Magnetic properties and temperature variation of spectra in the Hubbard model

Using the strong coupling diagram technique, magnetic and spectral properties of the two-dimensional repulsive Hubbard model are investigated in the ranges of repulsions $t\leq U\leq 10t$, temperatures $0.1t\lesssim T\lesssim 4t$ and electron concentrations $0.6\lesssim\bar{n}\leq 1$ with $t$ the hopping constant. The approach takes into account interactions of electrons with spin and charge fluctuations of all ranges and fulfils the Mermin-Wagner theorem. Temperature and concentration dependencies of the uniform magnetic susceptibility, the variation of the double occupancy with the repulsion and the temperature dependence of the square of the site spin are in satisfactory agreement with Monte Carlo results. Three types of the temperature variation of the electron energy spectrum can be distinguished at half-filling. For $U\lesssim 3t$, at low temperatures, there are two nonintersecting bands, which approach each other on the boundary of the magnetic Brillouin zone. With increasing $T$ these bands merge into one band crossing the Fermi level. For $4t\lesssim U \lesssim 6t$, the low-temperature picture described above is supplemented with a low-intensity spin-polaron band located near the Fermi level. As its counterpart in the strong-correlation case, the band is formed by bound states of electrons and spin excitations. However, in contrast to the former case, the band exists even at half-filling and occupies the entire Brillouin zone. As for lower $U$, with increasing temperature, all bands coalesce into a single band. For $U\gtrsim 7t$ and low temperatures the spectrum has a pronounced four-band structure, which with increasing $T$ transforms into two Hubbard subbands.Comment: 12 pages, 14 figure

Cooling by conversion of para to ortho-hydrogen

The cooling capacity of a solid hydrogen cooling system is significantly increased by exposing vapor created during evaporation of a solid hydrogen mass to a catalyst and thereby accelerating the endothermic para-to-ortho transition of the vapor to equilibrium hydrogen. Catalyst such as nickel, copper, iron or metal hydride gels of films in a low pressure drop catalytic reactor are suitable for accelerating the endothermic para-to-ortho conversion

Continuum of many-particle states near the metal-insulator transition in the Hubbard model

The strong coupling diagram technique is used for investigating states near the metal-insulator transition in the half-filled two-dimensional repulsive Hubbard model. The nonlocal third-order term is included in the irreducible part along with local terms of lower orders. Derived equations for the electron Green's function are solved by iteration for moderate Hubbard repulsions and temperatures. Starting iteration from Green's functions of the Hubbard-I approximation with various distances of poles from the real frequency axis continua of different metallic and insulating solutions are obtained. The insulating solutions vary in the width of the Mott gap, while the metallic solutions differ in the shape of the spectral function in the vicinity of the Fermi level. Besides, different scenarios of the metal-insulator transition -- with a sudden onset of a band of mobile states near the Fermi level and with gradual closure of the Mott gap -- are observed with a change in temperature. In spite of these dissimilarities, all solutions have a common curve separating metallic and insulating states in the phase diagram. Near this curve metallic and insulating solutions coexist. For moderate Hubbard repulsions metallic solutions are not Fermi liquids.Comment: 10 pages, 9 figure

The Hubbard model in the strong coupling theory at arbitrary filling

Equations for the electron Green's function of the two-dimensional Hubbard model, derived using the strong coupling diagram technique, are self-consistently solved for different electron concentrations $n$ and tight-binding dispersions. Comparison of spectral functions calculated for the ratio of Hubbard repulsion to the nearest neighbor hopping $U/t=8$ with Monte Carlo data shows not only qualitative, but in some cases quantitative agreement in position of maxima. General spectral shapes, their evolution with momentum and filling in the wide range $0.7\lesssim n\leq 1$ are also similar. At half-filling and for the next nearest neighbor hopping constant $t'=-0.3t$ the Mott transition occurs at $U_c\approx 7\Delta/8$, where $\Delta$ is the initial bandwidth. This value is close to those obtained in the cases of the semi-elliptical density of states and for $t'=0$. In the case $U=8t$ and $t'=-0.3t$ the Mott gap reaches maximum width at $n=1.04$, and it is larger than that at $t'=0$ for half-filling. In all considered cases positions of spectral maxima are close to those in the Hubbard-I approximation.Comment: 10 pages, 6 figures. arXiv admin note: text overlap with arXiv:1410.828

Thamnophis butleri

Number of Pages: 2Integrative BiologyEarth and Planetary Science

Shari\u27ah, Democracy, and the Modern Nation-State: Some Reflections on Islam, Popular Rule, and Pluralism

In this article, the author examines two considerations that are critical to a full and meaningful assessment of the degree to which Islam, and Islamic law in particular, can find authentic expressions of themselves under what may reasonably be considered a democratic form of government. The first of these has to do with the scope of Islamic law, or more properly, the scope of the interpretive authority of Muslim jurists, and whether a State that is governed by Shari‘ah must necessarily give priority to the views of religious scholars over those of all others in every aspect of life. Does establishing speed limits, formulating economic policy, or setting standards for medical licensing all fall under the legal authority of the jurists? If not, is there any basis other than political fiat upon which the scope of this jurisdiction might be defined? The second consideration is connected to the question of whether in contemplating the relationship between Islam and democracy, we have not conflated the framework within which modern democracy is packaged, namely the Nation-State (and some would insist on adding capitalism), with the spirit and essence of democratic rule. If we could imagine a State structure whose integrity was not equated with the ability to exercise an absolute monopoly over law-making and the concomitant imposition of a uniform standard of conduct on all of its citizens, would the idea of Islamic democracy present as many apparent difficulties as it presently does? The author’s objective is to add a dimension to the discussion on Islam and democracy that will render future assessments and proposals more nuanced and circumspect

Study of a solid hydrogen cooler for spacecraft instruments and sensors

The results of tests and studies to investigate the utilization of solid hydrogen for cooling of spacecraft instruments and sensors are presented. The results are presented in two sections; the first describing the tests in which an existing single stage solid cooler was filled and tested with solid hydrogen and the second which describes the analysis and design of a catalytic converter which will be tested in the vent line of the cooler

Incommensurate spin dynamics in underdoped cuprate perovskites

The incommensurate magnetic response observed in normal-state cuprate perovskites is interpreted based on the projection operator formalism and the t-J model of Cu-O planes. In agreement with experiment the calculated dispersion of maxima in the susceptibility has the shape of two parabolas with upward and downward branches which converge at the antiferromagnetic wave vector. The maxima are located at the momenta $({1/2},{1/2}\pm\delta)$, $({1/2}\pm\delta,{1/2})$ and at $({1/2}\pm\delta,{1/2}\pm\delta)$, $({1/2}\pm\delta,{1/2}\mp\delta)$ in the lower and upper parabolas, respectively. The upper parabola reflects the dispersion of magnetic excitations of the localized Cu spins, while the lower parabola arises due to a dip in the spin-excitation damping at the antiferromagnetic wave vector. For moderate doping this dip stems from the weakness of the interaction between the spin excitations and holes near the hot spots. The frequency dependence of the susceptibility is shown to depend strongly on the hole bandwidth and damping and varies from the shape observed in YBa$_2$Cu$_3$O$_{7-y}$ to that inherent in La$_{2-x}$Sr$_x$CuO$_4$.Comment: 15 pages, 7 figure