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Mathematical formalism used in quantum field theory
The random phase approximation (RPA) is an approximation method in condensed matter physics and nuclear physics. It was first introduced by David Bohm
Random_phase_approximation
Quantum-mechanical simulation framework
coupling strength and the Hartree (H) kernel linearly. Invoking the random phase approximation (RPA) i.e. f Hxc α ( r ′ , r ″ , ω ) ≈ α f H ( r , r ′ ) ; f
Adiabatic connection fluctuation dissipation theorem
Adiabatic_connection_fluctuation_dissipation_theorem
Quantum theory of interacting electron gas
on quantum mechanics (first-order perturbation theory) and the random phase approximation. It is named after Danish physicist Jens Lindhard, who first developed
Lindhard_theory
American-Brazilian-British scientist (1917–1992)
David Pines published the articles in which they introduced the random phase approximation and proposed the plasmon. In 1955, Bohm relocated to Israel, where
David_Bohm
Software for condensed matter physics
(the GW method) and dynamical electronic correlations within the random phase approximation (RPA) and MP2. Originally, VASP was based on code written by Mike
Vienna Ab initio Simulation Package
Vienna_Ab_initio_Simulation_Package
Microscopic interaction in metals
potential can be derived using quantum field theory under the random phase approximation (RPA), which captures the screening effects quantitatively. It
Bardeen–Pines_interaction
Model of electronic band structures of solids
regime. However, in combination with other methods such as the random phase approximation (RPA) model, the dynamic response of systems may also be studied
Tight_binding
implements the RPA (random phase approximation), the TDLDA or ALDA (adiabatic local-density approximation) plus other non-local approximations, including or
DP_code
Indian physicist, educator and administrator
S T (July 2021). "Photoionization of Atomic Systems Using the Random-Phase Approximation Including Relativistic Interactions". Atoms. 10 (3): 71. doi:10
Pranawachandra_Deshmukh
Mathematical operation in quantum optics, general relativity and other areas of physics
of metals and alloys. Westview press. Anderson, P. W. (1958). "Random-phase approximation in the theory of superconductivity". Physical Review. 112 (6):
Bogoliubov_transformation
Type of massless subatomic particle
1103/physrev.110.827. ISSN 0031-899X. Anderson, P. W. (1958-12-15). "Random-Phase Approximation in the Theory of Superconductivity". Physical Review. 112 (6)
Goldstone_boson
Physics of many interacting particles
to a rarefied gas. A quantum technique related in theme is the random phase approximation. BBGKY hierarchy: In liquids and dense gases, it is not valid
Statistical_mechanics
American theoretical physicist (1929–2019)
effect Kaon Non-linear sigma model Omega baryon Pseudoscalar meson Random phase approximation List of Jewish Nobel laureates In 1954, there, working with Francis
Murray_Gell-Mann
Problem in physics and quantum mechanics
plasma) Mean-field theory and extensions (e.g. Hartree–Fock, Random phase approximation) Dynamical mean field theory Many-body perturbation theory and
Many-body_problem
American theoretical physicist (1924–2014)
diagrams. He and Murray Gell-Mann collaborated to show that the random phase approximation (RPA) can be derived using Feynman diagrams in 1957. The relevance
Keith_Brueckner
L. (1972-03-15). "Coherent-Potential Approximation for a Nonoverlapping-Muffin-Tin-Potential Model of Random Substitutional Alloys". Physical Review
Coherent potential approximation
Coherent_potential_approximation
Computational chemistry program
year 2013, comes with post-Kohn–Sham calculations within the random-phase approximation. Turbomole also comes with another significant additions including
TURBOMOLE
Apparent lack of pattern or predictability in events
In common usage, randomness is the apparent or actual lack of definite patterns or predictability in information. A random sequence of events, symbols
Randomness
Topics referred to by the same term
Principado de Asturias, the public radio station of Asturias, Spain Random phase approximation, a method in physics Remotely piloted aircraft Replication protein
RPA
states, including configuration interaction singles (CIS), the random phase approximation (RPA), time-dependent density functional theory (TD-DFT), and
PSI_(computational_chemistry)
American quantum physicist (1924–2018)
density oscillations in metals. They pioneered the use of the random phase approximation. His work with John Bardeen, the Bardeen–Pines interaction between
David_Pines
Structure of the atomic nucleus
In this way, excited states can be reproduced by the means of random phase approximation (RPA), also eventually consistently calculating corrections to
Nuclear_structure
Quantum chemistry and physics software
methods Møller–Plesset perturbation theory Hartree–Fock method Random phase approximation Density functional theory Harris functional Tight binding Semi-empirical
CP2K
Probability of shared birthdays
theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share the same birthday. The birthday
Birthday_problem
Taiwanese physicist
and his contribution to the development of the relativistic random phase approximation for atomic photoionization. In 1990, Lin was appointed to a distinguished
Chii-Dong_Lin
carried out exactly. The final result corresponds to the so-called random phase approximation (RPA) which has been frequently used in solid-state physics. To
Path integrals in polymer science
Path_integrals_in_polymer_science
French physicist (1941–2000)
Hubert Flocard on mean field methods and with Nicole Vinh Mau on random phase approximation at finite temperature. Later, Dominique Vautherin also studied
Dominique_Vautherin
Topological bound state of an electron
field approximation the physics of free fermions in an effective field is recovered. Perturbation theory at the level of the random phase approximation captures
Composite_fermion
Li, Zhendong; Liu, Wenjian (2010). "Spin-adapted open-shell random phase approximation and time-dependent density functional theory. I. Theory". The
Spin_contamination
Israeli theoretical chemist
such as nanocrystals, including stochastic formulations of the random-phase approximation, second order Møller–Plesset perturbation theory and density functional
Eran_Rabani
Quantum algorithm for integer factorization
phase estimation (meaning the | k ⟩ {\displaystyle |k\rangle } where k / 2 2 n {\textstyle k/2^{2n}} is the most accurate approximation of the phase from
Shor's_algorithm
Approximation of physical behavior
Pierre Curie and Pierre Weiss to describe phase transitions. MFT has been used in the Bragg–Williams approximation, models on Bethe lattice, Landau theory
Mean-field_theory
Probability distribution
or phases. The sequence in which each of the phases occurs may itself be a stochastic process. The distribution can be represented by a random variable
Phase-type_distribution
NP-complete problem in computer science
Jennifer; Pittel, Boris (2001), "Phase transition and finite-size scaling for the integer partitioning problem", Random Structures and Algorithms, 19 (3–4):
Partition_problem
Matrix-valued random variable
the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy-Widom distribution". Journal of Multivariate
Random_matrix
Extension of Laplace's method for approximating integrals
roughly the direction of steepest descent or stationary phase. The saddle-point approximation is used with integrals in the complex plane, whereas Laplace’s
Method_of_steepest_descent
Chemical physicist
theory methods, especially density functional theory and the random phase approximation, and their application to materials and molecules, including two-dimensional
Adrienn_Ruzsinszky
Taiwanese theoretical physicist
interactions are evaluated using dielectric functions within the random-phase approximation (RPA). The resulting collective carrier excitations are found
Ming-Fa_Lin
Rule in statistics
occurrences in the population. When n is greater than 30, this is a good approximation of results from more sensitive tests. For example, a pain-relief drug
Rule_of_three_(statistics)
Rayleigh–Gans approximation, also known as Rayleigh–Gans–Debye approximation and Rayleigh–Gans–Born approximation, is an approximate solution to light
Rayleigh–Gans_approximation
Problem in computational complexity theory
where all weights are 1. Randomly assigning each variable to be true with probability 1/2 gives an expected 2-approximation. More precisely, if each clause
Maximum satisfiability problem
Maximum_satisfiability_problem
Light scattering by small particles
same phase. Because the particles are randomly positioned, the scattered light arrives at a particular point with a random collection of phases; it is
Rayleigh_scattering
Physical process of transition between basic states of matter
In physics, chemistry and biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another
Phase_transition
Branch of physics seeking to explain chaotic dynamical systems in terms of quantum theory
over positions) and calculate it again in stationary phase approximation to get an approximation for the density of states d ( E ) {\displaystyle d(E)}
Quantum_chaos
Physicist
Consideration Of Electron Scattering Problems In The Generalized Random Phase Approximation (Grpa) (Thesis). University of Southern California Digital Library
George_Csanak
Number, approximately 3.14
methods, which evaluate the results of multiple random trials, can be used to create approximations of π. Buffon's needle is one such technique: If a
Pi
Algorithm that estimates unknowns from a series of measurements over time
common sensor fusion and data fusion algorithm. Noisy sensor data, approximations in the equations that describe the system evolution, and external factors
Kalman_filter
Electrical circuit detecting phase difference
approximations. Assume that the phase differences will be small (much less than 1 radian, for example). The small-angle approximation for the sine function and
Phase_detector
LeVeque Randall–Sundrum model Random close pack Random energy model Random laser Random matrix Random phase approximation Range (particle radiation) Rangefinder
Index_of_physics_articles_(R)
Generalization of the one-dimensional normal distribution to higher dimensions
(univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination
Multivariate normal distribution
Multivariate_normal_distribution
Process by which dust, particulates, etc. scatter light
radiation by particles of arbitrary shape. The discrete dipole approximation is an approximation of the continuum target by a finite array of polarizable points
Light_scattering_by_particles
Nuclear physicist (born 1943)
used 33 energy density functionals to perform Hartree-Fock based random phase approximation calculations of isoscalar and isovector giant resonances, deducing
Shalom_Shlomo
Statistics function
( x ) {\displaystyle Q(x)} is the probability that a normal (Gaussian) random variable will obtain a value larger than x {\displaystyle x} standard deviations
Q-function
Method of approximating the properties of a composite material
In materials science, effective medium approximations (EMA) or effective medium theory (EMT) pertain to analytical or theoretical modeling that describes
Effective medium approximations
Effective_medium_approximations
Digital signal generator
trigonometric approximations and methods which take advantage of the quadrature symmetry exhibited by sinusoids. Alternatively, the PAC may consist of random access
Numerically controlled oscillator
Numerically_controlled_oscillator
Probability distribution
distributions of random matrices in the beta-ensembles were first presented by Edelman & Persson (2005) using MATLAB. These approximation techniques were
Tracy–Widom_distribution
Disordered magnetic state
condensed matter physics, a spin glass is a magnetic state characterized by randomness, besides cooperative behavior in freezing of spins at a temperature called
Spin_glass
Differential equations involving stochastic processes
listed company shares, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in
Stochastic differential equation
Stochastic_differential_equation
galaxy Radio halo Radio relics Railgun Radio Aurora Explorer (RAX) Random phase approximation Ray tracing (physics) Reactive-ion etching Reaction engine Rectifier
List of plasma physics articles
List_of_plasma_physics_articles
Selection of data points in statistics
determine if a production lot of material meets the governing specifications. Random sampling by using lots is an old idea, mentioned several times in the Bible
Sampling_(statistics)
Model of phase equilibrium in statistical thermodynamics
used in description of phase equilibria. The model is a so-called lattice model and has been derived from a first order approximation of interacting molecule
UNIQUAC
Family of continuous probability distributions
distribution, for which coefficients can be computed and bounds are known. An approximation is k λ ( 1 − 1 3 k + 0.2 ) , {\displaystyle {\frac {k}{\lambda }}\left(1-{\dfrac
Erlang_distribution
State of matter
requires the four state variables to follow the ideal gas law. This approximation is more suitable for applications in engineering although simpler models
Gas
Theory of stochastic processes
realizations of a random vector Y[n] of size N. To optimize the approximation we design a basis that minimizes the average approximation error. This section
Kosambi–Karhunen–Loève theorem
Kosambi–Karhunen–Loève_theorem
Form of scientific experiment
A randomized controlled trial (RCT) is a type of statistical experiment designed to evaluate the efficacy or safety of an intervention by minimizing bias
Randomized_controlled_trial
Type of AC electric motor
Three-phase squirrel-cage induction motors are widely used as industrial drives because they are self-starting, reliable, and economical. Single-phase induction
Induction_motor
Mechanism of light transport
on surface of the depth map. Alternatively, a different approach to approximation can be used, known as texture-space diffusion.[citation needed] As noted
Subsurface_scattering
State of matter with properties of both conventional liquids and crystals
have an isotropic phase at high temperature: heating will eventually drive them into a conventional liquid phase characterized by random and isotropic molecular
Liquid_crystal
Method for approximate evaluation of integrals
Symmetric functions and random partitions). In statistics and statistical physics, this approximation is called the saddle-point approximation. An extension of
Laplace's_method
Methods of mathematical approximation
to the deviation from the initial problem. Formally, we have for the approximation to the full solution A , {\displaystyle \ A\ ,} a series in the
Perturbation_theory
Lattice model of polymer solutions
obtain the total number of polymer-solvent molecular interactions. An approximation following mean field theory is made by following this procedure, thereby
Flory–Huggins_solution_theory
Its limitations stem from: The mean-field approximation ignores fluctuations and spatial correlations (random mixing), which becomes inaccurate at critical
Polymerization-induced phase separation
Polymerization-induced_phase_separation
Thermodynamic process in which no mass or heat is exchanged with surroundings
allowing a convenient "adiabatic approximation". For example, the adiabatic flame temperature uses this approximation to calculate the upper limit of flame
Adiabatic_process
Type of activation function
paper also introduces a few faster approximations for GELU. The first approximation follows from an approximation for Φ ( x ) {\displaystyle \Phi (x)}
Rectified_linear_unit
Dimensionality of space at which the character of the phase transition changes
group analysis of phase transitions in physics, a critical dimension is the dimensionality of space at which the character of the phase transition changes
Critical_dimension
Random temperature-influenced deviations of particles from their average state
effects of random drift and resistance to drift are related by the fluctuation-dissipation theorem. Thermal fluctuations play a major role in phase transitions
Thermal_fluctuations
Presence/absence of symmetry or correlation in a many-particle system
roles. Few techniques to approach each are known, most of which rely on approximations. Common techniques used to analyze systems with quenched disorder include
Order_and_disorder
Mathematical parameter in percolation theory
percolation is considered. This article deals with the critical exponents of random percolation. Percolating systems have a parameter p {\displaystyle p\,\
Percolation critical exponents
Percolation_critical_exponents
Quantum algorithm for eigenvalue estimation
producing a good approximation for θ {\displaystyle \theta } with a small number of gates and a high probability of success. The quantum phase estimation algorithm
Quantum phase estimation algorithm
Quantum_phase_estimation_algorithm
Transport of dissolved species from the highest to the lowest concentration region
diffusion Random walk, model for diffusion Reverse diffusion, against the concentration gradient, in phase separation Rotational diffusion, random reorientation
Diffusion
does not look random, but it satisfies the definition of random variable. This is useful because it puts deterministic variables and random variables in
List of probability distributions
List_of_probability_distributions
Scattering of an electromagnetic plane wave by a sphere
the particle subjects the wave to only a small phase shift. The extinction efficiency in this approximation is given by Q = 2 − 4 p sin p + 4 p 2 ( 1 −
Mie_scattering
Experiment using randomness in some aspect, usually to aid in removal of bias
In science, randomized experiments are the experiments that allow the greatest reliability and validity of statistical estimates of treatment effects.
Randomized_experiment
Probability distribution
Keefer, Donald L. and Bodily, Samuel E. (1983). Three-point Approximations for Continuous Random variables. Management Science 29(5), p. 595–609. "Defense
Beta_distribution
Measure of dependence between two variables
probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables
Mutual_information
Opposition to the passage of an electric current
parameter fitted from measurement data. Because the linear approximation is only an approximation, α {\displaystyle \alpha } is different for different reference
Electrical resistance and conductance
Electrical_resistance_and_conductance
Sequence of data points over time
distinguish two major classes of function approximation problems: First, for known target functions, approximation theory is the branch of numerical analysis
Time_series
20-volume series of books on physics
and R.K.P. Zia. Volume 18: (2001) ISBN 0122203186 'The Random Geometry of Equilibrium Phases', by O. Häggström, H.O. Georgii, and C. Maes. 'Exact Combinatorial
Phase Transitions and Critical Phenomena
Phase_Transitions_and_Critical_Phenomena
Method of statistical physics
written as a function of the relevant variables only, but is a good approximation for the actual density, in particular such that it gives the correct
Mori–Zwanzig_formalism
Fluid dynamics theory on gravity waves
can be estimated from its results. Airy wave theory is also a good approximation for tsunami waves in the ocean, before they steepen near the coast.
Airy_wave_theory
Type of stochastic process
series (like non-stationarities), is then randomized, typically by replacing it with a set of random phases drawn uniformly from [ − π , π ] {\displaystyle
Stationary_process
Probability distribution used in multivariate hypothesis testing
_{np}^{2}.} Another approximation is attributed to C. R. Rao. The distribution can be related to a product of independent beta-distributed random variables u
Wilks's_lambda_distribution
Machine learning technique useful for dimensionality reduction
nonlinear datasets, however, random initiation performed better. There are two ways to interpret a SOM. Because in the training phase weights of the whole neighborhood
Self-organizing_map
Definition of quantum circuits
Neil J.; Selinger, Peter (2014). "Optimal ancilla-free Clifford+ T approximation of z-rotations". arXiv:1403.2975 [quant-ph]. Kliuchnikov, Vadym; Maslov
Clifford_gate
Approach to finding numerical solutions of ordinary differential equations
y_{n+1}=y_{n}+hf(t_{n},y_{n}).} The value of y n {\displaystyle y_{n}} is an approximation of the solution at time t n {\displaystyle t_{n}} , i.e., y n ≈ y (
Euler_method
Notion in statistics
same result is used when approximating the posterior with Laplace's approximation, where the Fisher information appears as the covariance of the fitted
Fisher_information
Matrix decomposition
applications of the SVD include computing the pseudoinverse, matrix approximation, and determining the rank, range, and null space of a matrix. The SVD
Singular_value_decomposition
zero-component classical vector model of ferromagnetism near the phase transition and a self-avoiding random walk of a polymer chain of infinite length on a lattice
Polymer_field_theory
Model of quantum optics
use a mean-field approximation, in which the cavity field operators are substituted by their expectation values. Under this approximation, which is exact
Dicke_model
Electrical engineering problem
with an initial phase information that is a noisy or heavily quantized version( but not random or uniform phase) of the original phase information, results
Multidimensional signal restoration
Multidimensional_signal_restoration
RANDOM PHASE-APPROXIMATION
RANDOM PHASE-APPROXIMATION
Surname or Lastname
English
English : variant of Brandon.
Surname or Lastname
English
English : variant spelling of Randall.Americanized spelling of Randel.
Surname or Lastname
English (chiefly East Anglia)
English (chiefly East Anglia) : patronymic from the Middle English personal name Rand(e) (see Rand 1).
Female
English
Variant spelling of English Randy, RANDI means "worthy of admiration."
Male
Hungarian
 Variant spelling of Hungarian András, ANDOR means "man; warrior." Compare with another form of Andor.
Male
Norwegian
 Norwegian form of Old Norse Arnþórr, ANDOR means "eagle of Thor." Compare with another form of Andor.
Boy/Male
English
Son of Rand.
Male
English
Pet form of English Randall and Randolph, both RANDY means "shield-wolf." Compare with feminine Randy.
Male
English
Medieval form of English Randolf, RANDAL means "shield-wolf."
Surname or Lastname
English
English : unexplained; perhaps a variant of Francom.
Male
Scandinavian
 Scandinavian form of Old Norse Randolfr, RANDOLF means "shield-wolf." Compare with another form of Randolf.
Surname or Lastname
English
English : variant of Ransom.
Surname or Lastname
English
English : patronymic from Rand 1.
Surname or Lastname
English
English : probably a variant of Crandon, a habitational name from Crandon in Somerset or Crandean in Falmer, Sussex. Compare Grandin.
Surname or Lastname
English
English : variant of Rand 1, from the Old French oblique case.
Male
French
French form of Latin Stephanus, STÉPHANE means "crown."
Boy/Male
English American
Son of Rand.
Male
English
Middle English surname (of Norman French origin) transferred to forename use, CHASE means "hunter."Â
Male
English
 Variant spelling of Middle English Randulf, RANDOLF means "shield-wolf." Compare with other forms of Randolf.
Surname or Lastname
English
English : metonymic occupational name for a huntsman, or rather a nickname for an exceptionally skilled huntsman, from Middle English chase ‘hunt’ (Old French chasse, from chasser ‘to hunt’, Latin captare).Southern French : topographic name for someone who lived in or by a house, probably the occupier of the most distinguished house in the village, from a southern derivative of Latin casa ‘hut’, ‘cottage’, ‘cabin’.Thomas Chase came to MA from Chesham, Buckinghamshire, England, in the 1640s, and had many prominent descendants. Samuel Chase, born in Somerset Co., MD, in 1741, was one of the first members of the U.S. Supreme Court; Philander Chase, born in Cornish, NH, in 1741 was a prominent Episcopal clergyman, and his nephew Salmon Portland Chase (1808–73), also born in Cornish, was governor of OH, a U.S. senator, and secretary of the U.S. Treasury during the Civil War.
RANDOM PHASE-APPROXIMATION
RANDOM PHASE-APPROXIMATION
Surname or Lastname
English
English : variant of Jepson.
Boy/Male
Indian, Sanskrit
The Bird Chummum
Male
Egyptian
, the divine energetic spirit.
Girl/Female
Gujarati, Hindu, Indian, Kannada, Marathi, Sindhi, Telugu
Joined; United
Biblical
lifting up; profiting; taking away slander
Boy/Male
Hebrew American Biblical
God has helped.
Girl/Female
Hindu, Indian, Tamil
Wealthy
Boy/Male
Tamil
Lord of wealth, Lord Vishnu
Boy/Male
Hindu, Indian
Kind; Thankful; Loving; Gift to the World
Male
Czechoslovakian
, victor of the people.
RANDOM PHASE-APPROXIMATION
RANDOM PHASE-APPROXIMATION
RANDOM PHASE-APPROXIMATION
RANDOM PHASE-APPROXIMATION
RANDOM PHASE-APPROXIMATION
adv.
In a random manner.
a.
Going at random or by chance; done or made at hazard, or without settled direction, aim, or purpose; hazarded without previous calculation; left to chance; haphazard; as, a random guess.
n.
A particular appearance or state in a regularly recurring cycle of changes with respect to quantity of illumination or form of enlightened disk; as, the phases of the moon or planets. See Illust. under Moon.
pl.
of Phase
n.
Any appearance or aspect of an object of mental apprehension or view; as, the problem has many phases.
n.
To exact a ransom for, or a payment on.
p. pr. & vb. n.
of Ransom
n.
The liberty or franchise of having a chase; free chase.
n.
Random.
n.
Ransom.
n.
Extra hazard; chance; accident; random.
n.
To redeem from captivity, servitude, punishment, or forfeit, by paying a price; to buy out of servitude or penalty; to rescue; to deliver; as, to ransom prisoners from an enemy.
n.
A roving motion; course without definite direction; want of direction, rule, or method; hazard; chance; -- commonly used in the phrase at random, that is, without a settled point of direction; at hazard.
n.
The release of a captive, or of captured property, by payment of a consideration; redemption; as, prisoners hopeless of ransom.
n.
Distance to which a missile is cast; range; reach; as, the random of a rifle ball.
v. i.
To give chase; to hunt; as, to chase around after a doctor.
v. i.
To group notes into phrases; as, he phrases well. See Phrase, n., 4.
n.
Anything driven at random.
v. i.
To go or stray at random.