Spontaneous breaking of axial symmetry for Schroedinger's equation in the presence of a magnetic field
Jorge Berger
在适当的参数下，柱域中Schroedinger和Ampere耦合方程的基态不具有轴对称性。
For appropriate parameters, the ground state for the Schroedinger and Ampere coupled equations in a cylindric domain does not have axial symmetry.
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Spontaneous symmetry breaking (SSB) is mathematically tied to some limit, but must physically occur, approximately, before the limit. Approximate SSB has been independently understood for Schroedinger operators with double well potential in the classical limit (Jona-Lasinio et al, 1981; Simon, 1985) and for quantum spin systems in the thermodynamic limit (Anderson, 1952; Tasaki, 2019). We relate these to each other in the context of the Curie-Weiss model, establishing a remarkable relationship between this model (for finite N) and a discretized Schroedinger operator with double well potential.
Exact Solutions of the Time Dependent Schroedinger Equation in One Space Dimension
本文导出了任意时间依赖的线性信号通过后谐振子波函数的封闭表达式。转移概率很容易用拉盖尔多项式表示。自发的转变被忽略了。精确的结果对于短激光脉冲的物理学是有一定意义的，因为它可以作为数值方法的精度测试。
It is often claimed that the collapse of the wave function and Born's rule to interpret the square of the norm as a probability, have to be introduced as separate axioms in quantum mechanics besides the Schroedinger equation. Here we show that this is not true in certain models where quantum behavior can be attributed to underlying deterministic equations. It is argued that indeed the apparent spontaneous collapse of wave functions and Born's rule are features that strongly point towards determinism underlying quantum mechanics.
Optical control and entanglement of atomic Schroedinger fields
建立了一个完全量子化的玻色-爱因斯坦凝聚体模型，该凝聚体由远离共振的泵浦激光驱动，与光学环形腔的单模相互作用。在线性区，腔模表现出与两个原子场边模的出现相关的自发指数增益。这些侧模和腔场产生在一个高度纠缠的状态，其特征在于在各个模式的热强度波动，但与违反某些经典的不等式的双模关联函数。通过将初始相干场注入到光腔中，可以以降低相关性为代价显著降低强度波动，从而允许对物质波的量子统计特性进行光学控制。
The standard derivation of Schroedinger's equation from a Lorentz-invariant Feynman path integral consists in taking first the limit of infinite speed of light and then the limit of short time slice. In this order of limits the light cone of the path integral disappears, giving rise to an instantaneous spread of the wave function to the entire space. We ascribe the failure of Schroedinger's equation to retain the light cone of the path integral to the very nature of the limiting process: it is a regular expansion of a singular approximation problem, because the boundary conditions of the path …
On Spontaneous Wave Function Collapse and Quantum Field Theory
获得一种没有观察者的量子力学，从而解决量子力学悖论的一种方法是通过实现波函数的自发坍缩来修改薛定谔演化。1986年，Ghirardi、Rimini和Weber（GRW）提出了此类显式模型，涉及波函数的非线性随机演化。我们指出，如何集中在GRW模型的基本数学结构和一个明确的本体论，它可以推广到（正规化）量子场论在一个简单而自然的方式。
In nonrelativistic quantum mechanics the spontaneous generation of singularities in smooth and finite wave functions, is a well understood phenomenon also occurring for free particles. We use the familiar analogy between the two-dimensional Schroedinger equation and the optical paraxial wave equation to define a new class of square-integrable paraxial optical fields which develop a spatial singularity in the focal point of a weakly-focusing thin lens. These fields are characterized by a single real parameter whose value determines the nature of the singularity. This novel field enhancement mec…
The linearity of quantum mechanics leads, under the assumption that the wave function offers a complete description of reality, to grotesque situations famously known as Schroedinger's cat. Ways out are either adding elements of reality or replacing the linear evolution by a nonlinear one. Models of spontaneous wave function collapses took the latter path. The way such models are constructed leaves the question, whether such models are in some sense unique, i.e. whether the nonlinear equations replacing Schroedinger's equation, are uniquely determined as collapse equations. Various people work…
Unidirectional Inter-Axial Coupling and Spontaneous Cooling in a~Non-Hermitian Dynamics of a~Levitated Particle
本文通过操控真空悬浮纳米粒子的机械模式耦合，观察到非厄米特动力学中的PT对称相变和单向能量传输，实现无外部反馈的机械模式自发冷却。
A Stochastic Hamiltonian Approach for Quantum Jumps, Spontaneous Localizations, and Continuous Trajectories
我们给出了一个显式的随机哈密顿模型的不连续幺正演化的量子自发跳跃像在一个系统中的原子在量子光学，或在一个系统中的量子粒子的奇异相互作用与“泡沫”，承认一个连续的计数观察。该模型允许通过散射光子或气泡的动量的自发定位来观察光电探测器或云室中的量子轨迹。因此，连续约化和自发局域化理论是从作为量子滤波结果的哈密顿奇异相互作用得到的，即，通过输出测量数据对输入量子过程进行顺序时间连续调节。我们表明，在不可区分的粒子或原子的情况下，后验动力学是混合的，从而产生一个不可逆的玻尔兹曼型约化方程。后者仅在平均场近似下与非随机薛定谔方程一致，而中心极限产生由扩散型量子态约化方程描述的高斯混合涨落。
We analyze the influence of relativistic effects on the minimum evolution time between two orthogonal states of a quantum system. Defining the initial state as an homogeneous superposition between two Hamiltonian eigenstates of an electron in a uniform magnetic field, we obtain a relation between the minimum evolution time and the displacement of the mean radial position of the electron wavepacket. The quantum speed limit time is calculated for an electron dynamics described by Dirac and Schroedinger-Pauli equations considering different parameters, such as the strength of magnetic field and t…
We study the force of light on a two-level atom near an ultrathin optical fiber using the mode function method and the Green tensor technique. We show that the total force consists of the driving-field force, the spontaneous-emission recoil force, and the fiber-induced van der Waals potential force. Due to the existence of a nonzero axial component of the field in a guided mode, the Rabi frequency and, hence, the magnitude of the force of the guided driving field may depend on the propagation direction. When the atomic dipole rotates in the meridional plane, the spontaneous-emission recoil for…
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