Yang-Mills Integrals

Two results are presented for reduced Yang-Mills integrals with different symmetry groups and dimensions: the first is a compact integral representation in terms of the relevant variables of the integral, the second is a method to analytically evaluate the integrals in cases of low order. This is exhibited by evaluating a Yang-Mills integral over real symmetric matrices of order 3.Comment: LaTeX, 10 pages, references added and minimal change

Many-body excitations in tunneling current spectra of a few-electron quantum dot

Inherent asymmetry in the tunneling barriers of few-electron quantum dots induces intrinsically different tunneling currents for forward and reverse source-drain biases in the non-linear transport regime. Here we show that in addition to spin selection rules, overlap matrix elements between many-body states are crucial for the correct description of tunneling transmission through quantum dots at large magnetic fields. Signatures of excited (N-1)-electron states in the transport process through the N-electron system are clearly identified in the measured transconductances. Our analysis clearly confirms the validity of single-electron quantum transport theory in quantum dots.Comment: 5 pages, 2 figure

A new approach to the complex-action problem and its application to a nonperturbative study of superstring theory

Monte Carlo simulations of a system whose action has an imaginary part are considered to be extremely difficult. We propose a new approach to this `complex-action problem', which utilizes a factorization property of distribution functions. The basic idea is quite general, and it removes the so-called overlap problem completely. Here we apply the method to a nonperturbative study of superstring theory using its matrix formulation. In this particular example, the distribution function turns out to be positive definite, which allows us to reduce the problem even further. Our numerical results suggest an intuitive explanation for the dynamical generation of 4d space-time.Comment: 7 pages, 4 figures, PRD version somewhat extended from the original versio

Multi-matrix models and emergent geometry

Encouraged by the AdS/CFT correspondence, we study emergent local geometry in large N multi-matrix models from the perspective of a strong coupling expansion. By considering various solvable interacting models we show how the emergence or non-emergence of local geometry at strong coupling is captured by observables that effectively measure the mass of off-diagonal excitations about a semiclassical eigenvalue background. We find emergent geometry at strong coupling in models where a mass term regulates an infrared divergence. We also show that our notion of emergent geometry can be usefully applied to fuzzy spheres. Although most of our results are analytic, we have found numerical input valuable in guiding and checking our results.Comment: 1+34 pages, 4 figures. References adde

Dynamical aspects of the fuzzy CP2^{2} in the large NN reduced model with a cubic term

``Fuzzy CP^2'', which is a four-dimensional fuzzy manifold extension of the well-known fuzzy analogous to the fuzzy 2-sphere (S^2), appears as a classical solution in the dimensionally reduced 8d Yang-Mills model with a cubic term involving the structure constant of the SU(3) Lie algebra. Although the fuzzy S^2, which is also a classical solution of the same model, has actually smaller free energy than the fuzzy CP^2, Monte Carlo simulation shows that the fuzzy CP^2 is stable even nonperturbatively due to the suppression of tunneling effects at large N as far as the coefficient of the cubic term ($\alpha$) is sufficiently large. As \alpha is decreased, both the fuzzy CP$^2$ and the fuzzy S^2 collapse to a solid ball and the system is essentially described by the pure Yang-Mills model (\alpha = 0). The corresponding transitions are of first order and the critical points can be understood analytically. The gauge group generated dynamically above the critical point turns out to be of rank one for both CP^2 and S^2 cases. Above the critical point, we also perform perturbative calculations for various quantities to all orders, taking advantage of the one-loop saturation of the effective action in the large-N limit. By extrapolating our Monte Carlo results to N=\infty, we find excellent agreement with the all order results.Comment: 27 pages, 7 figures, (v2) References added (v3) all order analyses added, some typos correcte

Direct Coulomb and Exchange Interaction in Artificial Atoms

We determine the contributions from the direct Coulomb and exchange interactions to the total interaction in semiconductor artificial atoms. We tune the relative strengths of the two interactions and measure them as a function of the number of confined electrons. We find that electrons tend to have parallel spins when they occupy nearly degenerate single-particle states. We use a magnetic field to adjust the single-particle state degeneracy, and find that the spin-configurations in an arbitrary magnetic field are well explained in terms of two-electron singlet and triplet states.Comment: 4 pages, 5 figure

Exotic trees

We discuss the scaling properties of free branched polymers. The scaling behaviour of the model is classified by the Hausdorff dimensions for the internal geometry: d_L and d_H, and for the external one: D_L and D_H. The dimensions d_H and D_H characterize the behaviour for long distances while d_L and D_L for short distances. We show that the internal Hausdorff dimension is d_L=2 for generic and scale-free trees, contrary to d_H which is known be equal two for generic trees and to vary between two and infinity for scale-free trees. We show that the external Hausdorff dimension D_H is directly related to the internal one as D_H = \alpha d_H, where \alpha is the stability index of the embedding weights for the nearest-vertex interactions. The index is \alpha=2 for weights from the gaussian domain of attraction and 0<\alpha <2 for those from the L\'evy domain of attraction. If the dimension D of the target space is larger than D_H one finds D_L=D_H, or otherwise D_L=D. The latter result means that the fractal structure cannot develop in a target space which has too low dimension.Comment: 33 pages, 6 eps figure

Localization and entanglement of two interacting electrons in a quantum-dot molecule

The localization of two interacting electrons in a coupled-quantum-dots semiconductor structure is demonstrated through numerical calculations of the time evolution of the two-electron wave function including the Coulomb interaction between the electrons. The transition from the ground state to a localized state is induced by an external, time-dependent, uniform electric field. It is found that while an appropriate constant field can localize both electrons in one of the wells, oscillatory fields can induce roughly equal probabilities for both electrons to be localized in either well, generating an interesting type of localized and entangled state. We also show that shifting the field suddenly to an appropriate constant value can maintain in time both types of localization.Comment: 4 pages, 4 figure

Matrix Models, Emergent Gravity, and Gauge Theory

Matrix models of Yang-Mills type induce an effective gravity theory on 4-dimensional branes, which are considered as models for dynamical space-time. We review recent progress in the understanding of this emergent gravity. The metric is not fundamental but arises effectively in the semi-classical limit, along with nonabelian gauge fields. This leads to a mechanism for protecting certain geometries from corrections due to the vacuum energy.Comment: 8 pages. Based on invited talks given at the Conferences "Quantum Spacetime and Noncommutative Geometry", Rome, 2008 and at "Workshop on quantum gravity and nocommutative geometry", Lisbon, 2008 and at "Emergent Gravity", Boston, 2008 and at DICE2008, Italy, 2008 and at "QG2 2008 Quantum Geometry and Quantum Gravity", Nottingham, 200