101 research outputs found
N=4 super Yang-Mills matrix integrals for almost all simple gauge groups
In this paper the partition function of N=4 D=0 super Yang-Mills matrix
theory with arbitrary simple gauge group is discussed. We explicitly computed
its value for all classical groups of rank up to 11 and for the exceptional
groups G_2, F_4 and E_6. In the case of classical groups of arbitrary rank we
conjecture general formulas for the B_r, C_r and D_r series in addition to the
known result for the A_r series. Also, the relevant boundary term contributing
to the Witten index of the corresponding supersymmetric quantum mechanics has
been explicitly computed as a simple function of rank for the orthogonal and
symplectic groups SO(2N+1), Sp(2N), SO(2N).Comment: Latex2e, 21pp; v2: minor corrections, references adde
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
Polyakov Lines in Yang-Mills Matrix Models
We study the Polyakov line in Yang-Mills matrix models, which include the
IKKT model of IIB string theory. For the gauge group SU(2) we give the exact
formulae in the form of integral representations which are convenient for
finding the asymptotic behaviour. For the SU(N) bosonic models we prove upper
bounds which decay as a power law at large momentum p. We argue that these
capture the full asymptotic behaviour. We also indicate how to extend the
results to some correlation functions of Polyakov lines.Comment: 19 pages, v2 typos corrected, v3 ref adde
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
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
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
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