Landau Fermi Liquid Picture of Spin Density Functional Theory: Strutinsky Approach to Quantum Dots

We analyze the ground state energy and spin of quantum dots obtained from spin density functional theory (SDFT) calculations. First, we introduce a Strutinsky-type approximation, in which quantum interference is treated as a correction to a smooth Thomas-Fermi description. For large irregular dots, we find that the second-order Strutinsky expressions have an accuracy of about 5 percent compared to the full SDFT and capture all the qualitative features. Second, we perform a random matrix theory/random plane wave analysis of the Strutinsky SDFT expressions. The results are statistically similar to the SDFT quantum dot statistics. Finally, we note that the second-order Strutinsky approximation provides, in essence, a Landau Fermi liquid picture of spin density functional theory. For instance, the leading term in the spin channel is simply the familiar exchange constant. A direct comparison between SDFT and the perturbation theory derived ``universal Hamiltonian'' is thus made possible.Comment: Submitted to Physical Review

Electron-Electron Interactions in Isolated and Realistic Quantum Dots: A Density Functional Theory Study

We use Kohn-Sham spin-density-functional theory to study the statistics of ground-state spin and the spacing between conductance peaks in the Coulomb blockade regime for both 2D isolated and realistic quantum dots. We make a systematic investigation of the effects of electron-electron interaction strength and electron number on both the peak spacing and spin distributions. A direct comparison between the distributions from isolated and realistic dots shows that, despite the difference in the boundary conditions and confining potential, the statistical properties are qualitatively the same. Strong even/odd pairing in the peak spacing distribution is observed only in the weak e-e interaction regime and vanishes for moderate interactions. The probability of high spin ground states increases for stronger e-e interaction and seems to saturate around $r_s \sim 4$. The saturated value is larger than previous theoretical predictions. Both spin and conductance peak spacing distributions show substantial variation as the electron number increases, not saturating until $N \sim 150$. To interpret our numerical results, we analyze the spin distribution in the even $N$ case using a simple two-level model.Comment: 10 pages, 12 figures, submitted to Phys. Rev.

Localization in an Inhomogeneous Quantum Wire

We study interaction-induced localization of electrons in an inhomogeneous quasi-one-dimensional system--a wire with two regions, one at low density and the other high. Quantum Monte Carlo techniques are used to treat the strong Coulomb interactions in the low density region, where localization of electrons occurs. The nature of the transition from high to low density depends on the density gradient--if it is steep, a barrier develops between the two regions, causing Coulomb blockade effects. Ferromagnetic spin polarization does not appear for any parameters studied. The picture emerging here is in good agreement with measurements of tunneling between two wires.Comment: 4 pages; 2 new figures, substantial revisions and clarification

Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs

Algorithms are presented for the tanh- and sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and PDEs in terms of Jacobi's elliptic functions. For systems with parameters, the algorithms determine the conditions on the parameters so that the differential equations admit polynomial solutions in tanh, sech, combinations thereof, Jacobi's sn or cn functions. Examples illustrate key steps of the algorithms. The new algorithms are implemented in Mathematica. The package DDESpecialSolutions.m can be used to automatically compute new special solutions of nonlinear PDEs. Use of the package, implementation issues, scope, limitations, and future extensions of the software are addressed. A survey is given of related algorithms and symbolic software to compute exact solutions of nonlinear differential equations.Comment: 39 pages. Software available from Willy Hereman's home page at http://www.mines.edu/fs_home/whereman

Non-destructive measurement of the transition probability in a Sr optical lattice clock

We present the experimental demonstration of non-destructive probing of the 1S0-3P0 clock transition probability in an optical lattice clock with 87Sr atoms. It is based on the phase shift induced by the atoms on a weak off-resonant laser beam. The method we propose is a differential measurement of this phase shift on two modulation sidebands with opposite detuning with respect to the 1S0-1P1 transition, allowing a detection limited by the photon shot noise. We have measured an atomic population of 10^4 atoms with a signal to noise ratio of 100 per cycle, while keeping more than 95% of the atoms in the optical lattice with a depth of 0.1 mK. The method proves simple and robust enough to be operated as part of the whole clock setup. This detection scheme enables us to reuse atoms for subsequent clock state interrogations, dramatically reducing the loading time and thereby improving the clock frequency stability.Comment: 4 pages, 5 figure

Interactions and Broken Time-Reversal Symmetry in Chaotic Quantum Dots

When treating interactions in quantum dots within a RPA-like approach, time-reversal symmetry plays an important role as higher-order terms -- the Cooper series -- need to be included when this symmetry is present. Here we consider model quantum dots in a magnetic field weak enough to leave the dynamics of the dot chaotic, but strong enough to break time-reversal symmetry. The ground state spin and addition energy for dots containing 120 to 200 electrons are found using local spin density functional theory, and we compare the corresponding distributions with those derived from an RPA-like treatment of the interactions. The agreement between the two approaches is very good, significantly better than for analogous calculations in the presence of time-reversal symmetry. This demonstrates that the discrepancies between the two approaches in the time-reversal symmetric case indeed originate from the Cooper channel, indicating that these higher-order terms might not be properly taken into account in the spin density functional calculations.Comment: 4 pages, 3 figure

Spectra of Quarkonia at Finite Temperature

Finite-temperature spectra of heavy quarkonia are calculated by combining potential model and thermofield dynamics formalisms. The mass spectra of the heavy quarkonia with various quark contents are calculated. It is found that binding mass of the quarkonium decreases as temperature increases.Comment: 12 pages, 1 figure. To appear Mod.Phys.Lett.