Lattice study of two-dimensional N=(2,2) super Yang-Mills at large-N

We study two-dimensional N=(2,2) SU(N) super Yang-Mills theory on Euclidean two-torus using Sugino's lattice regularization. We perform the Monte-Carlo simulation for N=2,3,4,5 and then extrapolate the result to N = infinity. With the periodic boundary conditions for the fermions along both circles, we establish the existence of a bound state in which scalar fields clump around the origin, in spite of the existence of a classical flat direction. In this phase the global (Z_N)^2 symmetry turns out to be broken. We provide a simple explanation for this fact and discuss its physical implications.Comment: 24 pages, 13 figure

The Interplay of Spin and Charge Channels in Zero Dimensional Systems

We present a full fledged quantum mechanical treatment of the interplay between the charge and the spin zero-mode interactions in quantum dots. Quantum fluctuations of the spin-mode suppress the Coulomb blockade and give rise to non-monotonic behavior near this point. They also greatly enhance the dynamic spin susceptibility. Transverse fluctuations become important as one approaches the Stoner instability. The non-perturbative effects of zero-mode interaction are described in terms of charge (U(1)) and spin (SU(2)) gauge bosons.Comment: 4.5 pages, 2 figure

Orbital effects in manganites

In this paper I give a short review of some properties of the colossal magnetoresistance manganites, connected with the orbital degrees of freedom. Ions Mn{3+}, present in most of these compounds, have double orbital degeneracy and are strong Jahn-Teller ions, causing structural distortions and orbital ordering. Mechanisms leading to such ordering are shortly discussed, and the role of orbital degrees of freedom in different parts of the phase diagram of manganites is described. Special attention is paid to the properties of low-doped systems (doping 0.1 - 0.25), to overdoped systems (x > 0.5), and to the possibility of a novel type of orbital ordering in optimally doped ferromagnetic metallic manganites.Comment: 28 pages, 7 figures, to be published in J. Mod. Phys.

Absence of sign problem in two-dimensional N=(2,2) super Yang-Mills on lattice

We show that N=(2,2) SU(N) super Yang-Mills theory on lattice does not have sign problem in the continuum limit, that is, under the phase-quenched simulation phase of the determinant localizes to 1 and hence the phase-quench approximation becomes exact. Among several formulations, we study models by Cohen-Kaplan-Katz-Unsal (CKKU) and by Sugino. We confirm that the sign problem is absent in both models and that they converge to the identical continuum limit without fine tuning. We provide a simple explanation why previous works by other authors, which claim an existence of the sign problem, do not capture the continuum physics.Comment: 27 pages, 24 figures; v2: comments and references added; v3: figures on U(1) mass independence and references added, to appear in JHE

Spatial and temporal variations in seismicity in the Imperial Valley (1902-1984)

Earthquakes with M_L ≧ 4.5 that occurred between 1932 and 1973 in the Imperial Valley region and their related foreshocks and aftershocks are relocated using station delays derived from calibration events that were well recorded at regional distances between 1979 and 1981. The relocated seismicity shows that there was an increase in seismicity in regions northeast of the Imperial fault 5 to 6 yr prior to the 1940 (M_s = 7.1) Imperial Valley earthquake. A study of intensity reports for felt earthquakes prior to 1932 also suggests an increase in seismicity in regions surrounding the Imperial fault as early as 1917. Isoseismal patterns, description of the mainshock sequence, and patterns of seismicity before and after the 1915 Imperial Valley earthquakes suggest that the earthquakes occurred off the Imperial fault. In this case, seismicity between 1906 and 1940 would nearly encircle the portion of the Imperial fault that ruptured during 1940. In both the 1940 and 1979 Imperial Valley earthquake sequences, aftershocks of M_L ≧ 4.5 occurred only for 2 months following the mainshock. The aftershock sequences were followed by periods of quiescence lasting up to 10 yr in the region within 30 km of the mainshock. This is in contrast to M_L > 6.0 earthquakes occurring near the edges of the Imperial Valley that had aftershocks of M_L ≧ 4.5 occurring for up to 4 yr after the mainshock. These differences may be related to the high heat flow within the Imperial Valley

Depth of seismicity in the Imperial Valley Region (1977–1983) and its relationship to heat flow, crustal structure and the October 15, 1979, earthquake

Focal depths from over 1000 earthquakes occuring between 1977 and 1983 in the Imperial Valley-southern Peninsular Ranges are used to study relationships between the depth of seismicity, heat flow, and crustal structure. This study used relocated A and B quality events from the California Institute of Technology catalog that were carefully selected to insure focal depth precision of ±2 km. Regional variations in focal depth appear to be related to regional heat flow variation, whereas local variations in focal depth, especially in the central Imperial Valley, may be related to crustal structure. These variations are studied by rheologic modeling. A comparison of focal depths of earthquakes occurring before and after the October 15, 1979 (M=6.6), earthquake indicates that aftershocks during the first 2 months of the sequence were 2–3 km deeper than earthquakes occurring in other time periods. The deepest earthquakes in Imperial Valley are spatially associated with a subbasement dome near the northern end of the Imperial fault. This dome coincides with the region where the Imperial fault undergoes a transition from stick-slip behavior to aseismic fault creep. Models of slip during the 1979 mainshock are also compared with premainshock and postmainshock seismicity. A relocation of the 1940 (M=7.1) mainshock suggests that this sequence began by rupturing the same portion of the fault that experienced maximum slip during the 1979 mainshock

Dirac-Kaehler fermion with noncommutative differential forms on a lattice

Noncommutativity between a differential form and a function allows us to define differential operator satisfying Leibniz's rule on a lattice. We propose a new associative Clifford product defined on the lattice by introducing the noncommutative differential forms. We show that this Clifford product naturally leads to the Dirac-K\"ahler fermion on the lattice.Comment: 3 pages, Lattice2003(Theoretical Development

Long-period surface waves of four western United States earthquakes recorded by the Pasadena strainmeter

Long-period surface waves recorded on the north-south Pasadena strainmeter are used to determine the seismic moments and fault parameters of the 19 May 1940 Imperial Valley, California, the 16 December 1954 Dixie Valley and Fairview Peak, Nevada, and the 18 August 1959 Hebgen Lake, Montana, earthquakes. Synthetic strain seismograms are matched with the observed strainmeter seismograms. Source parameters from the strainmeter modeling are more consistent with source parameters estimated from geodetic and geologic information than parameters estimated from short-period (<15 sec) body wave data. Long-period surface wave moment estimates agree well with geodetic estimates of moment, but are 1.5 to 5 times greater than moments obtained from modeling of teleseismic body waves or geologic information. The Imperial Valley earthquake is best modeled as consisting of 5 point sources along a fault 87.5 km in length with a strike, rake, and dip of 326°, 180°, and 90°. The moment for the earthquake was 4.8 × 10^(19) N-m. The synthetic seismogram that best models the Fairview Peak and Dixie Valley earthquakes assumes that the Fairview Peak earthquake was twice the size of the Dixie Valley event. Moments of 5.9 to 13 × 10^(19) and 3 to 6.5 × 10^(19) N-m are obtained for these events. A moment of 1.5 × 10^(20) N-m is obtained for the Hebgen Lake earthquake. Love waves of this earthquake are best modeled by a fault striking 102°, although surface faulting produced during the earthquake strikes 130°

The chiral and flavour projection of Dirac-Kahler fermions in the geometric discretization

It is shown that an exact chiral symmetry can be described for Dirac-Kahler fermions using the two complexes of the geometric discretization. This principle is extended to describe exact flavour projection and it is shown that this necessitates the introduction of a new operator and two new structures of complex. To describe simultaneous chiral and flavour projection, eight complexes are needed in all and it is shown that projection leaves a single flavour of chiral field on each.Comment: v2: 17 pages, Latex. 5 images eps. Added references, reformatted and clarification of some point

Orbital ordering in frustrated Jahn-Teller systems

We consider the superexchange in `frustrated' Jahn-Teller systems, such as the transition metal oxides NaNiO_2, LiNiO_2, and ZnMn_2O_4, in which transition metal ions with doubly degenerate orbitals form a triangular or pyrochlore lattice and are connected by the 90-degree metal-oxygen-metal bonds. We show that this interaction is much different from a more familiar exchange in systems with the 180-degree bonds, e.g. perovskites. In contrast to the strong interplay between the orbital and spin degrees of freedom in perovskites, in the 90-degree exchange systems spins and orbitals are decoupled: the spin exchange is much weaker than the orbital one and it is ferromagnetic for all orbital states. Due to frustration, the mean-field orbital ground state is strongly degenerate. Quantum orbital fluctuations select particular ferro-orbital states, such as the one observed in NaNiO_2. We also discuss why LiNiO_2 may still behave as an orbital liquid.Comment: 5 pages, 3 figure