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Fracton (subdimensional Particle)
A fracton is an emergent topological quasiparticle excitation which is immobile when in isolation. Many theoretical systems have been proposed in which fractons exist as elementary excitations. Such systems are known as fracton models. Fractons have been identified in various CSS codes as well as in symmetric tensor gauge theories. Gapped fracton models often feature a topological ground state degeneracy that grows exponentially and sub-extensively with system size. Among the gapped phases of fracton models, there is a non-rigorous phenomenological classification into "type I" and "type II". Type I fracton models generally have fracton excitations that are completely immobile, as well as other excitations, including bound states, with restricted mobility. Type II fracton models generally have fracton excitations and no mobile particles of any form. Furthermore, isolated fracton particles in type II models are associated with nonlocal operators with intricate fractal structure. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fracton
A fracton is a collective quantized vibration on a substrate with a fractal structure.. Fractons are the fractal analog of phonons. Phonons are the result of applying translational symmetry to the potential in a Schrödinger equation. Fractal self-similarity can be thought of as a symmetry somewhat comparable to translational symmetry. Translational symmetry is symmetry under displacement or change of position, and fractal self-similarity is symmetry under change of scale. The quantum mechanical solutions to such a problem in general lead to a continuum of states with different frequencies Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from '' angular frequency''. Frequency is measured in hertz (Hz) which is e .... In other words, a fracton band is comparable to a phonon band. The vibrational modes are restricted to part of the substrate and are thus not f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Einstein Notation
In mathematics, especially the usage of linear algebra in Mathematical physics, Einstein notation (also known as the Einstein summation convention or Einstein summation notation) is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving brevity. As part of mathematics it is a notational subset of Ricci calculus; however, it is often used in physics applications that do not distinguish between tangent and cotangent spaces. It was introduced to physics by Albert Einstein in 1916. Introduction Statement of convention According to this convention, when an index variable appears twice in a single term and is not otherwise defined (see Free and bound variables), it implies summation of that term over all the values of the index. So where the indices can range over the set , : y = \sum_^3 c_i x^i = c_1 x^1 + c_2 x^2 + c_3 x^3 is simplified by the convention to: : y = c_i x^i The upper indices are not exponents but are in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystallographic Defect
A crystallographic defect is an interruption of the regular patterns of arrangement of atoms or molecules in crystalline solids. The positions and orientations of particles, which are repeating at fixed distances determined by the unit cell parameters in crystals, exhibit a periodic crystal structure, but this is usually imperfect.Ehrhart, P. (1991Properties and interactions of atomic defects in metals and alloys, volume 25 of Landolt-Börnstein, New Series III, chapter 2, p. 88, Springer, Berlin Several types of defects are often characterized: point defects, line defects, planar defects, bulk defects. Topological homotopy establishes a mathematical method of characterization. Point defects Point defects are defects that occur only at or around a single lattice point. They are not extended in space in any dimension. Strict limits for how small a point defect is are generally not defined explicitly. However, these defects typically involve at most a few extra or missing atoms. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Disclination
In crystallography, a disclination is a line defect in which rotational symmetry is violated. In analogy with dislocations in crystals, the term, ''disinclination'', for liquid crystals first used by Frederick Charles Frank and since then has been modified to its current usage, ''disclination''. It is a defect in the orientation of director whereas a dislocation is a defect in positional order. Example in two dimensions In 2D, disclinations and dislocations are point defects instead of line defects as in 3D. They are topological defects and play a central role in melting of 2D crystals within the KTHNY theory, based on two Kosterlitz–Thouless transitions. Equally sized discs (spheres, particles, atoms) form a hexagonal crystal as dense packing in two dimensions. In such a crystal, each particle has six nearest neighbors. Local strain and twist (for example induced by thermal motion) can cause configurations where discs (or particles) have a coordination number different of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the scientific study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." It is one of the most fundamental scientific disciplines. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linearized Gravity
In the theory of general relativity, linearized gravity is the application of perturbation theory to the metric tensor that describes the geometry of spacetime. As a consequence, linearized gravity is an effective method for modeling the effects of gravity when the gravitational field is weak. The usage of linearized gravity is integral to the study of gravitational waves and weak-field gravitational lensing. Weak-field approximation The Einstein field equation (EFE) describing the geometry of spacetime is given as (using natural units) :R_ - \fracRg_ = 8\pi GT_ where R_ is the Ricci tensor, R is the Ricci scalar, T_ is the energy–momentum tensor, and g_ is the spacetime metric tensor that represent the solutions of the equation. Although succinct when written out using Einstein notation, hidden within the Ricci tensor and Ricci scalar are exceptionally nonlinear dependencies on the metric which render the prospect of finding exact solutions impractical in most syst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Gravity
Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics; it deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vicinity of black holes or similar compact astrophysical objects, such as neutron stars. Three of the four fundamental forces of physics are described within the framework of quantum mechanics and quantum field theory. The current understanding of the fourth force, gravity, is based on Albert Einstein's general theory of relativity, which is formulated within the entirely different framework of classical physics. However, that description is incomplete: describing the gravitational field of a black hole in the general theory of relativity leads physical quantities, such as the spacetime curvature, to diverge at the center of the black hole. This signals the breakdown of the general theory of relativity and the need for a theory that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Computing
Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though current quantum computers may be too small to outperform usual (classical) computers for practical applications, larger realizations are believed to be capable of solving certain computational problems, such as integer factorization (which underlies RSA encryption), substantially faster than classical computers. The study of quantum computing is a subfield of quantum information science. There are several models of quantum computation with the most widely used being quantum circuits. Other models include the quantum Turing machine, quantum annealing, and adiabatic quantum computation. Most models are based on the quantum bit, or "qubit", which is somewhat analogous to the bit in classical computation. A qubit can be in a 1 or 0 quantu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hard Disk Drive
A hard disk drive (HDD), hard disk, hard drive, or fixed disk is an electro-mechanical data storage device that stores and retrieves digital data using magnetic storage with one or more rigid rapidly rotating platters coated with magnetic material. The platters are paired with magnetic heads, usually arranged on a moving actuator arm, which read and write data to the platter surfaces. Data is accessed in a random-access manner, meaning that individual blocks of data can be stored and retrieved in any order. HDDs are a type of non-volatile storage, retaining stored data when powered off. Modern HDDs are typically in the form of a small rectangular box. Introduced by IBM in 1956, HDDs were the dominant secondary storage device for general-purpose computers beginning in the early 1960s. HDDs maintained this position into the modern era of servers and personal computers, though personal computing devices produced in large volume, like cell phones and tablets, rely ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Qubit
In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two states can be taken to be the vertical polarization and the horizontal polarization. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of both states simultaneously, a property that is fundamental to quantum mechanics and quantum computing. Etymology The coining of the term ''qubit'' is attributed to Benjamin Schumacher. In the acknowledgments of his 1995 paper, Schumacher states that the term ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stabilizer Code
The theory of quantum error correction plays a prominent role in the practical realization and engineering of quantum computing and quantum communication devices. The first quantum error-correcting codes are strikingly similar to classical block codes in their operation and performance. Quantum error-correcting codes restore a noisy, decohered quantum state to a pure quantum state. A stabilizer quantum error-correcting code appends ancilla qubits to qubits that we want to protect. A unitary encoding circuit rotates the global state into a subspace of a larger Hilbert space. This highly entangled, encoded state corrects for local noisy errors. A quantum error-correcting code makes quantum computation and quantum communication practical by providing a way for a sender and receiver to simulate a noiseless qubit channel given a noisy qubit channel whose noise conforms to a particular error model. The stabilizer theory of quantum error correction allows one to import some classi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amorphous Solid
In condensed matter physics and materials science, an amorphous solid (or non-crystalline solid, glassy solid) is a solid that lacks the long-range order that is characteristic of a crystal. Etymology The term comes from the Greek ''a'' ("without"), and ''morphé'' ("shape, form"). In some older articles and books, the term was used synonymously with glass. Today, "glassy solid" or "amorphous solid" is considered the overarching concept. Polymers are often amorphous. Structure Amorphous materials have an internal structure comprising interconnected structural blocks that can be similar to the basic structural units found in the corresponding crystalline phase of the same compound. Unlike crystalline materials, however, no long-range order exists. Localized order in amorphous materials can be categorized as short or medium range order. By convention, short range order extends only to the nearest neighbor shell, typically only 1-2 atomic spacings. Medium range order is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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