Properties of the negative effective magnetic pressure instability

As was demonstrated in earlier studies, turbulence can result in a negative contribution to the effective mean magnetic pressure, which, in turn, can cause a large-scale instability. In this study, hydromagnetic mean-field modelling is performed for an isothermally stratified layer in the presence of a horizontal magnetic field. The negative effective magnetic pressure instability (NEMPI) is comprehensively investigated. It is shown that, if the effect of turbulence on the mean magnetic tension force vanishes, which is consistent with results from direct numerical simulations of forced turbulence, the fastest growing eigenmodes of NEMPI are two-dimensional. The growth rate is found to depend on a parameter beta_* characterizing the turbulent contribution of the effective mean magnetic pressure for moderately strong mean magnetic fields. A fit formula is proposed that gives the growth rate as a function of turbulent kinematic viscosity, turbulent magnetic diffusivity, the density scale height, and the parameter beta_*. The strength of the imposed magnetic field does not explicitly enter provided the location of the vertical boundaries are chosen such that the maximum of the eigenmode of NEMPI fits into the domain. The formation of sunspots and solar active regions is discussed as possible applications of NEMPI.Comment: 6 pages, 6 figures, 1 table; Astron. Nachr. (published

Fermi surface evolution of the 2D Hubbard model within a novel four-pole approximation

We present a novel solution of the 2D Hubbard model in the framework of the Composite Operator Method within a four-pole approximation. We adopt a basis of four fields: the two Hubbard operators plus two fields describing the Hubbard transitions dressed by nearest-neighbor spin fluctuations. We include these nonlocal operators because spin fluctuations play a dominant role in strongly correlated electronic systems with respect to other types of nonlocal charge, pair and double-occupancy fluctuations. The approximate solution performs very well once compared with advanced (semi-) numerical methods from the weak-to the strong-coupling regime, being by far less computational-resource demanding. We adopt this solution to study the single-particle properties of the model in the strong coupling regime, where the effects of strong short-range magnetic correlations are more relevant and could be responsible for anomalous features. In particular, we will focus on the characterization of the Fermi surface and of its evolution with doping.We present a novel solution of the 2D Hubbard model in the framework of the Composite Operator Method within a four-pole approximation. We adopt a basis of four fields: the two Hubbard operators plus two fields describing the Hubbard transitions dressed by nearest-neighbor spin fluctuations. We include these nonlocal operators because spin fluctuations play a dominant role in strongly correlated electronic systems with respect to other types of nonlocal charge, pair and double-occupancy fluctuations. The approximate solution performs very well once compared with advanced (semi-) numerical methods from the weak-to the strong-coupling regime, being by far less computational-resource demanding. We adopt this solution to study the single-particle properties of the model in the strong coupling regime, where the effects of strong short-range magnetic correlations are more relevant and could be responsible for anomalous features. In particular, we will focus on the characterization of the Fermi surface and of it..

Normal Fermi Liquid Behavior of Quasiholes in the Spin-Polaron Model for Copper Oxides

Based on the t-J model and the self-consistent Born approximation, the damping of quasiparticle hole states near the Fermi surface is calculated in a low doping regime. Renormalization of spin-wave excitations due to hole doping is taken into account. The damping is shown to be described by a familiar form $\text{Im}\Sigma({\bf k}^{\prime},\epsilon)\propto (\epsilon^{2}/ \epsilon_{F})\ln(\epsilon/ \epsilon_{F})$ characteristic of the 2-dimensional Fermi liquid, in contrast with the earlier statement reported by Li and Gong [Phys. Rev. B {\bf 51}, 6343 (1995)] on the marginal Fermi liquid behavior of quasiholes

Weakly Interacting, Dilute Bose Gases in 2D

This article surveys a number of theoretical problems and open questions in the field of two-dimensional dilute Bose gases with weak repulsive interactions. In contrast to three dimensions, in two dimensions the formation of long-range order is prohibited by the Bogoliubov-Hohenberg theorem, and Bose-Einstein condensation is not expected to be realized. Nevertheless, first experimental indications supporting the formation of the condensate in low dimensional systems have been recently obtained. This unexpected behaviour appears to be due to the non-uniformity, introduced into a system by the external trapping potential. Theoretical predictions, made for homogeneous systems, require therefore careful reexamination. We survey a number of popular theoretical treatments of the dilute weakly interacting Bose gas and discuss their regions of applicability. The possibility of Bose-Einstein condensation in a two-dimensional gas, the validity of perturbative t-matrix approximation and diluteness condition are issues that we discuss in detail.Comment: Survey, 25 pages RMP style, revised version, refs added, some changes made, accepted for publication in Rev. Mod. Phy

Parker/buoyancy instabilities with anisotropic thermal conduction, cosmic rays, and arbitrary magnetic field strength

We report the results of a local stability analysis for a magnetized, gravitationally stratified plasma containing cosmic rays. We account for cosmic-ray diffusion and thermal conduction parallel to the magnetic field and allow beta to take any value, where p is the plasma pressure and B is the magnetic field strength. We take the gravitational acceleration to be in the -z-direction and the equilibrium magnetic field to be in the y-direction, and we derive the dispersion relation for small-amplitude instabilities and waves in the large-|k_x| limit. We use the Routh-Hurwitz criterion to show analytically that the necessary and sufficient criterion for stability in this limit is n k_B dT/dz + dp_cr/dz + (1/8pi)dB^2/dz > 0, where T is the temperature, n is the number density of thermal particles, and p_cr is the cosmic-ray pressure. We present approximate analytical solutions for the normal modes in the low- and high-diffusivity limits, show that they are consistent with the derived stability criterion, and compare them to numerical results obtained from the full, unapproximated, dispersion relation. Our results extend earlier analyses of buoyancy instabilities in galaxy-cluster plasmas to the beta <= 1 regime. Our results also extend earlier analyses of the Parker instability to account for anisotropic thermal conduction, and show that the interstellar medium is more unstable to the Parker instability than was predicted by previous studies in which the thermal plasma was treated as adiabatic.Comment: 36 pages, 2 figures, Accepted for publication in Ap

Local Radiation MHD Instabilities in Magnetically Stratified Media

We study local radiation magnetohydrodynamic instabilities in static, optically thick, vertically stratified media with constant flux mean opacity. We include the effects of vertical gradients in a horizontal background magnetic field. Assuming rapid radiative diffusion, we use the zero gas pressure limit as an entry point for investigating the coupling between the photon bubble instability and the Parker instability. Apart from factors that depend on wavenumber orientation, the Parker instability exists for wavelengths longer than a characteristic wavelength lambda_{tran}, while photon bubbles exist for wavelengths shorter than lambda_{tran}. The growth rate in the Parker regime is independent of the orientation of the horizontal component of the wavenumber when radiative diffusion is rapid, but the range of Parker-like wavenumbers is extended if there exists strong horizontal shear between field lines (i.e. horizontal wavenumber perpendicular to the magnetic field). Finite gas pressure introduces an additional short wavelength limit to the Parker-like behavior, and also limits the growth rate of the photon bubble instability to a constant value at short wavelengths. We also consider the effects of differential rotation with accretion disk applications in mind. Our results may explain why photon bubbles have not yet been observed in recent stratified shearing box accretion disk simulations. Photon bubbles may physically exist in simulations with high radiation to gas pressure ratios, but higher spatial resolution will be needed to resolve the asymptotically growing unstable wavelengths.Comment: The Astrophysical Journal, in pres

Rotational effects on the negative magnetic pressure instability

The surface layers of the Sun are strongly stratified. In the presence of turbulence with a weak mean magnetic field, a large-scale instability resulting in the formation of non-uniform magnetic structures, can be excited over the scale of many turbulent eddies or convection cells. This instability is caused by a negative contribution of turbulence to the effective (mean-field) magnetic pressure and has previously been discussed in connection with the formation of active regions and perhaps sunspots. We want to understand the effects of rotation on this instability in both two and three dimensions. We use mean-field magnetohydrodynamics in a parameter regime in which the properties of the negative effective magnetic pressure instability have previously been found to be in agreement with those of direct numerical simulations. We find that the instability is suppressed already for relatively slow rotation with Coriolis numbers (i.e. inverse Rossby numbers) around 0.2. The suppression is strongest at the equator. In the nonlinear regime, we find traveling wave solutions with propagation in the prograde direction at the equator with additional poleward migration away from the equator. The prograde rotation of the magnetic pattern near the equator is argued to be a possible explanation for the faster rotation speed of magnetic tracers found on the Sun. In the bulk of the domain, kinetic and current helicities are negative in the northern hemisphere and positive in the southern.Comment: 8 pages, 13 figures, submitted to A&

Bosonic sector of the two-dimensional Hubbard model studied within a two-pole approximation

The charge and spin dynamics of the two-dimensional Hubbard model in the paramagnetic phase is first studied by means of the two-pole approximation within the framework of the Composite Operator Method. The fully self-consistent scheme requires: no decoupling, the fulfillment of both Pauli principle and hydrodynamics constraints, the simultaneous solution of fermionic and bosonic sectors and a very rich momentum dependence of the response functions. The temperature and momentum dependencies, as well as the dependency on the Coulomb repulsion strength and the filling, of the calculated charge and spin susceptibilities and correlation functions are in very good agreement with the numerical calculations present in the literature

Spin polaron damping in the spin-fermion model for cuprate superconductors

A self-consistent, spin rotational invariant Green's function procedure has been developed to calculate the spectral function of carrier excitations in the spin-fermion model for the CuO2 plane. We start from the mean field description of a spin polaron in the Mori-Zwanzig projection method. In order to determine the spin polaron lifetime in the self-consistent Born approximation, the self-energy is expressed by an irreducible Green's function. Both, spin polaron and bare hole spectral functions are calculated. The numerical results show a well pronounced quasiparticle peak near the bottom of the dispersion at (pi/2,pi/2), the absence of the quasiparticle at the Gamma-point, a rather large damping away from the minimum and an asymmetry of the spectral function with respect to the antiferromagnetic Brillouin zone. These findings are in qualitative agreement with photoemission data for undoped cuprates. The direct oxygen-oxygen hopping is responsible for a more isotropic minimum at (pi/2,pi/2).Comment: 18 pages, 13 figure

The Hubbard model within the equations of motion approach

The Hubbard model has a special role in Condensed Matter Theory as it is considered as the simplest Hamiltonian model one can write in order to describe anomalous physical properties of some class of real materials. Unfortunately, this model is not exactly solved except for some limits and therefore one should resort to analytical methods, like the Equations of Motion Approach, or to numerical techniques in order to attain a description of its relevant features in the whole range of physical parameters (interaction, filling and temperature). In this manuscript, the Composite Operator Method, which exploits the above mentioned analytical technique, is presented and systematically applied in order to get information about the behavior of all relevant properties of the model (local, thermodynamic, single- and two- particle ones) in comparison with many other analytical techniques, the above cited known limits and numerical simulations. Within this approach, the Hubbard model is shown to be also capable to describe some anomalous behaviors of the cuprate superconductors.Comment: 232 pages, more than 300 figures, more than 500 reference