Correlation energy of anisotropic quantum dots

Abstract

We study the $D$-dimensional high-density correlation energy $\Ec$ of the singlet ground state of two electrons confined by a harmonic potential with Coulombic repulsion. We allow the harmonic potential to be anisotropic, and examine the behavior of $\Ec$ as a function of the anisotropy $\alpha^{-1}$. In particular, we are interested in the limit where the anisotropy goes to infinity ($\alpha\to0$) and the electrons are restricted to a lower-dimensional space. We show that tuning the value of $\alpha$ from 0 to 1 allows a smooth dimensional interpolation and we demonstrate that the usual model, in which a quantum dot is treated as a two-dimensional system, is inappropriate. Finally, we provide a simple function which reproduces the behavior of $\Ec$ over the entire range of $\alpha$.Comment: 5 pages, 2 figures, 1 table, submitted to Phys. Rev.

Observation of three-mode parametric instability

“…Once again, results are in good agreement with Eq. (3), and the measured maximal value for the gain in this case is R = 0.41 for mode (1,7), for the same optical power as in the cooling experiment. Even with an incident power up to 5 mW, the three-mode parametric instability regime (corresponding to R ≥ 1) has eluded observation.…”

“…Similar measurements have been carried out for the neighboring mechanical modes (3,7) and (5,5) of the moving mirror. These results are also presented in Fig.…”

“…The high mechanical and optical mode density of these systems makes it likely that such interactions occur accidentally. Subsequently detailed modeling [3][4][5] verified the predictions and experimental tests on suspended optical cavities [6,7] demonstrated three-mode interactions below the instability threshold.…”

Fermionic stochastic Schrödinger equation and master equation: An open-system model

“…Several attempts to derive the evolution equation of open quantum systems beyond the Markov approximation have been proposed [2,[4][5][6][7][8]. Notably, the non-Markovian quantum state diffusion (QSD) approach developed by Strunz and his coworkers has showed momentous potential of solving large systems (multi-qubit or multi-cavity) [9][10][11][12][13][14][15]. Moreover, as a computing tool, many numerical advantages of the QSD * Email:xzhao1@stevens.edu † Email:wshi1@stevens.edu ‡ Email:Ting.Yu@stevens.edu approach permit its use in several domains such as highprecision measurement [16], entanglement dynamics [17] and coherence dynamics of the large molecules in biophysics [18] etc.…”

D-dimensional energies for scandium monoiodide

“…With the help of the D-scaling approach, Ferrón et al [13] investigated stability of two particles in a dipole field. Zhao et al [14] studied the electron correlation of anisotropic quantum dots in the high-density limit in terms of the D-scaling method. Chen et al [15] investigated mathematical analysis of the D-scaling method for solving the Schrödinger equation with the Coulomb potentials.…”