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Quantum Science傅里叶变换傅里叶变换 （法语：Transformation de Fourier，英语：Fourier transform，缩写：FT）是一种线性变换，通常定义为一种积分变换。其基本思想是一个函数可以用（可数或不可数，可数的情况对应于傅里叶级数）无穷多个周期函数的线性组合来逼近，从而这些组合系数在保有原函数的几乎全部信息的同时，还直接地反映了该函数的“频域特征”。因其基本思想首先由法国学者约瑟夫·傅里叶系统地提出，所以以其名字来命名以示纪念。在现代数学理论中，傅里叶积分变换可以得到各种推广，并在分析学中有广泛应用，构成了调和分析这一数学领域。 经过傅里叶变换生成的函数 f ^ {\displaystyle {\hat {f}}} 称作原函数 f {\displaystyle f} 的傅里叶变换，应用意义上称作频谱。在特定情况下，傅里叶变换是可逆的，即将 f ^ {\displaystyle {\hat {f}}} 通过逆变换可以得到其原函数 f {\displaystyle f} 。通常情况下， f {\displaystyle f} 是一个实函数，而 f ^ {\displaystyle {\hat {f}}} 则是一个复数值函数，其函数值作为复数可同时表示振幅和相位。
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex valued function of frequency. The term Fourier transform refers to both the mathematical operation and to this complex-valued function. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical chord into the intensities of its constituent pitches. Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle.
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View content license ↗ 拉普拉斯变换（英语：Laplace transform）是应用数学中常用的一种积分变换，又名拉氏变换，其符号为 L { f ( t ) } {\displaystyle \displaystyle {\mathcal {L}}\left\{f(t)\right\}} 。拉氏变换是一个线性变换，可将一个有实数变量 t ( t ≥ 0 ) {\displaystyle t(t\geq 0)} 的函数变换为一个变量为复数 s {\displaystyle s} 的函数： F ( s ) = ∫ 0 ∞ f ( t ) e − s t d t .
In mathematics, the Laplace transform, named after Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable (usually t {\displaystyle t} , in the time domain) to a function of a complex variable s {\displaystyle s} (in the complex-valued frequency domain, also known as s-domain or s-plane). The functions are often denoted using a lowercase symbol for the time-domain function and the corresponding uppercase symbol for the frequency-domain function, e.g. x ( t ) {\displaystyle x(t)} and X ( s ) {\displaystyle X(s)} . The transform is useful for converting differentiation and integration in the time domain into the algebraic operations multiplication and division in the Laplace domain (analogous to how logarithms are useful for simplifying multiplication and division into addition and subtraction).
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View content license ↗ 鲁派纳几何是热力学几何（信息几何的一种），利用黎曼几何的语言来研究热力学。 George Ruppeiner于1979年提出。他声称热力学系统可以用黎曼几何来表示，并且可以从模型中推导出统计性质。该几何模型基于将涨落理论纳入平衡热力学公理，即存在可以用二维表面（流形）上的点表示的平衡状态，并且这些平衡状态之间的距离与它们之间的涨落有关。这个概念与概率相关，即状态之间波动的可能性越小，它们之间的距离就越远。
Ruppeiner geometry is thermodynamic geometry (a type of information geometry) using the language of Riemannian geometry to study thermodynamics. George Ruppeiner proposed it in 1979. He claimed that thermodynamic systems can be represented by Riemannian geometry, and that statistical properties can be derived from the model. This geometrical model is based on the inclusion of the theory of fluctuations into the axioms of equilibrium thermodynamics, namely, there exist equilibrium states which can be represented by points on two-dimensional surface (manifold) and the distance between these equilibrium states is related to the fluctuation between them. This concept is associated to probabilities, i.e. the less probable a fluctuation between states, the further apart they are.
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View content license ↗ 对称保护拓扑（SPT）序是一种具有对称性和有限能隙的零温量子力学物质状态的序。为了以最不变的方式导出结果，使用重整化群方法（导致对应于某些固定点的等价类）。 SPT 阶具有以下定义属性：(a) 如果变形保持对称性，则具有给定对称性的不同 SPT 状态在没有相变的情况下不能平滑地变形为彼此。 (b) 然而，如果在变形过程中对称性被打破，它们都可以平滑地变形为相同的平凡产物状态，而无需相变。上述定义适用于玻色子系统和费米子系统，从而引出了玻色子SPT阶和费米子SPT阶的概念。
Symmetry-protected topological (SPT) order is a kind of order in zero-temperature quantum-mechanical states of matter that have a symmetry and a finite energy gap. To derive the results in a most-invariant way, renormalization group methods are used (leading to equivalence classes corresponding to certain fixed points). The SPT order has the following defining properties: (a) distinct SPT states with a given symmetry cannot be smoothly deformed into each other without a phase transition, if the deformation preserves the symmetry. (b) however, they all can be smoothly deformed into the same trivial product state without a phase transition, if the symmetry is broken during the deformation. The above definition works for both bosonic systems and fermionic systems, which leads to the notions of bosonic SPT order and fermionic SPT order.
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View content license ↗ 零点能量（可简称零点能）在物理学中是量子力学所描述的物理系统会有的最低能量，此时系统所处的态称为基态；所有量子力学系统都有零点能量。这个辞汇起源于量子谐振子处在基态时，量子数为零的考量。 在量子场论中，这个辞汇和真空能量是等义词，指空无一物的空间仍有一定能量存在，对一些系统可以造成扰动，并且导致一些量子电动力学会出现的现象，例如兰姆位移与卡西米尔效应；它的效应可在纳米尺度的元件直接观测得到。 在宇宙论中，真空能量被视为宇宙常数的来源，与造就宇宙加速膨胀的暗能量相关。 零点能量是一系统可能持有的最低能量，因此此项能量无法自系统移除。尽管如此，零点能量的概念以及自真空汲取“免费能量”的可能性引起业余发明者的注目，许多“永动机”或称“免费能量装置”等提案都运用这项概念来解释，但由于从较低或相同的能量状态之中汲取能量违反了热力学第二定律并造成熵的降低，运用零点能量被科学界认为是不可能的。这项热潮以及相伴的趣味理论诠释促成了大众文化中“零点能量”概念的成长，常出现在科幻书刊、游戏、电影等处。
Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly fluctuate in their lowest energy state as described by the Heisenberg uncertainty principle. Therefore, even at absolute zero, atoms and molecules retain some vibrational motion. Apart from atoms and molecules, the empty space of a vacuum also has these properties. According to quantum field theory, the universe can be thought of not as isolated particles but continuous fluctuating fields: matter fields, whose quanta are fermions (in other words, leptons and quarks), and force fields, whose quanta are bosons (such as photons and gluons). All these fields have zero-point energy. These fluctuating zero-point fields lead to a kind of reintroduction of an aether in physics since some systems can detect the existence of this energy.
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View content license ↗ 肖尔算法是一种用于查找整数素因数的量子算法。它是由美国数学家Peter Shor于1994年提出的。与最著名的经典（非量子）算法相比，它是为数不多的已知量子算法之一，具有引人注目的潜在应用和超多项式加速的有力证据。然而，由于量子纠错带来的开销，击败经典计算机可能需要具有数百万量子位的量子计算机。 Shor 提出了多种类似的算法来解决因式分解问题、离散对数问题和求周期问题。 “Shor算法”通常指因式分解算法，但也可以指这三种算法中的任何一种。
Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor. It is one of the few known quantum algorithms with compelling potential applications and strong evidence of superpolynomial speedup compared to best known classical (non-quantum) algorithms. However, beating classical computers may require quantum computers with millions of qubits due to the overhead caused by quantum error correction. Shor proposed multiple similar algorithms for solving the factoring problem, the discrete logarithm problem, and the period-finding problem. "Shor's algorithm" usually refers to the factoring algorithm, but may refer to any of the three algorithms.
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View content license ↗ 在量子计算中，量子算法是在量子计算的现实模型上运行的算法，最常用的模型是计算的量子电路模型。经典（或非量子）算法是有限的指令序列，或解决问题的逐步过程，其中每个步骤或指令都可以在经典计算机上执行。同样，量子算法是一个逐步的过程，其中每个步骤都可以在量子计算机上执行。尽管所有经典算法也可以在量子计算机上执行，但术语“量子算法”通常保留用于看起来本质上是量子的算法，或使用量子计算的某些基本特征（例如量子叠加或量子纠缠）的算法。使用经典计算机无法判定的问题使用量子计算机仍然无法判定。
In quantum computing, a quantum algorithm is an algorithm that runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. A classical (or non-quantum) algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem, where each step or instruction can be performed on a classical computer. Similarly, a quantum algorithm is a step-by-step procedure, where each of the steps can be performed on a quantum computer. Although all classical algorithms can also be performed on a quantum computer, the term quantum algorithm is generally reserved for algorithms that seem inherently quantum, or use some essential feature of quantum computation such as quantum superposition or quantum entanglement. Problems that are undecidable using classical computers remain undecidable using quantum computers.
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View content license ↗ 在量子计算中，量子相位估计算法是估计给定酉算子的特征值对应的相位的量子算法。由于酉算子的特征值总是具有单位模数，因此它们的特征在于其相位，因此该算法可以等效地描述为检索相位或特征值本身。该算法最初由 Alexei Kitaev 于 1995 年提出。相位估计经常用作其他量子算法的子程序，例如 Shor 算法、线性方程组的量子算法和量子计数算法。
In quantum computing, the quantum phase estimation algorithm is a quantum algorithm to estimate the phase corresponding to an eigenvalue of a given unitary operator. Because the eigenvalues of a unitary operator always have unit modulus, they are characterized by their phase, and therefore the algorithm can be equivalently described as retrieving either the phase or the eigenvalue itself. The algorithm was initially introduced by Alexei Kitaev in 1995. Phase estimation is frequently used as a subroutine in other quantum algorithms, such as Shor's algorithm, the quantum algorithm for linear systems of equations, and the quantum counting algorithm.
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View content license ↗ 在量子计算中，量子傅里叶变换（QFT）是量子比特上的线性变换，是离散傅里叶变换的量子模拟。量子傅立叶变换是许多量子算法的一部分，特别是用于因式分解和计算离散对数的肖尔算法、用于估计酉算子特征值的量子相位估计算法以及用于隐藏子群问题的算法。量子傅立叶变换是由唐·科珀史密斯 (Don Coppersmith) 发现的。通过对 QFT 进行少量修改，它还可以用于执行快速整数算术运算，例如加法和乘法。量子傅里叶变换可以在量子计算机上有效地执行，并将其分解为更简单的酉矩阵的乘积。
In quantum computing, the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform. The quantum Fourier transform is a part of many quantum algorithms, notably Shor's algorithm for factoring and computing the discrete logarithm, the quantum phase estimation algorithm for estimating the eigenvalues of a unitary operator, and algorithms for the hidden subgroup problem. The quantum Fourier transform was discovered by Don Coppersmith. With small modifications to the QFT, it can also be used for performing fast integer arithmetic operations such as addition and multiplication. The quantum Fourier transform can be performed efficiently on a quantum computer with a decomposition into the product of simpler unitary matrices.
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View content license ↗ 量子优化算法是用于解决优化问题的量子算法。数学优化涉及从一组可能的解决方案中找到问题的最佳解决方案（根据某些标准）。大多数情况下，优化问题被表述为目标函数的最小化。对于组合优化问题，尚未发现经过验证的指数加速。大多数可证明的结果与 Grover 的算法相似，并且有可能实现适度的多项式加速。
Quantum optimization algorithms are quantum algorithms that are used to solve optimization problems. Mathematical optimization deals with finding the best solution to a problem (according to some criteria) from a set of possible solutions. Mostly, the optimization problem is formulated as a minimization of a target functional. For combinatorial optimization problems no proven exponential speed up has ever been found. Most provable results are similar to Grover's algorithm and have the potential for a modest polynomial speed up.
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View content license ↗ 在量子计算中，量子霸权或量子优势的目标是证明可编程量子计算机可以解决经典计算机无法在任何可行的时间内解决的问题，无论问题的有用性如何。该术语由约翰·普雷斯基尔 (John Preskill) 在 2011 年创造，但这个概念可以追溯到尤里·马宁 (Yuri Manin) 1980 年和理查德·费曼 (Richard Feynman) 1981 年提出的量子计算。从概念上讲，量子霸权既涉及构建强大的量子计算机的工程任务，也涉及寻找可由该量子计算机解决的问题的计算复杂性理论任务，并且与该任务的最著名或可能的经典算法相比具有超多项式加速。
In quantum computing, quantum supremacy or quantum advantage is the goal of demonstrating that a programmable quantum computer can solve a problem that no classical computer can solve in any feasible amount of time, irrespective of the usefulness of the problem. The term was coined by John Preskill in 2011, but the concept dates to Yuri Manin's 1980 and Richard Feynman's 1981 proposals of quantum computing. Conceptually, quantum supremacy involves both the engineering task of building a powerful quantum computer and the computational-complexity-theoretic task of finding a problem that can be solved by that quantum computer and has a superpolynomial speedup over the best known or possible classical algorithm for that task.
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View content license ↗ 在量子计算中，变分量子本征求解器 (VQE) 是一种用于量子化学、量子模拟和优化问题的量子算法。它是一种混合算法，使用经典计算机和量子计算机来查找给定物理系统的基态。给定猜测或模拟，量子处理器计算系统相对于可观测值（通常是哈密顿量）的期望值，并使用经典优化器来改进猜测。该算法基于量子力学的变分法。它最初于 2014 年提出，通讯作者为 Alberto Peruzzo、Alán Aspuru-Guzik 和 Jeremy O'Brien。该算法还在量子机器学习中得到了应用，并通过量子计算机和经典计算机之间的通用混合算法得到了进一步证实。
In quantum computing, the variational quantum eigensolver (VQE) is a quantum algorithm for quantum chemistry, quantum simulations and optimization problems. It is a hybrid algorithm that uses both classical computers and quantum computers to find the ground state of a given physical system. Given a guess or ansatz, the quantum processor calculates the expectation value of the system with respect to an observable, often the Hamiltonian, and a classical optimizer is used to improve the guess. The algorithm is based on the variational method of quantum mechanics. It was originally proposed in 2014, with corresponding authors Alberto Peruzzo, Alán Aspuru-Guzik and Jeremy O'Brien. The algorithm has also found applications in quantum machine learning and has been further substantiated by general hybrid algorithms between quantum and classical computers.
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View content license ↗ 瞬子（或赝粒子）是理论和数学物理学中出现的一个概念。瞬子是量子力学或量子场论中具有有限非零作用的运动方程的经典解。更准确地说，它是欧几里得时空中经典场论运动方程的解。在这样的量子理论中，运动方程的解可以被认为是作用的临界点。动作的临界点可以是动作的局部最大值、局部最小值或鞍点。瞬子在量子场论中很重要，因为：它们出现在路径积分中，作为系统经典行为的主要量子修正，并且它们可用于研究各种系统中的隧道行为，例如杨-米尔斯理论。
An instanton (or pseudoparticle) is a notion appearing in theoretical and mathematical physics. An instanton is a classical solution to equations of motion with a finite, non-zero action, either in quantum mechanics or in quantum field theory. More precisely, it is a solution to the equations of motion of the classical field theory on a Euclidean spacetime. In such quantum theories, solutions to the equations of motion may be thought of as critical points of the action. The critical points of the action may be local maxima of the action, local minima, or saddle points. Instantons are important in quantum field theory because: they appear in the path integral as the leading quantum corrections to the classical behavior of a system, and they can be used to study the tunneling behavior in various systems such as a Yang–Mills theory.
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View content license ↗ 在量子力学中，本征宇称是一个相位因子，作为奇偶校验运算 x i → x i ′ = − x i {\displaystyle x_{i}\rightarrow x_{i}'=-x_{i}} 的特征值出现（关于原点的反映）。
In quantum mechanics, the intrinsic parity is a phase factor that arises as an eigenvalue of the parity operation x i → x i ′ = − x i {\displaystyle x_{i}\rightarrow x_{i}'=-x_{i}} (a reflection about the origin).
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View content license ↗ 系间跨越（ISC）是一种等能无辐射过程，涉及具有不同自旋多重性的两个电子态之间的跃迁。
Intersystem crossing (ISC) is an isoenergetic radiationless process involving a transition between the two electronic states with different spin multiplicity.
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View content license ↗ 在量子力学中，相互作用图（因提出它的保罗·狄拉克而被称为相互作用表示或狄拉克图）是薛定谔图和海森堡图之间的中间表示。在其他两张图中，状态向量或算子都带有时间依赖性，而在交互图中，两者都带有可观测量的部分时间依赖性。相互作用图对于处理由于相互作用而导致的波函数和可观测量的变化非常有用。大多数场论计算都使用相互作用表示，因为它们将多体薛定谔方程的解构造为存在一些未知相互作用部分的自由粒子的解。
In quantum mechanics, the interaction picture (also known as the interaction representation or Dirac picture after Paul Dirac, who introduced it) is an intermediate representation between the Schrödinger picture and the Heisenberg picture. Whereas in the other two pictures either the state vector or the operators carry time dependence, in the interaction picture both carry part of the time dependence of observables. The interaction picture is useful in dealing with changes to the wave functions and observables due to interactions. Most field-theoretical calculations use the interaction representation because they construct the solution to the many-body Schrödinger equation as the solution to free particles in presence of some unknown interacting parts.
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View content license ↗ 子带间跃迁（也称为带内跃迁）是半导体异质结构导带内量化电子能级之间允许的偶极光学激发。当与光学谐振器耦合时，子带间跃迁形成新的混合态光子。这种混合被称为子带间空腔极化子。这些跃迁表现出能量的反交叉，并具有称为真空拉比分裂的分离，类似于原子物理学中的能级排斥。
Intersubband transitions (also known as intraband transitions) are dipolar allowed optical excitations between the quantized electronic energy levels within the conduction band of semiconductor heterostructures. Intersubband transitions when coupled with an optical resonator form new, mixed-state photons. This mixing is referred to as an intersubband cavity-polariton. These transitions exhibit an anticrossing in energy with a separation known as vacuum-Rabi splitting, similar to level repulsion in atomic 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.
View content license ↗ 在量子力学中，电离杂质散射是晶格中电离导致的载流子散射。最原始的模型在概念上可以理解为对晶体杂质附近出现的不平衡局部电荷做出响应的粒子；类似于电子遇到电场。这种效应是掺杂降低迁移率的机制。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。晶体中的杂质原子具有类似于热振动的效应，其中电导率与温度有直接关系。
In quantum mechanics, ionized impurity scattering is the scattering of charge carriers by ionization in the lattice. The most primitive models can be conceptually understood as a particle responding to unbalanced local charge that arises near a crystal impurity; similar to an electron encountering an electric field. This effect is the mechanism by which doping decreases mobility. 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. Impurity atoms in a crystal have an effect similar to thermal vibrations where conductivity has a direct relationship with temperature.
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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 ↗ 原子间库仑衰变（ICD）是具有邻居的原子和分子的普遍基本性质。原子间（分子间）库仑衰变是嵌入环境中的电子激发原子或分子的非常有效的原子间（分子间）弛豫过程。没有环境，这个过程就无法发生。到目前为止，它主要针对原子和分子簇进行了论证，无论它们是范德华还是氢键类型。该过程的本质可以描述如下：考虑一个具有两个子基 A 和 B 的簇。假设从子基 A 中去除了一个内价电子。如果所得（电离）态的能量高于子基 A 的双电离阈值，则开始原子内（分子内）过程（在核心电离俄歇衰变的情况下自动电离）。
Interatomic Coulombic decay (ICD) is a general, fundamental property of atoms and molecules that have neighbors. Interatomic (intermolecular) Coulombic decay is a very efficient interatomic (intermolecular) relaxation process of an electronically excited atom or molecule embedded in an environment. Without the environment the process cannot take place. Until now it has been mainly demonstrated for atomic and molecular clusters, independently of whether they are of van-der-Waals or hydrogen bonded type. The nature of the process can be depicted as follows: Consider a cluster with two subunits, A and B. Suppose an inner-valence electron is removed from subunit A. If the resulting (ionized) state is higher in energy than the double ionization threshold of subunit A then an intraatomic (intramolecular) process (autoionization, in the case of core ionization Auger decay) sets in.
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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 ↗ 在相对论量子力学和量子场论中，Joos-Weinberg 方程是适用于任意自旋 j 的自由粒子的相对论波动方程，j 是玻色子的整数 (j = 1, 2, 3 ...) 或费米子的半整数 (j = 1⁄2, 3⁄2, 5⁄2 ...)。方程的解是波函数，在数学上是多分量旋量场的形式。在量子力学中，自旋量子数通常用 s 表示，但在本文中 j 在文献中更为典型（请参阅参考文献）。它以 20 世纪 60 年代初发现的 Hans H. Joos 和 Steven Weinberg 的名字命名。
In relativistic quantum mechanics and quantum field theory, the Joos–Weinberg equation is a relativistic wave equation applicable to free particles of arbitrary spin j, an integer for bosons (j = 1, 2, 3 ...) or half-integer for fermions (j = 1⁄2, 3⁄2, 5⁄2 ...). The solutions to the equations are wavefunctions, mathematically in the form of multi-component spinor fields. The spin quantum number is usually denoted by s in quantum mechanics, however in this context j is more typical in the literature (see references). It is named after Hans H. Joos and Steven Weinberg, found in the early 1960s.
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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 ↗ 反转恢复是一种磁共振成像序列，可提供组织和病变之间的高对比度。它可用于提供高T1加权图像、高T2加权图像，并抑制来自脂肪、血液或脑脊液的信号。
Inversion recovery is a magnetic resonance imaging sequence that provides high contrast between tissue and lesion. It can be used to provide high T1 weighted image, high T2 weighted image, and to suppress the signals from fat, blood, or cerebrospinal fluid.
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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 ↗ 量子混沌是物理学的一个分支，专注于如何用量子理论来描述混沌经典动力系统。量子混沌试图回答的首要问题是：“量子力学和经典混沌之间的关系是什么？”对应原理指出，经典力学是量子力学的经典极限，特别是普朗克常数与系统作用之比趋于零的极限。如果这是真的，那么经典混沌背后必定存在量子机制（尽管这可能不是研究经典混沌的有效方法）。如果量子力学没有表现出对初始条件的指数敏感性，那么经典混沌中如何会出现对初始条件的指数敏感性，这一定是量子力学的对应原理极限？
Quantum chaos is a branch of physics focused on how chaotic classical dynamical systems can be described in terms of quantum theory. The primary question that quantum chaos seeks to answer is: "What is the relationship between quantum mechanics and classical chaos?" The correspondence principle states that classical mechanics is the classical limit of quantum mechanics, specifically in the limit as the ratio of the Planck constant to the action of the system tends to zero. If this is true, then there must be quantum mechanisms underlying classical chaos (although this may not be a fruitful way of examining classical chaos). If quantum mechanics does not demonstrate an exponential sensitivity to initial conditions, how can exponential sensitivity to initial conditions arise in classical chaos, which must be the correspondence principle limit of quantum mechanics?
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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 ↗ 在量子力学和量子场论中，传播子是指定粒子在给定时间内从一个地方行进到另一个地方，或以一定的能量和动量行进的概率幅度的函数。在用于计算量子场论中的碰撞率的费曼图中，虚拟粒子将其传播者贡献给相应图所描述的散射事件的速率。传播子也可以被视为适合于粒子的波算子的逆函数，因此通常被称为（因果）格林函数（称为“因果”是为了将其与椭圆形拉普拉斯格林函数区分开来）。
In quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one place to another in a given period of time, or to travel with a certain energy and momentum. In Feynman diagrams, which serve to calculate the rate of collisions in quantum field theory, virtual particles contribute their propagator to the rate of the scattering event described by the respective diagram. Propagators may also be viewed as the inverse of the wave operator appropriate to the particle, and are, therefore, often called (causal) Green's functions (called "causal" to distinguish it from the elliptic Laplacian Green's function).
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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 ↗ 量子 1/f 噪声是量子力学固有的基本组成部分。战斗机飞行员、摄影师和科学家都欣赏由于考虑了量子 1/f 噪声而获得的更高质量的图像和信号。自 1925 年以来，工程师们一直在与不需要的 1/f 噪声作斗争，由于其神秘的性质，给它起了富有诗意的名字（例如闪烁噪声、funkelrauschen、bruit de scintillation 等）。大约 50 年后，量子 1/f 噪声理论得到发展，描述了 1/f 噪声的本质，使其可以通过简单的工程公式进行解释和计算。它可以对现代工业和科学的大多数高科技应用的材料、设备和系统进行低噪声优化。该理论包括传统的和相干的量子 1/f 效应 (Q1/fE)。
Quantum 1/f noise is an intrinsic and fundamental part of quantum mechanics. Fighter pilots, photographers, and scientists all appreciate the higher quality of images and signals resulting from the consideration of quantum 1/f noise. Engineers have battled unwanted 1/f noise since 1925, giving it poetic names (such as flicker noise, funkelrauschen, bruit de scintillation, etc.) due to its mysterious nature. The Quantum 1/f noise theory was developed about 50 years later, describing the nature of 1/f noise, allowing it to be explained and calculated via straightforward engineering formulas. It allows for the low-noise optimization of materials, devices and systems of most high-technology applications of modern industry and science. The theory includes the conventional and coherent quantum 1/f effects (Q1/fE).
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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，量子（复数：量子）是参与相互作用的任何物理实体（物理属性）的最小数量。属性可以被“量化”的基本概念被称为“量化假设”。这意味着物理性质的大小只能呈现由一个量子的整数倍组成的离散值。例如，光子是特定频率（或任何其他形式的电磁辐射）的单量子光。类似地，原子内电子的能量是量子化的，并且只能以某些离散值存在。原子和物质通常是稳定的，因为电子只能以原子内离散的能级存在。量子化是更广泛的量子力学物理学的基础之一。
In physics, a quantum (pl.: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum. For example, a photon is a single quantum of light of a specific frequency (or of any other form of electromagnetic radiation). Similarly, the energy of an electron bound within an atom is quantized and can exist only in certain discrete values. Atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom. Quantization is one of the foundations of the much broader physics of quantum mechanics.
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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，特别是量子信息论中，归一化量子态的纯度是一个标量，定义为 γ eq tr ( ρ 2 ) {\displaystyle \gamma \,\equiv \,\operatorname {tr} (\rho ^{2})} 其中 ρ {\displaystyle \rho \,} 是状态的密度矩阵，tr {\displaystyle \operatorname {tr} } 是迹运算。纯度定义了量子态的度量，提供了有关态混合程度的信息。
In quantum mechanics, and especially quantum information theory, the purity of a normalized quantum state is a scalar defined as γ ≡ tr ( ρ 2 ) {\displaystyle \gamma \,\equiv \,\operatorname {tr} (\rho ^{2})} where ρ {\displaystyle \rho \,} is the density matrix of the state and tr {\displaystyle \operatorname {tr} } is the trace operation. The purity defines a measure on quantum states, giving information on how much a state is mixed.
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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 ↗ 脉冲电子顺磁共振（EPR）是一种电子顺磁共振技术，涉及在恒定磁场中对齐电子自旋的净磁化矢量。通过施加短振荡场（通常是微波脉冲）来扰乱这种排列。然后可以测量由样品磁化产生的发射微波信号。微波信号的傅里叶变换产生频域中的 EPR 频谱。通过各种各样的脉冲序列，可以获得有关顺磁性化合物的结构和动力学特性的广泛知识。电子自旋回波包络调制 (ESEEM) 或脉冲电子核双共振 (ENDOR) 等脉冲 EPR 技术可以揭示电子自旋与其周围核自旋的相互作用。
Pulsed electron paramagnetic resonance (EPR) is an electron paramagnetic resonance technique that involves the alignment of the net magnetization vector of the electron spins in a constant magnetic field. This alignment is perturbed by applying a short oscillating field, usually a microwave pulse. One can then measure the emitted microwave signal which is created by the sample magnetization. Fourier transformation of the microwave signal yields an EPR spectrum in the frequency domain. With a vast variety of pulse sequences it is possible to gain extensive knowledge on structural and dynamical properties of paramagnetic compounds. Pulsed EPR techniques such as electron spin echo envelope modulation (ESEEM) or pulsed electron nuclear double resonance (ENDOR) can reveal the interactions of the electron spin with its surrounding nuclear spins.
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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，量子地毯是由波函数演化或概率密度在量子粒子位置坐标与时间的笛卡尔乘积的空间或时空中绘制的类似地毯艺术的规则艺术图案。它是波函数与反射边界相互作用时自干涉的结果。例如，在无限势阱中，最初定域的高斯波包在势阱中心传播后，波函数的各个部分从边界反射后开始相互重叠和干扰。量子地毯的几何形状主要由量子分数复兴决定。量子地毯展示了量子力学的许多原理，包括波粒二象性、量子复兴和退相干。
In quantum mechanics, a quantum carpet is a regular art-like pattern drawn by the wave function evolution or the probability density in the space of the Cartesian product of the quantum particle position coordinate and time or in spacetime resembling carpet art. It is the result of self-interference of the wave function during its interaction with reflecting boundaries. For example, in the infinite potential well, after the spread of the initially localized Gaussian wave packet in the center of the well, various pieces of the wave function start to overlap and interfere with each other after reflection from the boundaries. The geometry of a quantum carpet is mainly determined by the quantum fractional revivals. Quantum carpets demonstrate many principles of quantum mechanics, including wave-particle duality, quantum revivals, and decoherence.
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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 ↗ 质子隧道效应是一种量子隧道效应，涉及质子在一个位点的瞬时消失以及相同质子在由势垒隔开的相邻位点的出现。这两个可用地点以双井势为界，其形状、宽度和高度由一组边界条件决定。根据 WKB 近似，粒子隧穿的概率与其质量和势垒的宽度成反比。电子隧道效应是众所周知的。质子的质量大约是电子的 2000 倍，因此它发生隧道效应的概率要低得多；然而，质子隧道效应仍然会发生，尤其是在势垒宽度减小的低温和高压下。质子隧道效应通常与氢键有关。
Proton tunneling is a type of quantum tunneling involving the instantaneous disappearance of a proton in one site and the appearance of the same proton at an adjacent site separated by a potential barrier. The two available sites are bounded by a double well potential of which its shape, width and height are determined by a set of boundary conditions. According to the WKB approximation, the probability for a particle to tunnel is inversely proportional to its mass and the width of the potential barrier. Electron tunneling is well-known. A proton is about 2000 times more massive than an electron, so it has a much lower probability of tunneling; nevertheless, proton tunneling still occurs especially at low temperatures and high pressures where the width of the potential barrier is decreased. Proton tunneling is usually associated with hydrogen bonds.
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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 ↗ 量子回旋镖效应是一种量子力学现象，由于安德森局域化和系统固有的对称性，通过无序介质发射的波包平均返回到它们的起点。在早期，非零动量的初始宇称不对称性导致了不对称行为：波包从其原点的非零位移。在很长一段时间内，固有的时间反演对称性和安德森局域化的限制效应会导致相应的对称行为：最终速度为零，最终位移为零。
The quantum boomerang effect is a quantum mechanical phenomenon whereby wavepackets launched through disordered media return, on average, to their starting points, as a consequence of Anderson localization and the inherent symmetries of the system. At early times, the initial parity asymmetry of the nonzero momentum leads to asymmetric behavior: nonzero displacement of the wavepackets from their origin. At long times, inherent time-reversal symmetry and the confining effects of Anderson localization lead to correspondingly symmetric behavior: both zero final velocity and zero final displacement.
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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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