Temperature Dependence of Gluon and Quark Condensates as from Linear Confinement

The gluon and quark condensates and their temperature dependence are investigated within QCD premises. The input for the former is a gauge invariant $gg$ kernel made up of the direct (D), exchange (X) and contact(C) QCD interactions in the lowest order, but with the perturbative propagator $k^{-2}$ replaced by a `non-perturbative $k^{-4}$ form obtained via two differentiations: $\mu^2 \partial_m^2 (m^2+k^2)^{-1}$, ($\mu$ a scale parameter), and then setting $m=0$, to simulate linear confinement. Similarly for the input $q{\bar q}$ kernel the gluon propagator is replaced by the above $k^{-4}$ form. With these `linear' simulations, the respective condensates are obtained by `looping' up the gluon and quark lines in the standard manner. Using Dimensional regularization (DR), the necessary integrals yield the condensates plus temperature corrections, with a common scale parameter $\mu$ for both. For gluons the exact result is $$= {36\mu^4}\pi^{-3}\alpha_s(\mu^2)[2-\gamma - 4\pi^2 T^2/(3\mu^2)]$$. Evaluation of the quark condensate is preceded by an approximate solution of the SDE for the mass function $m(p)$, giving a recursive formula, with convergence achieved at the third iteration. Setting the scale parameter $\mu$ equal to the universal Regge slope $1 GeV^2$, the gluon and quark condensates at T=0 are found to be $0.586 Gev^4$ and $(240-260 MeV)^3$ respectively, in fair accord with QCD sum rule values. Next, the temperature corrections (of order $-T^2$ for both condensates) is determined via finite-temperature field theory a la Matsubara. Keywords: Gluon Condensate, mass tensor, gauge invariance, linear confinement, finite-temperature, contour-closing. PACS: 11.15.Tk ; 12.38.Lg ; 13.20.CzComment: 13 pages (LaTeX) including 2 figure

Edge and bulk merons in double quantum dots with spontaneous interlayer phase coherence

We have investigated nucleation of merons in double quantum dots when a lateral distortion with a reflection symmetry is present in the confinement potential. We find that merons can nucleate both inside and at the edge of the dots. In addition to these merons, our results show that electron density modulations can be also present inside the dots. An edge meron appears to have approximately a half integer winding number.Comment: 5 pages, 4 figures, Proceedings of 17th International Conference on High Magnetic Fields in Semiconductor Physic

Hole maximum density droplets of an antidot in strong magnetic fields

We investigate a quantum antidot in the integer quantum Hall regime (the filling factor is two) by using a Hartree-Fock approach and by transforming the electron antidot into a system which confines holes via an electron-hole transformation. We find that its ground state is the maximum density droplet of holes in certain parameter ranges. The competition between electron-electron interactions and the confinement potential governs the properties of the hole droplet such as its spin configuration. The ground-state transitions between the droplets with different spin configurations occur as magnetic field varies. For a bell-shape antidot containing about 300 holes, the features of the transitions are in good agreement with the predictions of a recently proposed capacitive interaction model for antidots as well as recent experimental observations. We show this agreement by obtaining the parameters of the capacitive interaction model from the Hartree-Fock results. An inverse parabolic antidot is also studied. Its ground-state transitions, however, display different magnetic-field dependence from that of a bell-shape antidot. Our study demonstrates that the shape of antidot potential affects its physical properties significantly.Comment: 12 pages, 11 figure

Single electron control in n-type semiconductor quantum dots using non-Abelian holonomies generated by spin orbit coupling

We propose that n-type semiconductor quantum dots with the Rashba and Dresselhaus spin orbit interactions may be used for single electron manipulation through adiabatic transformations between degenerate states. All the energy levels are discrete in quantum dots and possess a double degeneracy due to time reversal symmetryin the presence of the Rashba and/or Dresselhaus spin orbit coupling terms. We find that the presence of double degeneracy does not necessarily give rise to a finite non-Abelian (matrix) Berry phase. We show that a distorted two-dimensional harmonic potential may give rise to non-Abelian Berry phases. The presence of the non-Abelian Berry phase may be tested experimentally by measuring the optical dipole transitions.Comment: accepted in Phys. Rev.

Unified Analysis of Cosmological Perturbations in Generalized Gravity

In a class of generalized Einstein's gravity theories we derive the equations and general asymptotic solutions describing the evolution of the perturbed universe in unified forms. Our gravity theory considers general couplings between the scalar field and the scalar curvature in the Lagrangian, thus includes broad classes of generalized gravity theories resulting from recent attempts for the unification. We analyze both the scalar-type mode and the gravitational wave in analogous ways. For both modes the large scale evolutions are characterized by the same conserved quantities which are valid in the Einstein's gravity. This unified and simple treatment is possible due to our proper choice of the gauges, or equivalently gauge invariant combinations.Comment: 4 pages, revtex, no figure

The Fate of the Accelerating Universe

The presently accelerating universe may keep accelerating forever, eventually run into the event horizon problem, and thus be in conflict with the superstring idea. In the other way around, the current accelerating phase as well as the fate of the universe may be swayed by a negative cosmological constant, which dictates a big crunch. Based on the current observational data, in this paper we investigate how large the magnitude of a negative cosmological constant is allowed to be. In addition, for distinguishing the sign of the cosmological constant via observations, we point out that a measure of the evolution of the dark energy equation of state may be a good discriminator. Hopefully future observations will provide much more detailed information about dark energy and thereby indicates the sign of the cosmological constant as well as the fate of the presently accelerating universe.Comment: 16 pages, 5 figures, LaTe

Optimal Quantum State Estimation with Use of the No-Signaling Principle

A simple derivation of the optimal state estimation of a quantum bit was obtained by using the no-signaling principle. In particular, the no-signaling principle determines a unique form of the guessing probability independently of figures of merit, such as the fidelity or information gain. This proves that the optimal estimation for a quantum bit can be achieved by the same measurement for almost all figures of merit.Comment: 3 pages, 1 figur