Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOptimization of the lowest eigenvalue of a soft quantum ring
58
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We consider the self-adjoint two-dimensional Schrodinger operator $H_mu$ associated with the differential expression $-Delta -mu$ describing a particle exposed to an attractive interaction given by a measure $mu$ supported in a closed curvilinear strip and having fixed transversal one-dimensional profile measure $mu_bot$. This operator has nonempty negative discrete spectrum and we obtain two optimization results for its lowest eigenvalue. For the first one, we fix $mu_bot$ and maximize the lowest eigenvalue with respect to shape of the curvilinear strip the optimizer in the first problem turns out to be the annulus. We also generalize this result to the situation which involves an additional perturbation of $H_mu$ in the form of a positive multiple of the characteristic function of the domain surrounded by the curvilinear strip. Secondly, we fix the shape of the curvilinear strip and minimize the lowest eigenvalue with respect to variation of $mu_bot$, under the constraint that the total profile measure $alpha >0$ is fixed. The optimizer in this problem is $mu_bot$ given by the product of $alpha$ and the Dirac $delta$-function supported at an optimal position.
rate research
Read More
We consider the self-adjoint Schrodinger operator in $L^2(mathbb{R}^d)$, $dgeq 2$, with a $delta$-potential supported on a hyperplane $Sigmasubseteqmathbb{R}^d$ of strength $alpha=alpha_0+alpha_1$, where $alpha_0inmathbb{R}$ is a constant and $alpha_1in L^p(Sigma)$ is a nonnegative function. As the main result, we prove that the lowest spectral point of this operator is not smaller than that of the same operator with potential strength $alpha_0+alpha_1^*$, where $alpha_1^*$ is the symmetric decreasing rearrangement of $alpha_1$. The proof relies on the Birman-Schwinger principle and the reduction to an analogue of the P{o}lya-SzegH{o} inequality for the relativistic kinetic energy in $mathbb{R}^{d-1}$.
We prove various estimates for the first eigenvalue of the magnetic Dirichlet Laplacian on a bounded domain in two dimensions. When the magnetic field is constant, we give lower and upper bounds in terms of geometric quantities of the domain. We furthermore prove a lower bound for the first magnetic Neumann eigenvalue in the case of constant field.
In this work, we construct an alternative formulation to the traditional Algebraic Bethe ansatz for quantum integrable models derived from a generalised rational Gaudin algebra realised in terms of a collection of spins 1/2 coupled to a single bosonic mode. The ensemble of resulting models which we call Dicke-Jaynes-Cummings- Gaudin models are particularly relevant for the description of light-matter interaction in the context of quantum optics. Having two distinct ways to write any eigenstate of these models we then combine them in order to write overlaps and form factors of local operators in terms of partition functions with domain wall boundary conditions. We also demonstrate that they can all be written in terms of determinants of matrices whose entries only depend on the eigenvalues of the conserved charges. Since these eigenvalues obey a much simpler set of quadratic Bethe equations, the resulting expressions could then offer important simplifications for the numerical treatment of these models.
In this paper we study the quantum dynamics of an electron/hole in a two-dimensional quantum ring within a spherical space. For this geometry, we consider a harmonic confining potential. Suggesting that the quantum ring is affected by the presence of an Aharonov-Bohm flux and an uniform magnetic field, we solve the Schrodinger equation for this problem and obtain exactly the eigenvalues of energy and corresponding eigenfunctions for this nanometric quantum system. Afterwards, we calculate the magnetization and persistent current are calculated, and discuss influence of curvature of space on these values.
Extensive electrical characterization of ring oscillators (ROs) made in high-$kappa$ metal gate 28nm Fully-Depleted Silicon-on- Insulator (FD-SOI) technology is presented for a set of temperatures between 296 and 4.3K. First, delay per stage ($tau_P$), static current ($I_{STAT}$), and dynamic current ($I_{DYN}$) are analyzed for the case of the increase of threshold voltage ($V_{TH}$) observed at low temperature. Then, the same analysis is performed by compensating $V_{TH}$ to a constant, temperature independent value through forward body-biasing (FBB). Energy efficiency optimization is proposed for different supply voltages ($V_{DD}$) in order to find an optimal operating point combining both high RO frequencies and low power dissipation. We show that the Energy-Delay product ($EDP$) can be significantly reduced at low temperature by applying a forward body bias voltage ($V_{FBB}$). We demonstrate that outstanding performance of RO in terms of speed ($tau_P$=37ps) and static power (7nA/stage) can be achieved at 4.3K with $V_{DD}$ reduced down to 0.325V.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
