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Initial estimate or framework to the solution of a mathematical problem
In physics and mathematics, an ansatz (/ˈænsæts/; German: [ˈʔanzats] , meaning: "initial placement of a tool at a work piece", plural ansatzes or, from
Ansatz
Method for finding the exact solution of certain quantum mechanics models
In physics, the Bethe ansatz is used to calculate the exact wave functions of certain quantum-mechanical many-body systems, most commonly in one spatial
Bethe_ansatz
Method in general relativity
In mathematics, the Gibbons–Hawking ansatz is a method of constructing gravitational instantons introduced by Gary Gibbons and Stephen Hawking (1978, 1979)
Gibbons–Hawking_ansatz
Quantum algorithm
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
Variational quantum eigensolver
Variational_quantum_eigensolver
Statistical model in quantum mechanics of magnetic materials
Heisenberg model in one dimension may be solved exactly using the Bethe ansatz. In the algebraic formulation, these are related to particular quantum affine
Quantum_Heisenberg_model
Method used to solve integrable many-body quantum systems
inverse scattering method, similar to the closely related algebraic Bethe ansatz, is a method for solving integrable models in 1+1 dimensions, introduced
Quantum inverse scattering method
Quantum_inverse_scattering_method
Quantum optical theoretical system
as the complex roots λ p , j {\displaystyle \lambda _{p,j}} of a Bethe ansatz. Every λ p , j {\displaystyle \lambda _{p,j}} for p ∈ { 1 , 2 , . . . m
Tavis–Cummings_model
German historian (born 1966)
Historische Institut Paris und seine Gründungsväter. Ein personengeschichtlicher Ansatz. Munich 2007, ISBN 978-3-486-58519-3. Vorgeschichte und Gründung des Deutschen
Ulrich_Pfeil
Solvable 1+1 dimensional quantum field theory
Thirring model by Bethe ansatz was first published in Russian. Ultraviolet renormalization was done in the frame of the Bethe ansatz. The fractional charge
Thirring_model
German-American physicist (1906–2005)
was a professor at Cornell University. In 1931, Bethe developed the Bethe ansatz, which is a method for finding the exact solutions for the eigenvalues and
Hans_Bethe
Physics model in statistical mechanics
Hamiltonians. There are several methods of solution, including Algebraic Bethe ansatz, used by Gaudin Separation of variables, used by Sklyanin Correlation functions/opers
Gaudin_model
Technique for solving linear ordinary differential equations
desired. The method also applies to n-th order equations. In this case the ansatz will yield an (n−1)-th order equation for v {\displaystyle v} . Consider
Reduction_of_order
Method of solution for inhomogeneous ODEs
in order to find the best possible form of the particular solution, an ansatz or 'guess' is made as to the appropriate form, which is then tested by differentiating
Method of undetermined coefficients
Method_of_undetermined_coefficients
Method for approximating many-body systems
wavefunction of the coupled-cluster theory is written as an exponential ansatz: | Ψ ⟩ = e T | Φ 0 ⟩ , {\displaystyle |\Psi \rangle =e^{T}|\Phi _{0}\rangle
Coupled_cluster
Quantum mechanics principle
dimension, and for other models solvable by Bethe ansatz. The ground state in models solvable by Bethe ansatz is a Fermi sphere. The Pauli exclusion principle
Pauli_exclusion_principle
Semi-automatic pistol
Charakterdesign für Computer- und Videospiele: Ein medienpsychologischer Ansatz (in German). Springer VS. p. 46. ISBN 9783658026264. Milburn, Colin; Raley
AMT_Hardballer
Numerical variational technique
(the orbitals basically) used in the simulation. The matrices in the MPS ansatz are not unique, one can, for instance, insert B − 1 B {\displaystyle B^{-1}B}
Density matrix renormalization group
Density_matrix_renormalization_group
Coordinate system used to represent certain spacetimes
undetermined functions of the isotropic coordinate r, is often used as a metric Ansatz in deriving static spherically symmetric solutions in general relativity
Isotropic_coordinates
Type of integrable system
chains Examples Quantum Heisenberg model Gaudin model Theory Algebraic Bethe ansatz Quantum inverse scattering method Yang–Baxter equation Contributors Classical
Hitchin_system
1984 studio album by Manuel Göttsching
Side one No. Title Length 1. "Ruhige Nervosität" 13:00 2. "Gemäßigter Aufbruch" 10:00 3. "...Und Mittelspiel" 7:00 4. "Ansatz" 1:00
E2-E4
Type of ordinary differential equation
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
Bernoulli differential equation
Bernoulli_differential_equation
dune-geometry, grid interface: dune-grid, linear algebra classes: dune-istl, local ansatz functions: dune-localfunctions. In addition, there are several further modules
Dune_(mathematics_software)
Property of certain dynamical systems
incorporated into the quantum inverse scattering method where the algebraic Bethe ansatz can be used to obtain explicit solutions. Examples of quantum integrable
Integrable_system
English theoretical physicist (1942–2018)
Bekenstein–Hawking formula Hawking energy Hawking–Page phase transition Gibbons–Hawking ansatz Gibbons–Hawking effect Gibbons–Hawking space Gibbons–Hawking–York boundary
Stephen_Hawking
Type of model in quantum statistical physics
Heisenberg model was determined, by Hans Bethe using the Bethe ansatz. Now the term Bethe ansatz is used generally to refer to many ansatzes used to solve
Spin_chain
Gauge theory providing unifying formalism for integrable systems
chains Examples Quantum Heisenberg model Gaudin model Theory Algebraic Bethe ansatz Quantum inverse scattering method Yang–Baxter equation Contributors Classical
Four-dimensional Chern–Simons theory
Four-dimensional_Chern–Simons_theory
Class of numerical techniques
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
Finite_difference_method
Russian-Soviet mathematical physicist
with Ludvig Faddeev and Evgeny Sklyanin he formulated the algebraic Bethe ansatz and quantum inverse scattering method. Together with Ludvig Faddeev and
Leon_Takhtajan
Equation for two-body bound states
\phi _{i}} into a bound state ψ {\displaystyle \psi } , and then makes an Ansatz for the Green function in the vicinity of the pole as G ≈ Ψ Ψ ¯ P 2 − M
Bethe–Salpeter_equation
Computational model used in machine learning
June 2019). "Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems". Physical Review Letters. 122 (25) 250501. arXiv:1902
Neural network (machine learning)
Neural_network_(machine_learning)
Optimization algorithms using quantum computing
have been proposed, which include variations to the ansatz of the basic algorithm. The choice of ansatz typically depends on the problem type, such as combinatorial
Quantum optimization algorithms
Quantum_optimization_algorithms
Ansatz in condensed matter physics
In condensed matter physics, the Laughlin wavefunction is an ansatz, proposed by Robert Laughlin for the ground state of a two-dimensional electron gas
Laughlin_wavefunction
Regular infinite tree structure used in statistical mechanics
than on other lattices. The solutions are related to the often used Bethe ansatz for these systems. When working with the Bethe lattice, it is often convenient
Bethe_lattice
Topics referred to by the same term
Europe Movement 2025 (DiEM25) Multi-scale entanglement renormalization ansatz, proposed by Spanish physicist Guifré Vidal All pages with titles containing
Mera
Type of differential equation
conditions, then it is the solution (this also applies to ODEs). We assume as an ansatz that the dependence of a solution on the parameters space and time can be
Partial_differential_equation
Chinese-American mathematician (born 1949)
[TY91] With Brian Greene, Alfred Shapere, and Cumrun Vafa, Yau introduced an ansatz for a Kähler metric on the set of regular points of certain surjective holomorphic
Shing-Tung_Yau
Differential equation that is linear with respect to the unknown function
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
Linear_differential_equation
Theoretical physicist
applications of non-perturbative quantum field theory methods and the Bethe Ansatz. He graduated from the Moscow Physical Technical Institute in 1977, before
Alexei_Tsvelik
Attempt to find a consistent theory of quantum gravity
onto subspaces spanned by a suitable ansatz for Γ k {\displaystyle \Gamma _{k}} . In its simplest form, such an ansatz is given by the Einstein–Hilbert action
Asymptotic_safety
Coordinate system in black hole physics
functions of the Schwarzschild radial coordinate r, is often used as a metric ansatz in deriving static spherically symmetric solutions in general relativity
Schwarzschild_coordinates
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
List of nonlinear ordinary differential equations
List_of_nonlinear_ordinary_differential_equations
German–American philosopher, sociologist, and political theorist (1898–1979)
"Protosozialismus und Spätkapitalismus. Versuch einer theoretischen Synthese von Bahros Ansatz (von Herbert Marcuse)". Open theory. Archived from the original on 2013-05-30
Herbert_Marcuse
{\displaystyle O_{k}(X)} are time-independent operators that define the specific ansatz. The time evolution of the parameters a k ( t ) {\displaystyle a_{k}(t)}
Time-dependent variational Monte Carlo
Time-dependent_variational_Monte_Carlo
Function specifying the behavior of a component in an electronic or control system
y(t)=|g(j\omega )|\sin(\omega t+\arg(g(j\omega ))).} To show this, use the ansatz function y ( t ) = c e j ω t , {\displaystyle y(t)=ce^{j\omega t},} plug
Transfer_function
Existence and uniqueness of solutions to initial value problems
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
Picard–Lindelöf_theorem
Approximating method in quantum mechanics
is some overlap between the ansatz and the ground state (otherwise, it's a bad ansatz). We wish to normalize the ansatz, so we have the constraints ⟨
Variational method (quantum mechanics)
Variational_method_(quantum_mechanics)
Mathematical relation defining a sequence
form as a n = r n {\displaystyle a_{n}=r^{n}} ? Substituting this guess (ansatz) in the recurrence relation, we find that r n = A r n − 1 + B r n − 2 {\displaystyle
Linear recurrence with constant coefficients
Linear_recurrence_with_constant_coefficients
Physics models of a 1D gas of bosons
the Bethe Ansatz. Oxford University Press. ISBN 978-0-19-166804-3. Dorlas, Teunis C. (1993). "Orthogonality and Completeness of the Bethe Ansatz Eigenstates
Lieb–Liniger_model
Type of functional equation (mathematics)
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
Differential_equation
19th-century German school of painting
allgemein durchgesetzt. Der vom Kunsthistoriker Wolfgang Hütt vertretene Ansatz, das Jahr 1869 als das Datum einer gescheiterten Künstler-Revolte gegen
Düsseldorf_School_of_painting
chosen either by the program according to some perturbation theoretical ansatz according to a threshold provided by the user or simply by truncating excitations
Multireference configuration interaction
Multireference_configuration_interaction
Experimental technique to determine the distribution of electrons in solids
the previous two equations. The algorithm is as follows: start with an ansatz bare band, calculate Σ ″ ( E ) {\displaystyle \Sigma ''(E)} by eq. (2),
Angle-resolved photoemission spectroscopy
Angle-resolved_photoemission_spectroscopy
Technique for solving hyperbolic partial differential equations
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
Method_of_characteristics
Theorem regarding the existence of a solution to a differential equation
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
Peano_existence_theorem
Microscopic theory of superconductivity
attraction. Within this potential, a variational ansatz for the wave function is proposed. This ansatz was later shown to be exact in the dense limit of
BCS_theory
Differential equation containing derivatives with respect to only one variable
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
Ordinary differential equation
Ordinary_differential_equation
American jazz trumpeter and singer (1901–1971)
with a razor blade. By the 1950s, Armstrong was an official spokesman for Ansatz-Creme Lip Salve. During a backstage meeting with trombonist Marshall Brown
Louis_Armstrong
Assumption in the kinetic theory of gases
allows using the principle of maximum entropy in order to generalize the ansatz to higher-order distribution functions. Free molecular flow Ergodic hypothesis
Molecular_chaos
Solution method for linear differential equations
determined by the equation. See the example below. Substituting the above ansatz into the differential equation and cancelling out the exponential terms
WKB_approximation
Standardized variety of German language
abseilen (v.) abseil to descend by rope / to fastrope Angst angst fear Ansatz ansatz onset / entry / math / approach Anschluß/Anschluss Anschluss connection
Standard_German
Generalized function whose value is zero everywhere except at zero
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
Dirac_delta_function
Methods of mathematical approximation
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
Perturbation_theory
Branch of ordinary differential equations
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
Floquet_theory
Geometric representation of material yield
{\displaystyle \chi _{6}=\{1,-1\}} . The isogonal dodecagons of the multiplicative ansatz criterion of hexagonal symmetry containing the Ishlinsky-Ivlev criterion
Yield_surface
Space of all possible states that a system can take
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
Phase_space
Four-dimensional complete Riemannian manifold satisfying the vacuum Einstein equations
for constructing gravitational instantons, including the Gibbons–Hawking Ansatz, twistor theory, and the hyperkähler quotient construction. Gravitational
Gravitational_instanton
Concept in theoretical physics
{\displaystyle S_{\text{eff}}=A+BL+CL^{2}+DL^{3}+\cdots .} Using the above ansatz, it is possible to solve the renormalization group equation perturbatively
Renormalization_group
Approach to finding numerical solutions of ordinary differential equations
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
Euler_method
American science fiction editor and writer
Tweek, Ecce Fanno, Telos, Zed, and Flash Point. Through their small press, Ansatz Press, Patrick and Teresa Nielsen Hayden published Samuel R. Delany's Wagner/Artaud:
Patrick_Nielsen_Hayden
Settlement in Omaheke Region, Namibia
Retrieved 28 October 2020. Anne Kammesheidt: Das Projekt Otjivero - ein neuer Ansatz der Entwicklungspolitik in Namibia: Entwicklungsökonomische Voraussetzungen
Omitara
Chinese-American physicist (1922–2025)
scattering many-body system, which resurrected the interest in the Bethe ansatz and allowed to better description of 1D fermions. Finite temperature (1969):
Yang_Chen-Ning
Statistical lattice model with long-range interactions
chain. The system has been exactly solved by means of an 'extended' Bethe ansatz method. The model was solved by Inozemtsev first in the infinite lattice
Inozemtsev_model
Determinant of the matrix of first derivatives of a set of functions
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
Wronskian
Spanish physicist
time-evolving block decimation (TEBD) and multiscale entanglement renormalization ansatz (MERA). He was previously a faculty member of Perimeter Institute in Waterloo
Guifré_Vidal
German song
Liederspatz – via liederlexikon.de Anna Ernst:"Dieses Ausmaß habe ich im Ansatz nicht erwartet", Süddeutsche Zeitung, 29 December 2019. "Zeljo Davutovic
Meine Oma fährt im Hühnerstall Motorrad
Meine_Oma_fährt_im_Hühnerstall_Motorrad
Process of finding an approximation
package contents are close to the nominal contents. Abundance estimation Ansatz Ballpark estimate Back-of-the-envelope calculation Conjecture Cost estimate
Estimation
German association football club
original on 30 July 2023. Retrieved 3 June 2017. "Fortuna Düsseldorf: 'Ansatz des gut Spielens zu hoch angesiedelt'". RP ONLINE. 19 May 2013. Archived
Fortuna_Düsseldorf
Portuguese theoretical physicist
Perimeter Institute ICTP-SAIFR Thesis Integrability in AdS/CFT – Bethe ansatz and String quantization beyond infinite volume (2008) Website Perimeter
Pedro_Vieira
Numerical method for solving physical or engineering problems
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
Finite_element_method
Conformal field theory on a 2D spacetime
Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz". Communications in Mathematical Physics. 177 (2): 381–398. arXiv:hep-th/9412229
Two-dimensional conformal field theory
Two-dimensional_conformal_field_theory
Class of ordinary differential equations
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
Sturm–Liouville_theory
Theorem of dynamical systems
chains Examples Quantum Heisenberg model Gaudin model Theory Algebraic Bethe ansatz Quantum inverse scattering method Yang–Baxter equation Contributors Classical
Liouville–Arnold_theorem
Wave where gravity is the main restoring force
invariance of the system in the x-direction, it is possible to make the ansatz ψ ( x , z , t ) = e i k ( x − c t ) Ψ ( z ) , {\displaystyle \psi \left(x
Gravity_wave
German physicist (born 1977)
solid-state physics (such as one-dimensional spin chains and the Bethe ansatz), Beisert, Staudacher, and colleagues made progress in gauge/string duality
Niklas_Beisert
Description of the ground state of a quantum system
make a variational approximation. The basic idea is to make a variational ansatz for the wavefunction with free parameters, plug it into the free energy
Gross–Pitaevskii_equation
Physical interaction in post-classical physics
of charges spread by the wave function. The Laughlin wavefunction is an ansatz for the quasiparticle wavefunction. If the expectation value of the interaction
Static forces and virtual-particle exchange
Static_forces_and_virtual-particle_exchange
Methods of calculating definite integrals
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
Numerical_integration
Identity relating to differential equations
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
Abel's_identity
Physics of many interacting particles
solutions have been found for a few toy models. Some examples include the Bethe ansatz, square-lattice Ising model in zero field, hard hexagon model. Although
Statistical_mechanics
Physical theory with fields invariant under the action of local "gauge" Lie groups
can obtain the equations for the gauge theory by: starting from a naïve ansatz without the gauge field (in which the derivatives appear in a "bare" form);
Gauge_theory
Nonlinear partial differential equation
doi:10.1103/RevModPhys.51.659. Faddeev, L. D. (1996). "How Algebraic Bethe Ansatz works for integrable model". arXiv:hep-th/9605187. sine-Gordon equation
Sine-Gordon_equation
Method for solving certain nonlinear partial differential equations
chains Examples Quantum Heisenberg model Gaudin model Theory Algebraic Bethe ansatz Quantum inverse scattering method Yang–Baxter equation Contributors Classical
Inverse_scattering_transform
Nigerian-American anthropologist (1939–2003)
(2012). Bildung als Adaptation? John U. Ogbu und der kulturökologische Ansatz der Minderheiten- und Sozialisationsforschung. Wissenschaftlicher Verlag
John_Ogbu
Experimental technology level
energy. The algorithm constructs a parameterized quantum circuit called an ansatz∣ψ(θ)⟩, to approximate the ground state of a molecular Hamiltonian H ^ :
Noisy intermediate-scale quantum computing
Noisy_intermediate-scale_quantum_computing
attack. Angriffsmuster – attack pattern. Angriffsziel – attack objective. Ansatz (attack) – First World War military term, used in National Socialist vocabulary
Glossary of German military terms
Glossary_of_German_military_terms
and Cumrun Vafa, who first described it in 1996 using the Gibbons–Hawking ansatz. Another construction was given by Davide Gaiotto, Gregory Moore and Andrew
Ooguri–Vafa_metric
Indian theoretical physicist (born 1951)
model. Working on directed-site animals-enumeration problem using Bethe ansatz method, he proposed the evolution operator which has since been subjected
Deepak_Dhar
German virologist (1936–2023)
PMID 6036237. S2CID 30764560. Müller-Jung, Joachim (30 May 2023). "Sein Ansatz war die radikale Krebsprävention". FAZ (in German). Retrieved 31 May 2023
Harald_zur_Hausen
Visual representation used in non-linear control system analysis
Dirac delta function Solution methods Inspection Method of characteristics Ansatz Euler Exponential response formula Finite difference Crank–Nicolson Finite
Phase_plane
Unstable behavior of two contacting fluids of different densities
invariance of the system in the x-direction, it is possible to make the ansatz ψ ( x , z , t ) = e i α ( x − c t ) Ψ ( z ) , {\displaystyle \psi \left(x
Rayleigh–Taylor_instability
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