for a multi-band Hubbard Hamiltonian in one dimension is described. Based on the limit of many bands, it is argued that this Hamiltonian with bare repulsive electron-electron interactions is scaled under specific conditions to a model in which superconducting fluctuations dominate.Comment: 12 pages + 1 fig, Revtex, Preprint - Los Alamo

Dynamical symmetry breaking in the external gravitational and constant magnetic fields

We investigate the effects of the external gravitational and constant magnetic fields to the dynamical symmetrybreaking. As simple models of the dynamical symmetry breaking we consider the Nambu-Jona-Lasinio (NJL) model and the supersymmetric Nambu-Jona-Lasinio (SUSY NJL) model non-minimally interacting with the external gravitational field and minimally interacting with constant magnetic field. The explicit expressions for the scalar and spinor Green functions are found up to the linear terms on the spacetime curvature and exactly for a constant magnetic field. We obtain the effective potential of the above models from the Green functions in the magnetic field in curved spacetime. Calculating the effective potential numerically with the varying curvature and/or magnetic fields we show the effects of the external gravitational and magnetic fields to the phase structure of the theories. In particular, increase of the curvature in the spontaneously broken chiral symmetry phase due to the fixed magnetic field makes this phase to be less broken. On the same time strong magnetic field quickly induces chiral symmetry breaking even at the presence of fixed gravitational field within nonbroken phase.Comment: 23 pages, Latex, epic.sty and eepic.sty are use

Ferromagnetism in the Hubbard model with orbital degeneracy in infinite dimensions

We study the ferromagnetism due to orbital degeneracy in the Hubbard model in infinite dimensions. The model contains the intraorbital repulsion $U$, the interorbital repulsion $U^\prime$, the exchange $J$ (Hund coupling) and the pair hopping $J^\prime$, where all of them originate from the on-site Coulomb interaction. The ground state of the effective one-site problem was obtained by exact diagonalizations. At the 1/4-filling, we found two insulating phases; one is a ferromagnetic phase with alternating orbital order and the other is antiferromagnetic one with uniform orbital order. If electrons are doped into the 1/4-filling, the ferromagnetic phase still survives and becomes metallic, while the antiferromagnetic phase disappears. This result indicates that the double-exchange mechanism is relevant to stabilize metallic ferromagnetism in infinite dimensions.Comment: 4 pages, Revtex, 3 figures, corrected some typos and references, to be published in Phys. Rev. B (Rapid Communication

Low temperature magnetization and the excitation spectrum of antiferromagnetic Heisenberg spin rings

Accurate results are obtained for the low temperature magnetization versus magnetic field of Heisenberg spin rings consisting of an even number N of intrinsic spins s = 1/2, 1, 3/2, 2, 5/2, 3, 7/2 with nearest-neighbor antiferromagnetic (AF) exchange by employing a numerically exact quantum Monte Carlo method. A straightforward analysis of this data, in particular the values of the level-crossing fields, provides accurate results for the lowest energy eigenvalue E(N,S,s) for each value of the total spin quantum number S. In particular, the results are substantially more accurate than those provided by the rotational band approximation. For s <= 5/2, data are presented for all even N <= 20, which are particularly relevant for experiments on finite magnetic rings. Furthermore, we find that for s > 1 the dependence of E(N,S,s) on s can be described by a scaling relation, and this relation is shown to hold well for ring sizes up to N = 80 for all intrinsic spins in the range 3/2 <= s <= 7/2. Considering ring sizes in the interval 8 <= N <= 50, we find that the energy gap between the ground state and the first excited state approaches zero proportional to 1/N^a, where a = 0.76 for s = 3/2 and a = 0.84 for s = 5/2. Finally, we demonstrate the usefulness of our present results for E(N,S,s) by examining the Fe12 ring-type magnetic molecule, leading to a new, more accurate estimate of the exchange constant for this system than has been obtained heretofore.Comment: Submitted to Physical Review B, 10 pages, 10 figure

Independent, Reciprocal Neuromodulatory Control of Sweet and Bitter Taste Sensitivity during Starvation in Drosophila

An organism’s behavioral decisions often depend upon the relative strength of appetitive and aversive sensory stimuli, the relative sensitivity to which can be modified by internal states like hunger. However, whether sensitivity to such opposing influences is modulated in a unidirectional or bidirectional manner is not clear. Starved flies exhibit increased sugar and decreased bitter sensitivity. It is widely believed that only sugar sensitivity changes, and that this masks bitter sensitivity. Here we use gene- and circuit-level manipulations to show that sweet and bitter sensitivity are independently and reciprocally regulated by starvation in Drosophila. We identify orthogonal neuromodulatory cascades that oppositely control peripheral taste sensitivity for each modality. Moreover, these pathways are recruited at increasing hunger levels, such that low-risk changes (higher sugar sensitivity) precede high-risk changes (lower sensitivity to potentially toxic resources). In this way, state-intensity-dependent, reciprocal regulation of appetitive and aversive peripheral gustatory sensitivity permits flexible, adaptive feeding decisions

Linear theory and violent relaxation in long-range systems: a test case

In this article, several aspects of the dynamics of a toy model for longrange Hamiltonian systems are tackled focusing on linearly unstable unmagnetized (i.e. force-free) cold equilibria states of the Hamiltonian Mean Field (HMF). For special cases, exact finite-N linear growth rates have been exhibited, including, in some spatially inhomogeneous case, finite-N corrections. A random matrix approach is then proposed to estimate the finite-N growth rate for some random initial states. Within the continuous, $N \rightarrow \infty$, approach, the growth rates are finally derived without restricting to spatially homogeneous cases. All the numerical simulations show a very good agreement with the different theoretical predictions. Then, these linear results are used to discuss the large-time nonlinear evolution. A simple criterion is proposed to measure the ability of the system to undergo a violent relaxation that transports it in the vicinity of the equilibrium state within some linear e-folding times