On the Quantum Geometry of String Theory

The IKKT or IIB matrix model has been proposed as a non-perturbative definition of type IIB superstring theories. It has the attractive feature that space--time appears dynamically. It is possible that lower dimensional universes dominate the theory, therefore providing a dynamical solution to the reduction of space--time dimensionality. We summarize recent works that show the central role of the phase of the fermion determinant in the possible realization of such a scenario.Comment: 3 pages, 2 figures, Lattice2001(surfaces

Gate Adjustable Coherent Three and Four Level Mixing in a Vertical Quantum Dot Molecule

We study level mixing in the single particle energy spectrum of one of the constituent quantum dots in a vertical double quantum dot by performing magneto-resonant-tunneling spectroscopy. The device used in this study differs from previous vertical double quantum dot devices in that the single side gate is now split into four separate gates. Because of the presence of natural perturbations caused by anharmonicity and anistrophy, applying different combinations of voltages to these gates allows us to alter the effective potential landscape of the two dots and hence influence the level mixing. We present here preliminary results from one three level crossing and one four level crossings high up in the energy spectrum of one of the probed quantum dots, and demonstrate that we are able to change significantly the energy dispersions with magnetic field in the vicinity of the crossing regions.Comment: 5 pages, 4 figures. MSS-14 conference proceedings submitted to Physica

Two level anti-crossings high up in the single-particle energy spectrum of a quantum dot

We study the evolution with magnetic field of the single-particle energy levels high up in the energy spectrum of one dot as probed by the ground state of the adjacent dot in a weakly coupled vertical quantum dot molecule. We find that the observed spectrum is generally well accounted for by the calculated spectrum for a two-dimensional elliptical parabolic confining potential, except in several regions where two or more single-particle levels approach each other. We focus on two two-level crossing regions which show unexpected anti-crossing behavior and contrasting current dependences. Within a simple coherent level mixing picture, we can model the current carried through the coupled states of the probed dot provided the intrinsic variation with magnetic field of the current through the states (as if they were uncoupled) is accounted for by an appropriate interpolation scheme.Comment: 4 pages, 4 figures, accepted for publication in Physica E in MSS 13 conference proceeding

Bosonization approach to the edge reconstruction of two dimentional electron systems in a quantum dot

We consider the edge reconstruction of electrons in a two dimensional harmonic trap under a strong magnetic field. In this system the edge reconstruction occurs as a result of competition between electron-electron interaction and confining potential. To describe it, we develop a bosonization scheme for two dimensional electron systems. With this method we obtain the excitation spectrum and demonstrate that the edge reconstruction occurs when the value of the magnetic field reaches a critical value. We also show that the edge reconstruction depends on the number of electrons. Additionally, we calculate the third order terms of bosons in Hamiltonian and examine the effect of those terms with a perturbation theory.Comment: 5pages, 6figure

Ellipsoidal deformation of vertical quantum dots

Addition energy spectra at 0 T of circular and ellipsoidally deformed few-electron vertical quantum dots are measured and compared to results of model calculations within spin-density functional theory. Because of the rotational symmetry of the lateral harmonic confining potential, circular dots show a pronounced shell structure. With the lifting of the single- particle level degeneracies, even a small deformation is found to radically alter the shell structure leading to significant modifications in the addition energy spectra. Breaking the circular symmetry with deformation also induces changes in the total spin. This "piezo-magnetic" behavior of quantum dots is discussed, and the addition energies for a set of realistic deformation parameters are provided. For the case of the four-electron ground state at 0 T, a spin-triplet to spin-singlet transition is predicted, i.e. Hund's first rule no longer applies. Application of a magnetic field parallel to the current confirms that this is the case, and also suggests that the anisotropy of an elliptical dot, in practice, may be higher than that suggested by the geometry of the device mesa in which the dot is located.Comment: 11 pages, 5 figures (original figures available on request

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

Transport properties of two laterally coupled vertical quantum dots in series with tunable inter-dot coupling

We describe the electronic properties of a double dot for which the lateral coupling between the two vertical dots can be controlled in-situ with a center gate voltage (Vc) and the current flows through the two dots in series. When Vc is large and positive, the two dots merge. As Vc is made less positive, two dots are formed whose coupling is reduced. We measure charging diagrams for positive and negative source-drain voltages in the weak coupling regime and observe current rectification due to the Pauli spin blockade when the hyperfine interaction between the electrons and the nuclei is suppressed.Comment: 16 pages, 3 figures, accepted for Applied Physics Letter

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

Quantum control of two interacting electrons in a coupled quantum dot

Quantum-state engineering, i.e., active manipulation over the coherent dynamics of suitable quantum-mechanical systems, has become a fascinating prospect of modern physics. Here we discuss the dynamics of two interacting electrons in a coupled quantum dot driven by external electric field. We show the two quantum dots can be used to prepare maximally entangled Bell state by varying the strength and duration of an oscillatory electric field. Different from suggestion given by Loss \QTR{it}{et al}.[Phys. Rev. A, \QTR{bf}{57} (1998) 120], the present entanglement involves the spatial degree of freedom for the two electrons. We also find that the coherent tunneling suppression discussed by Grossmann \QTR{it}{et al}.[Phys. Rev. Lett., \QTR{bf}{67} (1991) 516] persists in the two-particle case, i.e., two electrons initially localized in one dot can remain dynamically localized, although the strong Coulomb repulsion prevents them behaving so. Surprisingly, the interaction enhances the degree of localization to a larger extent compared to non-interacting case. We can call this phenomenon Coulomb-enhanced dynamical localization.Comment: 9 pages, 10 figure