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Quantum Science时间演变时间演化是随着时间的推移而带来的状态变化，适用于具有内部状态的系统（也称为有状态系统）。在这个公式中，时间不需要是连续参数，但可以是离散的甚至是有限的。在经典物理学中，刚体集合的时间演化受经典力学原理的支配。这些原理以最基本的形式表达了作用在物体上的力与牛顿运动定律给出的加速度之间的关系。这些原理可以用哈密顿力学或拉格朗日力学等价地更抽象地表达。时间演化的概念也可能适用于其他有状态系统。
Time evolution is the change of state brought about by the passage of time, applicable to systems with internal state (also called stateful systems). In this formulation, time is not required to be a continuous parameter, but may be discrete or even finite. In classical physics, time evolution of a collection of rigid bodies is governed by the principles of classical mechanics. In their most rudimentary form, these principles express the relationship between forces acting on the bodies and their acceleration given by Newton's laws of motion. These principles can be equivalently expressed more abstractly by Hamiltonian mechanics or Lagrangian mechanics. The concept of time evolution may be applicable to other stateful systems as well.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 在线性代数和泛函分析中，部分迹是迹的推广。迹是运算符上的标量值函数，而部分迹是运算符值函数。部分迹在量子信息和退相干中具有应用，这与量子测量相关，从而与解释量子力学的退相干方法相关，包括一致的历史和相对状态解释。
In linear algebra and functional analysis, the partial trace is a generalization of the trace. Whereas the trace is a scalar-valued function on operators, the partial trace is an operator-valued function. The partial trace has applications in quantum information and decoherence which is relevant for quantum measurement and thereby to the decoherent approaches to interpretations of quantum mechanics, including consistent histories and the relative state interpretation.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 在量子计算中，量子寄存器是包含多个量子位的系统。它是经典处理器寄存器的量子模拟。量子计算机通过操纵量子寄存器内的量子位来执行计算。
In quantum computing, a quantum register is a system comprising multiple qubits. It is the quantum analogue of the classical processor register. Quantum computers perform calculations by manipulating qubits within a quantum register.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 在量子力学，特别是量子信息和开放量子系统的研究中，迹线距离是密度矩阵空间上的度量，并给出了两种状态之间可区分性的度量。它是经典概率分布的柯尔莫哥洛夫距离的量子推广。
In quantum mechanics, and especially quantum information and the study of open quantum systems, the trace distance is a metric on the space of density matrices and gives a measure of the distinguishability between two states. It is the quantum generalization of the Kolmogorov distance for classical probability distributions.
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View content license ↗ 品质因子或Q因子是物理及工程中的无量纲参数，是表示振子阻尼性质的物理量，也可表示振子的共振频率相对于带宽的大小， 高Q因子表示振子能量损失的速率较慢，振动可持续较长的时间，例如一个单摆在空气中运动，其Q因子较高，而在油中运动的单摆Q因子较低。高Q因子的振子一般其阻尼也较小。
In physics and engineering, the quality factor or Q factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. Resonators with high quality factors have low damping, so that they ring or vibrate longer. For example, a pendulum suspended from a precision bearing, oscillating in air, has a high Q, while a pendulum immersed in oil has a low Q. There are two definitions of Q that give numerically similar, but not identical, results. The more general definition is the ratio of the initial energy stored in the resonator to the energy lost in one radian of the cycle of oscillation. An alternative definition of Q factor, more applicable to high Q oscillators, is the ratio of a resonator's centre frequency to its bandwidth when subject to an oscillating driving force.
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View content license ↗ 标定（英语：Calibration），即为科学上之校准行为，意指“对某仪器、药物或须有精确单位之物品，其只知的体积、浓度......等刻度或单位之准确度，进行检测是否合乎标准，若否则修正。”
In measurement technology and metrology, calibration is the comparison of measurement values delivered by a device under test with those of a calibration standard of known accuracy. Such a standard could be another measurement device of known accuracy, a device generating the quantity to be measured such as a voltage, a sound tone, or a physical artifact, such as a meter ruler. The outcome of the comparison can result in one of the following: no significant error being noted on the device under test a significant error being noted but no adjustment made an adjustment made to correct the error to an acceptable level Strictly speaking, the term "calibration" means just the act of comparison and does not include any subsequent adjustment. The calibration standard is normally traceable to a national or international standard held by a metrology body.
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View content license ↗ 再现性与可重复性和可重复性密切相关，是支撑科学方法的主要原则。研究结果的可重复性意味着，当研究被重复时，通过实验或观察性研究或数据集统计分析获得的结果应该再次获得高度的可靠性。复制有不同类型，但复制研究通常涉及使用相同方法的不同研究人员。只有在一次或多次成功复制之后，结果才能被视为科学知识。
Reproducibility, closely related to replicability and repeatability, is a major principle underpinning the scientific method. For the findings of a study to be reproducible means that results obtained by an experiment or an observational study or in a statistical analysis of a data set should be achieved again with a high degree of reliability when the study is replicated. There are different kinds of replication but typically replication studies involve different researchers using the same methodology. Only after one or several such successful replications should a result be recognized as scientific knowledge.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 绝热不变量，又称浸渐不变量或缓渐不变量，是指一个物理系统中，经过一个缓慢的变化而几乎保持不变的物理量，比如理想气体在绝热过程中的熵。这可以理解为，物理系统从一个状态向另一个状态过渡时，假如这个过程的持续时间趋向于无穷大，那么绝热不变量的变化就趋向于零。 浸渐不变量有一种错误的写法是寝渐不变量。出现这种错误的原因是繁体“浸”的一种字体是“寖”，和“寝”很像。 在热力学中，绝热过程是一个隔绝系统与外界热交换的过程，可快可慢。如果一个热力学过程发生得非常缓慢，以至于比体系达到平衡还要慢，那么这个过程就是可逆的，也被称为准静态过程。在可逆的绝热过程中，系统时刻保持平衡，而且系统的熵是定值。在20世纪上半叶，量子物理学家用“绝热过程”来描述可逆的绝热过程和其他缓慢变化的过程。这种量子力学的定义更接近于热力学中的准静态过程，与绝热过程没有直接关系。 在力学里面，绝热变化是哈密顿函数的缓慢变化，其中能量的相对变化速度要远远缓于周期运动的频率。相空间内，周期运动轨道所围成的体积就是绝热不变量。 在量子力学中，绝热变化的变化率远远低于本征态间的频率差。在这种情况下系统的能级不会变化，所以系统的量子数是绝热不变量。 在旧量子论中，系统的量子数等于经典的绝热不变量。这就确定了玻尔-索末菲量子化条件：量子数等于相空间内运动轨道所围成的体积。 在等离子体物理学中，绝热不变量有三个μ、J、Φ，每个都与不同类型的周期性运动相对应。
A property of a physical system, such as the entropy of a gas, that stays approximately constant when changes occur slowly is called an adiabatic invariant. By this it is meant that if a system is varied between two end points, as the time for the variation between the end points is increased to infinity, the variation of an adiabatic invariant between the two end points goes to zero. In thermodynamics, an adiabatic process is a change that occurs without heat flow; it may be slow or fast. A reversible adiabatic process is an adiabatic process that occurs slowly compared to the time to reach equilibrium. In a reversible adiabatic process, the system is in equilibrium at all stages and the entropy is constant.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements.
View content license ↗ 在固态物理学和固态化学中，带隙，也称为带隙或能隙，是固体中不存在电子态的能量范围。在固体的电子能带结构图中，带隙是指绝缘体和半导体中价带顶部和导带底部之间的能量差（通常以电子伏特表示）。它是将电子从价带提升到导带所需的能量。由此产生的导带电子（以及价带中的电子空穴）可以在晶格内自由移动，并充当载流子来传导电流。它与化学中的HOMO-LUMO能隙密切相关。
In solid-state physics and solid-state chemistry, a band gap, also called a bandgap or energy gap, is an energy range in a solid where no electronic states exist. In graphs of the electronic band structure of solids, the band gap refers to the energy difference (often expressed in electronvolts) between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. It is the energy required to promote an electron from the valence band to the conduction band. The resulting conduction-band electron (and the electron hole in the valence band) are free to move within the crystal lattice and serve as charge carriers to conduct electric current. It is closely related to the HOMO–LUMO gap in chemistry.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 玻色气体（英语：Bose gas）是一个经典的理想气体的量子力学模型。其概念相似于费米气体。 结合萨特延德拉·玻色和爱因斯坦共同提出的理想的玻色气体，指的是在足够低的温度下〈接近0K〉一群玻色子会形成所谓的固化物。但这样的行为和经典的理想气体不同。而固化物的形成即所认知的玻色–爱因斯坦凝聚。
An ideal Bose gas is a quantum-mechanical phase of matter, analogous to a classical ideal gas. It is composed of bosons, which have an integer value of spin and abide by Bose–Einstein statistics. The statistical mechanics of bosons were developed by Satyendra Nath Bose for a photon gas and extended to massive particles by Albert Einstein, who realized that an ideal gas of bosons would form a condensate at a low enough temperature, unlike a classical ideal gas. This condensate is known as a Bose–Einstein condensate.
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View content license ↗ 在散射理论中，约斯特函数是微分方程 − ψ ″ + V ψ = k 2 ψ {\displaystyle -\psi ''+V\psi =k^{2}\psi } 的正则解和（不规则）约斯特解的朗斯基式。它是由Res Jost 介绍的。
In scattering theory, the Jost function is the Wronskian of the regular solution and the (irregular) Jost solution to the differential equation − ψ ″ + V ψ = k 2 ψ {\displaystyle -\psi ''+V\psi =k^{2}\psi } . It was introduced by Res Jost.
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View content license ↗ 在量子基础中，KCBS 五角星是反驳非上下文隐变量模型的一个例子。它是由 Alexander Klyachko、M. Ali Can、Sinem Binicioglu 和 Alexander Shumovsky 发现的，其名字来源于他们名字的首字母缩写。
In quantum foundations, the KCBS pentagram is an example disproving noncontextual hidden variable models. It was discovered by Alexander Klyachko, M. Ali Can, Sinem Binicioglu, and Alexander Shumovsky, whose last initials provide its name.
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View content license ↗ 踢动转子，也拼写为踢动转子，是哈密顿混沌（哈密顿系统中的混沌研究）和量子混沌的范例模型。它描述了一个在不均匀的“类重力”场中自由旋转的棒（惯性矩为 I {\displaystyle I} ），该场以短脉冲周期性地开启。
The kicked rotator, also spelled as kicked rotor, is a paradigmatic model for both Hamiltonian chaos (the study of chaos in Hamiltonian systems) and quantum chaos. It describes a free rotating stick (with moment of inertia I {\displaystyle I} ) in an inhomogeneous "gravitation like" field that is periodically switched on in short pulses.
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View content license ↗ 久保公式以 1957 年首次提出该公式的久保良吾 (Ryogo Kubo) 命名，是一个表达可观测量因时间相关扰动而产生的线性响应的方程。在 Kubo 公式的众多应用中，人们可以计算电子系统响应所施加的电场和磁场的电荷和自旋磁化率。还可以计算对外部机械力和振动的响应。
The Kubo formula, named for Ryogo Kubo who first presented the formula in 1957, is an equation which expresses the linear response of an observable quantity due to a time-dependent perturbation. Among numerous applications of the Kubo formula, one can calculate the charge and spin susceptibilities of systems of electrons in response to applied electric and magnetic fields. Responses to external mechanical forces and vibrations can be calculated as well.
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View content license ↗ 朗道-齐纳公式是控制二态量子系统过渡动力学的运动方程的解析解，其中随时间变化的半经典哈密顿量使得两个状态的能量分离是时间的线性函数。该公式给出了两个绝热能态之间非绝热跃迁的概率，由 Lev Landau、Clarence Zener、Ernst Stueckelberg 和 Ettore Majorana 于 1932 年分别发表。如果系统在无限的过去开始于较低能量本征态，我们希望计算在无限未来找到系统处于较高能量本征态的概率（所谓的朗道-齐纳跃迁）。
The Landau–Zener formula is an analytic solution to the equations of motion governing the transition dynamics of a two-state quantum system, with a time-dependent semi-classical Hamiltonian varying such that the energy separation of the two states is a linear function of time. The formula, giving the probability of a non-adiabatic transition between the two adiabatic energy states, was published separately by Lev Landau, Clarence Zener, Ernst Stueckelberg, and Ettore Majorana, in 1932. If the system starts, in the infinite past, in the lower energy eigenstate, we wish to calculate the probability of finding the system in the upper energy eigenstate in the infinite future (a so-called Landau–Zener transition).
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 在介观物理学中，兰道尔公式（以 Rolf Landauer 的名字命名，他于 1957 年首次提出其原型）是一个将量子导体的电阻与导体的散射特性联系起来的公式。对于空间尺寸等于或小于电荷载流子（电子和空穴）的相位相干长度的介观电路，它等效于欧姆定律。在金属中，当温度低于 1 K 时，相位相干长度为微米量级。
In mesoscopic physics, the Landauer formula—named after Rolf Landauer, who first suggested its prototype in 1957—is a formula relating the electrical resistance of a quantum conductor to the scattering properties of the conductor. It is the equivalent of Ohm's law for mesoscopic circuits with spatial dimensions in the order of or smaller than the phase coherence length of charge carriers (electrons and holes). In metals, the phase coherence length is of the order of the micrometre for temperatures less than 1 K.
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View content license ↗ 在量子力学中，朗缪尔态是氦的某些量子态，在经典极限下对应于电子的两个平行圆形轨道，一个在另一个之上，原子核位于其间。当电子具有最大角动量并在圆上移动时，它们的构造类似于氢的圆形状态。由于氦核电荷 2e 的神奇值，在圆周运动期间扫过构型空间的三角形核-电子-电子是等边的。
In quantum mechanics Langmuir states are certain quantum states of Helium that in the classical limit correspond to two parallel circular orbits of electrons one above the other and with the nucleus in between. They are constructed in analogy to circular states of Hydrogen when the electron has the maximum angular momentum and moves on the circle. Because of the magic value of the Helium nucleus charge 2e the triangle nucleus-electron-electron which sweeps the configuration space during the circular motion is equilateral.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 晶格散射是离子通过与晶格中的原子相互作用而发生的散射。这种效应可以定性地理解为声子与载流子的碰撞。在当前电导率的量子力学图中，电子穿过晶格的容易程度取决于该晶格中离子的近乎完全规则的间距。只有当晶格包含完全规则的间距时，离子-晶格相互作用（散射）才能导致晶格几乎透明的行为。在量子理解中，电子被视为穿过介质的波。当电子的波长大于晶体间距时，电子将在整个金属中自由传播而不会发生碰撞。
Lattice scattering is the scattering of ions by interaction with atoms in a lattice. This effect can be qualitatively understood as phonons colliding with charge carriers. In the current quantum mechanical picture of conductivity the ease with which electrons traverse a crystal lattice is dependent on the near perfectly regular spacing of ions in that lattice. Only when a lattice contains perfectly regular spacing can the ion-lattice interaction (scattering) lead to almost transparent behavior of the lattice. In the quantum understanding, an electron is viewed as a wave traveling through a medium. When the wavelength of the electrons is larger than the crystal spacing, the electrons will propagate freely throughout the metal without collision.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 能级斥力在量子力学中相当于振荡器中的斥力效应。两个耦合振荡器的系统具有两个固有频率。随着振荡器之间的耦合强度增加，较低频率降低而较高频率增加。
Level repulsion is the quantum mechanical equivalent to a repulsion effect in oscillators. A system of two coupled oscillators has two natural frequencies. As the coupling strength between the oscillators increases, the lower frequency decreases and the higher increases.
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View content license ↗ 悬浮光力学是介观物理学的一个领域，它研究光学、电或磁悬浮的介观粒子的机械运动。通过使用悬浮，可以将粒子的机械运动与环境完美地分离。这反过来又使得高质量量子物理、非平衡态和纳米热力学的研究成为可能，并为精确传感应用提供了基础。
Levitated optomechanics is a field of mesoscopic physics which deals with the mechanical motion of mesoscopic particles which are optically or electrically or magnetically levitated. Through the use of levitation, it is possible to decouple the particle's mechanical motion exceptionally well from the environment. This in turn enables the study of high-mass quantum physics, out-of-equilibrium- and nano-thermodynamics and provides the basis for precise sensing applications.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 在量子力学中，Lévy-Leblond 方程描述了自旋 1/2 粒子的动力学。它是薛定谔方程和泡利方程的线性化版本。它是由法国物理学家Jean-Marc Lévy-Leblond于1967年推导出来的。Lévy-Leblond方程是在与狄拉克方程类似的启发式推导下得到的，但与后者相反，Lévy-Leblond方程不是相对论性的。由于两个方程都恢复了电子旋磁比，因此表明自旋不一定是相对论现象。
In quantum mechanics, the Lévy-Leblond equation describes the dynamics of a spin-1/2 particle. It is a linearized version of the Schrödinger equation and of the Pauli equation. It was derived by French physicist Jean-Marc Lévy-Leblond in 1967. The Lévy-Leblond equation was obtained under similar heuristic derivations as the Dirac equation, but contrary to the latter, the Lévy-Leblond equation is not relativistic. As both equations recover the electron gyromagnetic ratio, it is suggested that spin is not necessarily a relativistic phenomenon.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 多体定位（MBL）是一种动力学现象，会导致孤立多体系统中平衡统计力学的崩溃。这样的系统永远不会达到局部热平衡，并且无限次地保留其初始条件的局部记忆。人们仍然可以在这些非平衡系统中定义相结构的概念。引人注目的是，MBL 甚至可以实现热平衡中不允许的新型奇异序，这种现象被称为局域保护量子序 (LPQO) 或本征态序。
Many-body localization (MBL) is a dynamical phenomenon which leads to the breakdown of equilibrium statistical mechanics in isolated many-body systems. Such systems never reach local thermal equilibrium, and retain local memory of their initial conditions for infinite times. One can still define a notion of phase structure in these out-of-equilibrium systems. Strikingly, MBL can even enable new kinds of exotic orders that are disallowed in thermal equilibrium – a phenomenon that goes by the name of localization-protected quantum order (LPQO) or eigenstate order.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 在量子力学中，宏观量子自陷是指两个玻色-爱因斯坦凝聚体通过能量势垒弱连接，粒子可以隧道穿过该能量势垒，但最终结点一侧的玻色子平均数量高于另一侧。两种玻色-爱因斯坦凝聚体的结点主要类似于约瑟夫森结，它由两个通过非导电势垒连接的超导体组成。然而，超导约瑟夫森结不表现出宏观量子自捕获，因此宏观量子自隧道是玻色-爱因斯坦凝聚结的一个显着特征。当玻色子之间的自相互作用能量 Λ {\displaystyle \Lambda } 大于称为 Λ c MJJ {\displaystyle \Lambda _{c}^{\text{MJJ}}} 的临界值时，就会发生自捕获。
In quantum mechanics, macroscopic quantum self-trapping is when two Bose–Einstein condensates weakly linked by an energy barrier which particles can tunnel through, nevertheless end up with a higher average number of bosons on one side of the junction than the other. The junction of two Bose–Einstein condensates is mostly analogous to a Josephson junction, which is made of two superconductors linked by a non-conducting barrier. However, superconducting Josephson junctions do not display macroscopic quantum self-trapping, and thus macroscopic quantum self-tunneling is a distinguishing feature of Bose–Einstein condensate junctions. Self-trapping occurs when the self-interaction energy Λ {\displaystyle \Lambda } between the Bosons is larger than a critical value called Λ c MJJ {\displaystyle \Lambda _{c}^{\text{MJJ}}} .
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 在理论物理学中，马德隆方程或量子流体动力学方程是欧文·马德隆对无自旋非相对论粒子薛定谔方程的替代表述，以流体动力学变量的形式编写，类似于流体动力学的纳维-斯托克斯方程。马德隆方程的推导与德布罗意-玻姆公式类似，将薛定谔方程表示为量子汉密尔顿-雅可比方程。在这两种情况下，如果不添加量子化条件，流体动力学解释并不等同于薛定谔方程。最近，通过用流体动力学变量编写狄拉克方程来扩展自旋相对论情况。在相对论情况下，汉密尔顿-雅可比方程也是制导方程，因此不必进行假设。
In theoretical physics, the Madelung equations, or the equations of quantum hydrodynamics, are Erwin Madelung's alternative formulation of the Schrödinger equation for a spinless non-relativistic particle, written in terms of hydrodynamical variables, similar to the Navier–Stokes equations of fluid dynamics. The derivation of the Madelung equations is similar to the de Broglie–Bohm formulation, which represents the Schrödinger equation as a quantum Hamilton–Jacobi equation. In both cases the hydrodynamic interpretations are not equivalent to Schrödinger's equation without the addition of a quantization condition. Recently, the extension to the relativistic case with spin was done by having the Dirac equation written with hydrodynamic variables. In the relativistic case, the Hamilton–Jacobi equation is also the guidance equation, which therefore does not have to be postulated.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 在量子信息论中，魔法是一种量化描述稳定态之外的量子态所需的计算资源的属性，可以在经典计算机上有效地模拟。这个概念源于 20 世纪 90 年代证明的 Gottesman-Knill 定理，该定理表明高度纠缠的稳定态不提供量子计算优势，因为它们可以在经典计算机上同样有效地模拟。 2014 年，人们发现魔法状态与情境相关：在量子力学中，它表明测量结果取决于同时测量的其他属性。魔法通常使用稳定器 Rényi 熵来测量，它可以通过量子处理器上的随机测量协议通过实验确定。
In quantum information theory, magic is a property that quantifies the computational resources needed to describe quantum states beyond stabilizer states, which can be efficiently simulated on classical computers. The concept emerged from the Gottesman-Knill theorem proven in the 1990s, which showed that highly entangled stabilizer states offer no quantum computational advantage because they can be simulated just as efficiently on classical computers. In 2014, it was found that magic states are connected to contextuality: in quantum mechanics, it shows that measurement outcomes depend on what other properties are simultaneously measured. Magic is commonly measured using the stabilizer Rényi entropy, which can be experimentally determined through randomized measurement protocols on quantum processors.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 在量子力学中，磁共振是一种共振效应，当磁偶极子暴露于静态磁场并受到另一个振荡电磁场的扰动时，就会出现这种效应。由于存在静态场，偶极子可以呈现许多离散的能量本征态，具体取决于其角动量（方位角）量子数的值。然后，振荡场可以使偶极子以一定的概率和一定的速率在其能态之间跃迁。总体跃迁概率将取决于场的频率，而速率将取决于其幅度。当该场的频率导致两种状态之间的最大可能转变概率时，就实现了磁共振。在这种情况下，组成振荡场的光子的能量与所述状态之间的能量差匹配。
In quantum mechanics, magnetic resonance is a resonant effect that can appear when a magnetic dipole is exposed to a static magnetic field and perturbed with another, oscillating electromagnetic field. Due to the static field, the dipole can assume a number of discrete energy eigenstates, depending on the value of its angular momentum (azimuthal) quantum number. The oscillating field can then make the dipole transit between its energy states with a certain probability and at a certain rate. The overall transition probability will depend on the field's frequency and the rate will depend on its amplitude. When the frequency of that field leads to the maximum possible transition probability between two states, a magnetic resonance has been achieved. In that case, the energy of the photons composing the oscillating field matches the energy difference between said states.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 多体局域化（MBL）是一种发生在孤立多体量子系统中的动力学现象。其特点是系统无法达到热平衡，并且在局部可观测值中无限次地保留其初始条件的记忆。
Many-body localization (MBL) is a dynamical phenomenon occurring in isolated many-body quantum systems. It is characterized by the system failing to reach thermal equilibrium, and retaining a memory of its initial condition in local observables for infinite times.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 马格瑙-希尔准概率分布 (MH) 是量子力学中使用的数学工具，特别是在量子信息科学、量子光学和量子热力学中，用于描述多个潜在非交换可观测量（无法同时精确测量的数量）测量结果的联合“准概率”。它通常用作量子态的相空间描述，类似于维格纳准概率分布和柯克伍德-狄拉克准概率分布。它由 Henry Margenau 和 Robert Nyden Hill 于 1961 年提出。
The Margenau-Hill quasiprobability distribution (MH) is a mathematical tool used in quantum mechanics, particularly in quantum information science, quantum optics, and quantum thermodynamics, to describe the joint "quasiprobability" of outcomes for measurements of multiple, potentially non-commuting observables (quantities that cannot be precisely measured simultaneously). It is commonly used as a phase-space description of quantum states, similar to the Wigner quasiprobability distribution and Kirkwood–Dirac quasiprobability distribution. It was introduced by Henry Margenau and Robert Nyden Hill in 1961.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 在物理学中，马什洪效应描述了粒子的固有自旋与旋转观察者的角速度的耦合。该效应以伊朗裔美国物理学家巴赫拉姆·马什霍恩 (Bahram Mashhoon) 的名字命名，他于 1988 年首次提出了该效应的存在。该效应考虑了旋转参考系中的量子力学，从而导致本征自旋与测量装置旋转的角速度耦合。在干涉测量中，固有的自旋-旋转耦合导致相移通常小于萨格纳克相移，这是由于粒子的轨道角动量与干涉仪的旋转耦合所致。
In physics, the Mashhoon effect describes the coupling of the intrinsic spin of a particle with the angular velocity of a rotating observer. The effect is named after Iranian-American physicist Bahram Mashhoon, who first formulated its existence in 1988. The effect considers quantum mechanics in a rotating frame of reference, which leads to a coupling of intrinsic spin with the angular velocity of the rotation of a measuring device. In interferometry, the intrinsic spin-rotation coupling leads to a phase shift that is generally smaller than the Sagnac phase shift, which is due to the coupling of the orbital angular momentum of the particle with the rotation of the interferometer.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
View content license ↗ 在物理学中，特别是在量子微扰理论中，矩阵元素是指使用狄拉克符号的修正哈密顿量的线性算子。它实际上指的是哈密顿算子的矩阵元素，其目的是计算不同量子态之间的跃迁概率。矩阵元素考虑新修改的哈密顿量（即未扰动的哈密顿量加上相互作用势的线性叠加）对量子态的影响。矩阵元素在原子、核和粒子物理学中很重要。
In physics, particularly in quantum perturbation theory, the matrix element refers to the linear operator of a modified Hamiltonian using Dirac notation. It is in fact referring to the matrix elements of a Hamiltonian operator which serves the purpose of calculating transition probabilities between different quantum states. The matrix element considers the effect of the newly modified Hamiltonian (i.e. the linear superposition of the unperturbed Hamiltonian plus interaction potential) on the quantum state. Matrix elements are important in atomic, nuclear and particle physics.
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Wikipedia contributors · Retrieved2026-10-04 · CC BY-SA 4.0. Introductions were extracted as plain text and shortened. Language versions may emphasize different aspects.For concept reference; consult the original standards for authoritative requirements. The Chinese definition is a machine-assisted translation of the cited English introduction; check technical terminology against the original.
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