Time Interval Operators

构建一个自由一维KFGM粒子在区间内的哈密顿量

Constructing the Hamiltonian for a free 1D KFGM particle in an interval

研究构建自由一维KFGM粒子在区间内的哈密顿量，通过确定边界条件和能量流密度限制，得出周期性和反周期性边界条件作为主要贡献。

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…

Probability Distributions for Quantum Stress Tensors Measured in a Finite Time Interval

A meaningful probability distribution for measurements of a quantum stress tensor operator can only be obtained if the operator is averaged in time or in spacetime. This averaging can be regarded as a description of the measurement process. Realistic measurements can be expected to begin and end at finite times, which means that they are described by functions with compact support, which we will also take to be smooth. Here we study the probability distributions for stress tensor operators averaged with such functions of time, in the vacuum state of a massless free field. Our primary aim is to…

Machine Learning Regression for Operator Dynamics

Determining the dynamics of the expectation values for operators acting on a quantum many-body (QMB) system is a challenging task. Matrix product states (MPS) have traditionally been the "go-to" models for these systems because calculating expectation values in this representation can be done with relative simplicity and high accuracy. However, such calculations can become computationally costly when extended to long times. Here, we present a solution for efficiently extending the computation of expectation values to long time intervals. We utilize a multi-layer perceptron (MLP) model as a too…

Local and non-local properties of the entanglement Hamiltonian for two disjoint intervals

We consider free-fermion chains in the ground state and the entanglement Hamiltonian for a subsystem consisting of two separated intervals. In this case, one has a peculiar long-range hopping between the intervals in addition to the well-known and dominant short-range hopping. We show how the continuum expressions can be recovered from the lattice results for general filling and arbitrary intervals. We also discuss the closely related case of a single interval located at a certain distance from the end of a semi-infinite chain and the continuum limit for this problem. Finally, we show that for…