2,957 research outputs found
The large N limit of M2-branes on Lens spaces
We study the matrix model for N M2-branes wrapping a Lens space L(p,1) =
S^3/Z_p. This arises from localization of the partition function of the ABJM
theory, and has some novel features compared with the case of a three-sphere,
including a sum over flat connections and a potential that depends
non-trivially on p. We study the matrix model both numerically and analytically
in the large N limit, finding that a certain family of p flat connections give
an equal dominant contribution. At large N we find the same eigenvalue
distribution for all p, and show that the free energy is simply 1/p times the
free energy on a three-sphere, in agreement with gravity dual expectations.Comment: 28 pages, 4 figure
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, , of the system and the magic-number angular momentum are
intimately linked because of strong electron correlation. Thus 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
Nonequilibrium Kondo Effect in a Quantum Dot Coupled to Ferromagnetic Leads
We study the Kondo effect in the electron transport through a quantum dot
coupled to ferromagnetic leads, using a real-time diagrammatic technique which
provides a systematic description of the nonequilibrium dynamics of a system
with strong local electron correlations. We evaluate the theory in an extension
of the `resonant tunneling approximation', introduced earlier, by introducing
the self-energy of the off-diagonal component of the reduced propagator in spin
space. In this way we develop a charge and spin conserving approximation that
accounts not only for Kondo correlations but also for the spin splitting and
spin accumulation out of equilibrium. We show that the Kondo resonances, split
by the applied bias voltage, may be spin polarized. A left-right asymmetry in
the coupling strength and/or spin polarization of the electrodes significantly
affects both the spin accumulation and the weight of the split Kondo resonances
out of equilibrium. The effects are observable in the nonlinear differential
conductance. We also discuss the influence of decoherence on the Kondo
resonance in the frame of the real-time formulation.Comment: 13 pages, 13 figure
Charged particle-like branes in ABJM
We study the effect of adding lower dimensional brane charges to the 't Hooft
monopole, di-baryon and baryon vertex configurations in . We show that these configurations capture the background fluxes
in a way that depends on the induced charges, and therefore, require additional
fundamental strings in order to cancel the worldvolume tadpoles. The study of
the dynamics reveals that the charges must lie inside some interval in order to
find well defined configurations, a situation familiar from the baryon vertex
in with charges. For the baryon vertex and the di-baryon the
number of fundamental strings must also lie inside an allowed interval. Our
configurations are sensitive to the flat -field recently suggested in the
literature. We make some comments on its possible role. We also discuss how
these configurations are modified in the presence of a non-zero Romans mass.Comment: 31 pages, 14 figures, discussion of charges improved, published
versio
Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition
The one-dimensional totally asymmetric simple exclusion process (TASEP) is
considered. We study the time evolution property of a tagged particle in TASEP
with the step-type initial condition. Calculated is the multi-time joint
distribution function of its position. Using the relation of the dynamics of
TASEP to the Schur process, we show that the function is represented as the
Fredholm determinant. We also study the scaling limit. The universality of the
largest eigenvalue in the random matrix theory is realized in the limit. When
the hopping rates of all particles are the same, it is found that the joint
distribution function converges to that of the Airy process after the time at
which the particle begins to move. On the other hand, when there are several
particles with small hopping rate in front of a tagged particle, the limiting
process changes at a certain time from the Airy process to the process of the
largest eigenvalue in the Hermitian multi-matrix model with external sources.Comment: 48 pages, 8 figure
Semi-simple group unification in the supersymmetric brane world
The conventional supersymmetric grand unified theories suffer from two
serious problems, the large mass splitting between doublet and triplet Higgs
multiplets, and the too long lifetime of the proton. A unification model based
on a semi-simple group SU(5)_{GUT} \times U(3)_H has been proposed to solve
both of the problems simultaneously. Although the proposed model is perfectly
consistent with observations, there are various mysteries. In this paper, we
show that such mysterious features in the original model are naturally
explained by embedding the model into the brane world in a higher dimensional
space-time. In particular, the relatively small gauge coupling constant of the
SU(5)_{GUT} at the unification energy scale is a consequence of relatively
large volume of extra dimensions. Here, we put the SU(5)_{GUT} gauge multiplet
in a 6-dimensional bulk and assume all fields in the U(3)_H sector to reside on
a 3-dimensional brane located in the bulk. On the other hand, all chiral
multiplets of quarks, leptons and Higgs are assumed to reside on a 3-brane at a
T^2/Z_4 orbifold fixed point. The quasi-N=2 supersymmetry in the hypercolor
U(3)_H sector is understood as a low-energy remnant of the N=4 supersymmetry in
a 6-dimensional space-time. We further extend the 6-dimensional model to a
10-dimensional theory. Possible frameworks of string theories are also
investigated to accommodate the present brane-world model. We find that the
type IIB string theory with D3-D7 brane structure is an interesting candidate.Comment: 45 pages, including 1 figure, minor correctio
Conductance Quantization and Magnetoresistance in Magnetic Point Contacts
We theoretically study the electron transport through a magnetic point
contact (PC) with special attention to the effect of an atomic scale domain
wall (DW). The spin precession of a conduction electron is forbidden in such an
atomic scale DW and the sequence of quantized conductances depends on the
relative orientation of magnetizations between left and right electrodes. The
magnetoresistance is strongly enhanced for the narrow PC and oscillates with
the conductance.Comment: 4 pages, 4 figures, revised version with new figure
Cartan-Weyl 3-algebras and the BLG Theory I: Classification of Cartan-Weyl 3-algebras
As Lie algebras of compact connected Lie groups, semisimple Lie algebras have
wide applications in the description of continuous symmetries of physical
systems. Mathematically, semisimple Lie algebra admits a Cartan-Weyl basis of
generators which consists of a Cartan subalgebra of mutually commuting
generators H_I and a number of step generators E^\alpha that are characterized
by a root space of non-degenerate one-forms \alpha. This simple decomposition
in terms of the root space allows for a complete classification of semisimple
Lie algebras. In this paper, we introduce the analogous concept of a
Cartan-Weyl Lie 3-algebra. We analyze their structure and obtain a complete
classification of them. Many known examples of metric Lie 3-algebras (e.g. the
Lorentzian 3-algebras) are special cases of the Cartan-Weyl 3-algebras. Due to
their elegant and simple structure, we speculate that Cartan-Weyl 3-algebras
may be useful for describing some kinds of generalized symmetries. As an
application, we consider their use in the Bagger-Lambert-Gustavsson (BLG)
theory.Comment: LaTeX. 34 pages.v2. deleted some distracting paragraphs in the
introduction to bring more out the main results of the paper. typos corrected
and references adde
Resonant electron transmission through a finite quantum spin chain
Electron transport in a finite one dimensional quantum spin chain (with
ferromagnetic exchange) is studied within an exchange Hamiltonian. Spin
transfer coefficients strongly depend on the sign of the exchange
constant. For a ferromagnetic coupling, they exhibit a novel resonant pattern,
reflecting the salient features of the combined electron-spin system. Spin-flip
processes are inelastic and feasible at finite voltage or at finite
temperature.Comment: 4 pages including 4 .eps figure
Relation between the 4d superconformal index and the S^3 partition function
A relation between the 4d superconformal index and the S^3 partition function
is studied with focus on the 4d and 3d actions used in localization. In the
case of vanishing Chern-Simons levels and round S^3 we explicitly show that the
3d action is obtained from the 4d action by dimensional reduction up to terms
which do not affect the exact results. By combining this fact and a recent
proposal concerning a squashing of S^3 and SU(2) Wilson line, we obtain a
formula which gives the partition function depending on the Weyl weight of
chiral multiplets, real mass parameters, FI parameters, and a squashing
parameter as a limit of the index of a parent 4d theory.Comment: 20 pages, LaTeX; v2: comments added; v3: minor corrections, version
published in JHE
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