Impenetrable Barriers and Canonical Quantization

Canonical Quantization and Impenetrable Barriers

We address an apparent conflict between the traditional canonical quantization framework of quantum theory and the spatially restricted quantum dynamics, when the translation invariance of the otherwise free quantum system is broken by boundary conditions. By invoking an exemplary case of a particle in an infinite well, we analyze spectral problems for related, confined and global, observables. In particular, we show how one can make sense of various operators pertaining to trapped particles by not ignoring the rest of the real line (e.g., that space which is never occupied by the particle in …

克尔旋转黑洞周围运动粒子相空间中的不可穿透势垒

Impenetrable Barriers in the Phase Space of a Particle Moving Around a Kerr Rotating Black Hole

本研究从几何视角探究克尔旋转黑洞周围运动粒子的相空间，构建法向双曲不变流形及其稳定/不稳定不变流形，证实其分隔相空间且具微扰鲁棒性，并用拉格朗日描述符方法可视化多维不变集。

Quantization of edge currents along magnetic barriers and magnetic guides

We investigate the edge conductance of particles submitted to an Iwatsuka magnetic field, playing the role of a purely magnetic barrier. We also consider magnetic guides generated by generalized Iwatsuka potentials. In both cases we prove quantization of the edge conductance. Next, we consider magnetic perturbations of such magnetic barriers or guides, and prove stability of the quantized value of the edge conductance. Further, we establish a sum rule for edge conductances. Regularization within the context of disordered systems is discussed as well.

Canonical quantization on the half-line and in an interval based upon a new concept for the momentum in a space with boundaries

For a particle moving on a half-line or in an interval the operator $\hat p = - i \partial_x$ is not self-adjoint and thus does not qualify as the physical momentum. Consequently canonical quantization based on $\hat p$ fails. Based upon a new concept for a self-adjoint momentum operator $\hat p_R$, we show that canonical quantization can indeed be implemented on the half-line and on an interval. Both the Hamiltonian $\hat H$ and the momentum operator $\hat p_R$ are endowed with self-adjoint extension parameters that characterize the corresponding domains $D(\hat H)$ and $D(\hat p_R)$ in the H…

Affine Quantization and the Initial Cosmological Singularity

The Affine Coherent State Quantization procedure is applied to the case of a FRLW universe in the presence of a cosmological constant. The quantum corrections alter the dynamics of the system in the semiclassical regime, providing a potential barrier term which avoids all classical singularities, as already suggested in other models studied in the literature. Furthermore the quantum corrections are responsible for an accelerated cosmic expansion. This work intends to explore some of the implications of the recently proposed "Enhanced Quantization" procedure in a simplified model of cosmology.

所有扇区中的精确 WKB 方法 I：具有简并鞍点的势

Exact WKB in all sectors I: Potentials with degenerate saddles

本文提出一种对能量参数 $u$ 进行复化的新精确 WKB 方法，解决了多扇区局部谐和势的精确量子化问题，揭示了量子作用量中的 resurgence 结构与 $S$-对偶性。