有限方势阱中粒子量子动力学的超回复

量子引力在无限深方势阱中诱导的纠缠

Entanglement induced by quantum gravity in an infinite square well

本研究探讨无限深方势阱中两有质量粒子在引力诱导下的纠缠动力学，通过假设粒子初始处于基态并绝热相向运动，发现合适参数下纠缠迅速产生，且显著降低粒子质量与实验阈值。

方井系统加速器模式

Accelerator modes of square well system

研究了一维无限深方势阱中粒子在时间周期脉冲场作用下的加速模。这样一个粒子的动力学可以用一个被踢转子的概括来描述。在比较踢转子，这种推广被证明有一个更大的参数空间的模式的存在。利用这种自由，我们提供的证据表明，加速器模式辅助异常运输时，低阶共振暴露在混沌的边界大大增强。我们还提出了在量子域中的增强传输的签名。

无限深方势阱中粒子广义相干态的梯形算符和非经典性

On the ladder operators and nonclassicality of generalized coherent state associated with a particle in an infinite square well

本文利用因式分解方法求出了一维无限深势阱中量子粒子的本征值和本征函数。从所提到的方法的输出结果，使我们能够探索一个适当的新的一对上升和下降的运营商所考虑的物理系统。从对称性的考虑出发，明确地建立了所得到的梯形算子与$su(1,1)$李代数之间的联系.其次，在构造了与所考虑的系统相关的相干态的Barut-Girardello和Gilmore-Perelomov表示之后，详细说明了它们的一些重要性质，如恒等式的分解，包括一些非经典特征.最后，提出了一种利用广义Janes-Cummings模型制备Gilmore-Perelomov型相干态的理论方案。

Quantum mechanical virial-like theorem for confined quantum systems

Confinement of atoms inside impenetrable (hard) and penetrable (soft) cavities has been studied for nearly eight decades. However, a unified virial theorem for such systems has not yet been found. Here we provide a general virial-like equation in terms of mean square and expectation values of potential and kinetic energy operators. It appears to be applicable in both free and confined situations. Apart from that, we have derived an equation using the time-independent Schrödinger equation, which can be treated as a sufficient condition for a given stationary quantum state. A change of boundary …

硬壁盒中玻色气体中的量子暗孤子

Quantum dark solitons in Bose gas confined in a hard wall box

一维空间中具有排斥接触相互作用的玻色气体的薛定谔方程，在周期性边界条件下，可以借助于Bethe方法解析求解。结果表明，在这样的系统中，存在直接对应于平均场方程暗孤子解的多体本征态。如果从周期边界条件转换到无限方势阱，系统仍然是可积的。相应的本征态由M.高汀我们分析了Gaudin解的弱相互作用极限，确定了与单个和多个暗孤子严格相关的本征态的参数化。对粒子位置探测的数值模拟揭示了弱相互作用下的暗孤子和强相互作用下暗孤子的量子性质。

受限量子气体的伯努利公式和泊松方程：运动活塞的影响

Bernoulli's formula and Poisson's equations for a confined quantum gas: Effects due to a moving piston

本文研究了当腔壁在时间原点处突然开始运动时，腔中的理想量子气体在活塞以有限小速度运动时的非平衡态方程。在绝热过程的限制下，阐明了量子非绝热（QNA）对Poisson绝热方程和连接压力和内能的Bernoulli公式的贡献。我们对我们在前一篇论文中发现的非绝热（时间反演对称）力算子进行了统计平均。Nakamura等人，Phys.Rev.EVol.83，041133，（2011））在低温量子力学和高温准经典机制中。QNA的贡献，这是成比例的活塞的速度的平方和空腔的纵向尺寸的倒数，具有依赖于温度，气体密度和空腔的维数的系数。研究了单向膨胀的三维矩形平行六面体腔及其一维腔。它在一个现实的纳米尺度热机的相关性进行了讨论。

Solving two-dimensional quantum eigenvalue problems using physics-informed machine learning

A particle confined to an impassable box is a paradigmatic and exactly solvable one-dimensional quantum system modeled by an infinite square well potential. Here we explore some of its infinitely many generalizations to two dimensions, including particles confined to rectangle, elliptic, triangle, and cardioid-shaped boxes, using physics-informed neural networks. In particular, we generalize an unsupervised learning algorithm to find the particles' eigenvalues and eigenfunctions. During training, the neural network adjusts its weights and biases, one of which is the energy eigenvalue, so its o…

Electronic Properties of Graphene Quantum Ring with Wedge Disclination

We study the energy spectrum and persistent current of charge carriers confined in a graphene quantum ring geometry of radius $R$ and width $w$ subjected to a magnetic flux. We consider the case where the crystal symmetry is locally modified by replacing a hexagon by a pentagon, square, heptagon or octagon. To model this type of defect we include appropriate boundary conditions for the angular coordinate. The electrons are confined to a finite width strip in radial direction by setting infinite mass boundary conditions at the edges of the strip. The solutions are expressed in terms of Hankel f…

Quantum particle in a spherical well confined by a cone

We consider the quantum problem of a particle in either a spherical box or a finite spherical well confined by a circular cone with an apex angle $2θ_0$ emanating from the center of the sphere, with $0<θ_0<π$. This non-central potential can be solved by an extension of techniques used in spherically-symmetric problems. The angular parts of the eigenstates depend on azimuthal angle $φ$ and polar angle $θ$ as $P_λ^m(\cosθ){\rm e}^{imφ}$ where $P_λ^m$ is the associated Legendre function of integer order $m$ and (usually noninteger) degree $λ$. There is an infinite discrete set of values $λ=λ_i^m$…