Dirac oscillator in dynamical noncommutative space

In this paper, we address the energy eigenvalues of two-dimensional Dirac oscillator perturbed by a dynamical noncommutative space. We derived the relativistic Hamiltonian of Dirac oscillator in the dynamical noncommutative space, in which the space-space Heisenberg-like commutation relations and noncommutative parameter are position-dependent. Then, we used this Hamiltonian to calculate the first-order correction to the eigenvalues and eigenvectors, based on the language of creation and annihilation operators and using the perturbation theory. It is shown that the energy shift depends on the dynamical noncommutative parameter τ . Knowing that, with a set of two-dimensional Bopp-shift transformation, we mapped the noncommutative problem to the standard commutative one.

Superconformal boundaries in 4 − ϵ dimensions

Boundaries in three-dimensional $$ \mathcal{N} $$ N = 2 superconformal theories may preserve one half of the original bulk supersymmetry. There are two possibilities which are characterized by the chirality of the leftover supercharges. Depending on the choice, the remaining 2d boundary algebra exhibits $$ \mathcal{N} $$ N = (0, 2) or $$ \mathcal{N} $$ N = (1) supersymmetry. In this work we focus on correlation functions of chiral fields for both types of supersymmetric boundaries. We study a host of correlators using superspace techniques and calculate superconformal blocks for two- and three-point functions. For $$ \mathcal{N} $$ N = (1) supersymmetry, some of our results can be analytically continued in the spacetime dimension while keeping the codimension fixed. This opens the door for a bootstrap analysis of the ϵ-expansion in supersymmetric BCFTs. Armed with our analytically-continued superblocks, we prove that in the free theory limit two-point functions of chiral (and antichiral) fields are unique. The first order correction, which already describes interactions, is universal up to two free parameters. As a check of our analysis, we study the Wess-Zumino model with a super-symmetric boundary using Feynman diagrams, and find perfect agreement between the perturbative and bootstrap results.

Dirac Oscillator in Dynamical Noncommutative Space

In this paper, we address the energy eigenvalues of two-dimensional Dirac oscillator perturbed by dynamical noncommutative space. We derived the relativistic Hamiltonian of Dirac oscillator in dynamical noncommutative space ( τ -space), in which the space-space Heisenberg–like commutation relations and noncommutative parameter are position-dependent. Then used this Hamiltonian to calculate the first-order correction to the eigenvalues and eigenvectors, based on the second quantization and using the perturbation theory. It is shown that the energy shift depends on the dynamical noncommutative parameter τ . Knowing that with a set of two-dimensional Bopp-shift transformation, we mapped the noncommutative problem to the standard commutative one.

Correlated Log-Normal Random Variables under a Multiscale Volatility Model

The study focuses on extending the fast mean-reversion volatility, which was developed by the author in a previous work, to the multiscale volatility model so that it can express a well-separated time scale. The leading-order term and first-order correction terms are analytically computed using the perturbation theory based on the Lie–Trotter operator splitting method. Finally, the study is concluded by deriving the numerical results that further validate the effectiveness of the model.

Quantum Mechanical Analysis on Modeling of Surface Potential and Drain Current for Nanowire JLFET

This paper presents an analytical model for ultra scaled symmetric double gate (SDG) nanowire junctionless field effect transistor (JLFET), which includes charge quantization in all the regions of operation. This model is based on a first-order correction for the confined energies obtained by solving the Schrodinger’s equation. The model is able to predict the quantum mechanical effects (QME) on the surface potential, drain current and transconductance for a highly doped and extremely thin silicon layer of thickness down to 4nm. The results obtained are validated by comparing with GENIUS 3D TCAD quantum simulations.

Homogenisation with error estimates of attractors for damped semi-linear anisotropic wave equations

Homogenisation of global 𝓐ε and exponential 𝓜ε attractors for the damped semi-linear anisotropic wave equation $\begin{array}{} \displaystyle \partial_t ^2u^\varepsilon + y \partial_t u^\varepsilon-\operatorname{div} \left(a\left( \tfrac{x}{\varepsilon} \right)\nabla u^\varepsilon \right)+f(u^\varepsilon)=g, \end{array}$ on a bounded domain Ω ⊂ ℝ3, is performed. Order-sharp estimates between trajectories uε(t) and their homogenised trajectories u0(t) are established. These estimates are given in terms of the operator-norm difference between resolvents of the elliptic operator $\begin{array}{} \displaystyle \operatorname{div}\left(a\left( \tfrac{x}{\varepsilon} \right)\nabla \right) \end{array}$ and its homogenised limit div (ah∇). Consequently, norm-resolvent estimates on the Hausdorff distance between the anisotropic attractors and their homogenised counter-parts 𝓐0 and 𝓜0 are established. These results imply error estimates of the form distX(𝓐ε, 𝓐0) ≤ Cεϰ and $\begin{array}{} \displaystyle \operatorname{dist}^s_X(\mathcal M^\varepsilon, \mathcal M^0) \le C \varepsilon^\varkappa \end{array}$ in the spaces X = L2(Ω) × H–1(Ω) and X = (Cβ(Ω))2. In the natural energy space 𝓔 := $\begin{array}{} \displaystyle H^1_0 \end{array}$(Ω) × L2(Ω), error estimates dist𝓔(𝓐ε, Tε 𝓐0) ≤ $\begin{array}{} \displaystyle C \sqrt{\varepsilon}^\varkappa \end{array}$ and $\begin{array}{} \displaystyle \operatorname{dist}^s_\mathcal{E}(\mathcal M^\varepsilon, \text{T}_\varepsilon \mathcal M^0) \le C \sqrt{\varepsilon}^\varkappa \end{array}$ are established where Tε is first-order correction for the homogenised attractors suggested by asymptotic expansions. Our results are applied to Dirchlet, Neumann and periodic boundary conditions.