Decoherence of localized spins interacting via RKKY interaction

We theoretically study decoherence of two localized spins interacting via the RKKY interaction in one-, two-, and three-dimensional electron gas. We derive the kinetic equation for the reduced density matrix of the localized spins and show that energy relaxation caused by singlet-triplet transition is suppressed when the RKKY interaction is ferromagnetic. We also estimate the decoherence time of the system consisting of two quantum dots embedded in a two dimensional electron gas.Comment: 4pages, 2figure

Aspects of ABJM orbifolds with discrete torsion

We analyze orbifolds with discrete torsion of the ABJM theory by a finite subgroup $\Gamma$ of $SU(2)\times SU(2)$ . Discrete torsion is implemented by twisting the crossed product algebra resulting after orbifolding. It is shown that, in general, the order $m$ of the cocycle we chose to twist the algebra by enters in a non trivial way in the moduli space. To be precise, the M-theory fiber is multiplied by a factor of $m$ in addition to the other effects that were found before in the literature. Therefore we got a $\mathbb{Z}_{\frac{k|\Gamma|}{m}}$ action on the fiber. We present a general analysis on how this quotient arises along with a detailed analysis of the cases where $\Gamma$ is abelian

Vertically coupled double quantum dots in magnetic fields

Ground-state and excited-state properties of vertically coupled double quantum dots are studied by exact diagonalization. Magic-number total angular momenta that minimize the total energy are found to reflect a crossover between electron configurations dominated by intra-layer correlation and ones dominated by inter-layer correlation. The position of the crossover is governed by the strength of the inter-layer electron tunneling and magnetic field. The magic numbers should have an observable effect on the far infra-red optical absorption spectrum, since Kohn's theorem does not hold when the confinement potential is different for two dots. This is indeed confirmed here from a numerical calculation that includes Landau level mixing. Our results take full account of the effect of spin degrees of freedom. A key feature is that the total spin, $S$, of the system and the magic-number angular momentum are intimately linked because of strong electron correlation. Thus $S$ jumps hand in hand with the total angular momentum as the magnetic field is varied. One important consequence of this is that the spin blockade (an inhibition of single-electron tunneling) should occur in some magnetic field regions because of a spin selection rule. Owing to the flexibility arising from the presence of both intra-layer and inter-layer correlations, the spin blockade is easier to realize in double dots than in single dots.Comment: to be published in Phys. Rev. B1

New Gauged Linear Sigma Models for 8D HyperKahler Manifolds and Calabi-Yau Crystals

We propose two kinds of gauged linear sigma models whose moduli spaces are real eight-dimensional hyperKahler and Calabi-Yau manifolds, respectively. Here, hyperKahler manifolds have sp(2) holonomy in general and are dual to Type IIB (p,q)5-brane configurations. On the other hand, Calabi-Yau fourfolds are toric varieties expressed as quotient spaces. Our model involving fourfolds is different from the usual one which is directly related to a symplectic quotient procedure. Remarkable features in newly-found three-dimensional Chern-Simons-matter theories appear here as well, such as dynamical Fayet-Iliopoulos parameters, one dualized photon and its residual discrete gauge symmetry.Comment: 20 pages, 1 figure; v2: minor changes and references added; v3: statements improved, newer than JHEP versio

Semi-Static Hedging Based on a Generalized Reflection Principle on a Multi Dimensional Brownian Motion

On a multi-assets Black-Scholes economy, we introduce a class of barrier options. In this model we apply a generalized reflection principle in a context of the finite reflection group acting on a Euclidean space to give a valuation formula and the semi-static hedge.Comment: Asia-Pacific Financial Markets, online firs

Non-singlet Baryons in Less Supersymmetric Backgrounds

We analyze the holographic description of non-singlet baryons in various backgrounds with reduced supersymmetries and/or confinement. We show that they exist in all AdS_5xY_5 backgrounds with Y_5 an Einstein manifold bearing five form flux, for a number of quarks 5N/8< k< N, independently on the supersymmetries preserved. This result still holds for gamma_i deformations. In the confining Maldacena-Nunez background non-singlet baryons also exist, although in this case the interval for the number of quarks is reduced as compared to the conformal case. We generalize these configurations to include a non-vanishing magnetic flux such that a complementary microscopical description can be given in terms of lower dimensional branes expanding into fuzzy baryons. This description is a first step towards exploring the finite 't Hooft coupling region.Comment: 36 Pages, 1 figure, Latex, v2: few minor changes, JHEP versio

Anomalies and O-plane charges in orientifolded brane tilings

We investigate orientifold of brane tilings. We clarify how the cancellations of gauge anomaly and Witten's anomaly are guaranteed by the conservation of the D5-brane charge. We also discuss the relation between brane tilings and the dual Calabi-Yau cones realized as the moduli spaces of gauge theories. Two types of flavor D5-branes in brane tilings and corresponding superpotentials of fundamental quark fields are proposed, and it is shown that the massless loci of these quarks in the moduli space correctly reproduce the worldvolume of flavor D7-branes in the Calabi-Yau cone dual to the fivebrane system.Comment: 46 pages, 19 figure

Duality between N=5 and N=6 Chern-Simons matter theory

We provide evidences for the duality between ${\cal N}=6$ $U(M)_{4} \times U(N)_{-4}$ Chern-Simons matter theory and ${\cal N}=5$ $O(\hat{M})_{2} \times USp(2\hat{N})_{-1}$ theory for a suitable $\hat{M},\hat{N}$ by working out the superconformal index, which shows perfect matching. For ${\cal N}=5$ theories, we show that supersymmetry is enhanced to ${\cal N}=6$ by explicitly constructing monopole operators filling in $SO(6)_R$ $R$-currents. Finally we work out the large $N$ index of $O(2N)_{2k} \times USp(2N)_{-k}$ and show that it exactly matches with the gravity index on $AdS_4 \times S^7/D_k$, which further provides additional evidence for the duality between the ${\cal N}=5$ and ${\cal N}=6$ theory for $k=1$Comment: 15 pages; references adde

Spin-Blockade in Single and Double Quantum Dots in Magnetic Fields: a Correlation Effect

The total spin of correlated electrons in a quantum dot changes with magnetic field and this effect is generally linked to the change in the total angular momentum from one magic number to another, which can be understood in terms of an `electron molecule' picture for strong fields. Here we propose to exploit this fact to realize a spin blockade, i.e., electrons are prohibited to tunnel at specific values of the magnetic field. The spin-blockade regions have been obtained by calculating both the ground and excited states. In double dots the spin-blockade condition is found to be less stringent than in single dots.Comment: 4pages, to be published in Phys. Rev. B (Rapid Communication

Phases of M2-brane Theories

We investigate different toric phases of 2+1 dimensional quiver gauge theories arising from M2-branes probing toric Calabi-Yau 4 folds. A brane tiling for each toric phase is presented. We apply the 'forward algorithm' to obtain the toric data of the mesonic moduli space of vacua and exhibit the equivalence between the vacua of different toric phases of a given singularity. The structures of the Master space, the mesonic moduli space, and the baryonic moduli space are examined in detail. We compute the Hilbert series and use them to verify the toric dualities between different phases. The Hilbert series, R-charges, and generators of the mesonic moduli space are matched between toric phases.Comment: 60 pages, 28 figures, 6 tables. v2: minor correction