Close-packed structures and phase diagram of soft spheres in cylindrical pores

It is shown for a model system consisting of spherical particles confined in cylindrical pores that the first ten close-packed phases are in one-to-one correspondence with the first ten ways of folding a triangular lattice, each being characterized by a roll-up vector like the single-walled carbon nanotube. Phase diagrams in pressure-diameter and temperature-diameter planes are obtained by inherent-structure calculation and molecular dynamics simulation. The phase boundaries dividing two adjacent phases are infinitely sharp in the low-temperature limit but are blurred as temperature is increased. Existence of such phase boundaries explains rich, diameter-sensitive phase behavior unique for cylindrically confined systems

Universal properties from local geometric structure of Killing horizon

We consider universal properties that arise from a local geometric structure of a Killing horizon. We first introduce a non-perturbative definition of such a local geometric structure, which we call an asymptotic Killing horizon. It is shown that infinitely many asymptotic Killing horizons reside on a common null hypersurface, once there exists one asymptotic Killing horizon. The acceleration of the orbits of the vector that generates an asymptotic Killing horizon is then considered. We show that there exists the $\textit{diff}(S^1)$ or $\textit{diff}(R^1)$ sub-algebra on an asymptotic Killing horizon universally, which is picked out naturally based on the behavior of the acceleration. We also argue that the discrepancy between string theory and the Euclidean approach in the entropy of an extreme black hole may be resolved, if the microscopic states responsible for black hole thermodynamics are connected with asymptotic Killing horizons.Comment: 14 pages, v2. minor correction

Numerical Renormalization Group Study of non-Fermi-liquid State on Dilute Uranium Systems

We investigate the non-Fermi-liquid (NFL) behavior of the impurity Anderson model (IAM) with non-Kramers doublet ground state of the f$^2$ configuration under the tetragonal crystalline electric field (CEF). The low energy spectrum is explained by a combination of the NFL and the local-Fermi-liquid parts which are independent with each other. The NFL part of the spectrum has the same form to that of two-channel-Kondo model (TCKM). We have a parameter range that the IAM shows the $- \ln T$ divergence of the magnetic susceptibility together with the positive magneto resistance. We point out a possibility that the anomalous properties of U$_x$Th$_{1-x}$Ru$_2$Si$_2$ including the decreasing resistivity with decreasing temperature can be explained by the NFL scenario of the TCKM type. We also investigate an effect of the lowering of the crystal symmetry. It breaks the NFL behavior at around the temperature, $\delta /10$, where $\delta$ is the orthorhombic CEF splitting. The NFL behavior is still expected above the temperature, $\delta/10$.Comment: 25 pages, 12 figure

Asymptotic symmetries on Kerr--Newman horizon without anomaly of diffeomorphism invariance

We analyze asymptotic symmetries on the Killing horizon of the four-dimensional Kerr--Newman black hole. We first derive the asymptotic Killing vectors on the Killing horizon, which describe the asymptotic symmetries, and find that the general form of these asymptotic Killing vectors is the universal one possessed by arbitrary Killing horizons. We then construct the phase space associated with the asymptotic symmetries. It is shown that the phase space of an extreme black hole either has the size comparable with a non-extreme black hole, or is small enough to exclude degeneracy, depending on whether or not the global structure of a Killing horizon particular to an extreme black hole is respected. We also show that the central charge in the Poisson brackets algebra of these asymptotic symmetries vanishes, which implies that there is not an anomaly of diffeomorphism invariance. By taking into account other results in the literature, we argue that the vanishing central charge on a black hole horizon, in an effective theory, looks consistent with the thermal feature of a black hole. We furthermore argue that the vanishing central charge implies that there are infinitely many classical configurations that are associated with the same macroscopic state, while these configurations are distinguished physically.Comment: 14 pages, v2: references added, minor corrections, v3: new pars and refs. added and corresponding correction

Small Energy Scale for Mixed-Valent Uranium Materials

We investigate a two-channel Anderson impurity model with a $5f^1$ magnetic and a $5f^2$ quadrupolar ground doublet, and a $5f^2$ excited triplet. Using the numerical renormalization group method, we find a crossover to a non-Fermi liquid state below a temperature $T^*$ varying as the $5f^2$ triplet-doublet splitting to the 7/2 power. To within numerical accuracy, the non-linear magnetic susceptibility and the $5f^1$ contribution to the linear susceptibility are given by universal one-parameter scaling functions. These results may explain UBe$_{13}$ as mixed valent with a small crossover scale $T^*$.Comment: 4 pages, 3 figures, REVTeX, to appear in Phys. Rev. Let

On the thermodynamic stability and structural transition of clathrate hydrates

Gas mixtures of methane and ethane form structure II clathrate hydrates despite the fact that each of pure methane and pure ethane gases forms the structure I hydrate. Optimization of the interaction potential parameters for methane and ethane is attempted so as to reproduce the dissociation pressures of each simple hydrate containing either methane or ethane alone. An account for the structural transitions between type I and type II hydrates upon changing the mole fraction of the gas mixture is given on the basis of the van der Waals and Platteeuw theory with these optimized potentials. Cage occupancies of the two kinds of hydrates are also calculated as functions of the mole fraction at the dissociation pressure and at a fixed pressure well above the dissociation pressure

Critical Nature of Non-Fermi Liquid in Spin 3/2 Multipolar Kondo Model

A multipolar Kondo model of an impurity spin S_I=3/2 interacting with conduction electrons with spin s_c=3/2 is investigated using boundary conformal field theory. A two-channel Kondo (2CK) -like non-Fermi liquid (NFL) under the particle-hole symmetry is derived explicitly using a ``superspin absorption'' in the sector of a hidden symmetry, SO(5). We discuss the difference between the usual spin-1/2 2CK NFL fixed point and the present one. In particular, we find that, unlike the usual 2CK model, the low temperature impurity specific heat is proportional to temperature.Comment: 4 pages, 2 figure

Spin splitting and precession in quantum dots with spin-orbit coupling: the role of spatial deformation

Extending a previous work on spin precession in GaAs/AlGaAs quantum dots with spin-orbit coupling, we study the role of deformation in the external confinement. Small elliptical deformations are enough to alter the precessional characteristics at low magnetic fields. We obtain approximate expressions for the modified $g$ factor including weak Rashba and Dresselhaus spin-orbit terms. For more intense couplings numerical calculations are performed. We also study the influence of the magnetic field orientation on the spin splitting and the related anisotropy of the $g$ factor. Using realistic spin-orbit strengths our model calculations can reproduce the experimental spin-splittings reported by Hanson et al. (cond-mat/0303139) for a one-electron dot. For dots containing more electrons, Coulomb interaction effects are estimated within the local-spin-density approximation, showing that many features of the non-iteracting system are qualitatively preserved.Comment: 7 pages, 7 figure

Solution of the Two-Channel Anderson Impurity Model - Implications for the Heavy Fermion UBe13_{13} -

We solve the two-channel Anderson impurity model using the Bethe-Ansatz. We determine the ground state and derive the thermodynamics, obtaining the impurity entropy and specific heat over the full range of temperature. We show that the low temperature physics is given by a line of fixed points decribing a two-channel non Fermi liquid behavior in the integral valence regime associated with moment formation as well as in the mixed valence regime where no moment forms. We discuss relevance for the theory of UBe$_{13}$.Comment: 4 pages, 2 figures, (to be published in PRL

Orbital Localization and Delocalization Effects in the U 5f^2 Configuration: Impurity Problem

Anderson models, based on quantum chemical studies of the molecule of U(C_8H_8)_2, are applied to investigate the problem of an U impurity in a metal. The special point here is that the U 5f-orbitals are divided into two subsets: an almost completely localized set and a considerably delocalized one. Due to the crystal field, both localized and delocalized U 5f-orbitals affect the low-energy physics. A numerical renormalization group study shows that every fixed point is characterized by a residual local spin and a phase shift. The latter changes between 0 and \pi/2, which indicates the competition between two different fixed points. Such a competition between the different local spins at the fixed points reflects itself in the impurity magnetic susceptibility at high temperatures. These different features cannot be obtained if the special characters of U 5f-orbitals are neglected.Comment: 4 pages, REVTeX, email to [email protected]