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Role of coherent states
generalizations: A mathematical overview, Reviews in Mathematical Physics 7 (1995) 1013-1104. S.T. Ali, J-P. Antoine, and J-P. Gazeau, Coherent States, Wavelets
Coherent states in mathematical physics
Coherent_states_in_mathematical_physics
Specific quantum state of a quantum harmonic oscillator
In physics, specifically in quantum mechanics, a coherent state is the specific quantum state of the quantum harmonic oscillator, often described as a
Coherent_state
problem from 1998. United States DARPA issued 23 mathematical challenges in 2008. Physics problems included: advancing techniques in modelling fluid dynamics
List of unsolved problems in physics
List_of_unsolved_problems_in_physics
Potential for two waves to interfere
In physics, coherence expresses the potential for two waves to interfere. Two monochromatic beams from a single source always interfere. Even for wave
Coherence_(physics)
Standard that diagrams must satisfy up to isomorphism
In mathematics, specifically in homotopy theory and (higher) category theory, coherency is the standard that equalities or diagrams must satisfy when
Coherency_(homotopy_theory)
Mathematical structures that allow quantum mechanics to be explained
The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
Work by Henri Poincaré
in the natural world, when there may well be only one part of mathematics that applies to theoretical physics. The primary objective of mathematical physics
The_Value_of_Science
2006 book by Ingemar Bengtsson and Karol Życzkowski
Quantum States: An Introduction to Quantum Entanglement is a book by Ingemar Bengtsson and Karol Życzkowski about the mathematics used in quantum physics. The
Geometry_of_Quantum_States
Category of mathematics papers in ArXiv
quandles Mathematics portal Science portal Technology portal Coherent states in mathematical physics Glossary of areas of mathematics Mathematics Subject
Quantum_algebra
Techniques to maintain quantum coherence
(target) states, the coherent control is termed state-to-state control. A generalization is steering simultaneously an arbitrary set of initial pure states to
Coherent_control
This is a list of mathematical topics in quantum theory, by Wikipedia page. See also list of functional analysis topics, list of Lie group topics, list
List of mathematical topics in quantum theory
List_of_mathematical_topics_in_quantum_theory
Topics referred to by the same term
united whole. More specifically, coherence, coherency, or coherent may refer to the following: Coherence (physics), an ideal property of waves that enables
Coherence
Branch of applied mathematics
development of mathematical ideas inspired by physics, known as physical mathematics. There are several distinct branches of mathematical physics, and these
Mathematical_physics
Theorem in quantum information theory
1978). "Proof of an entropy conjecture of Wehrl". Communications in Mathematical Physics. 62 (1): 35–41. Bibcode:1978CMaPh..62...35L. doi:10.1007/BF01940328
Lieb_conjecture
Multi-scale chaotic motions
components, referred to coherent turbulent structures. Such a structure must have temporal coherence, i.e. it must persist in its form for long enough
Coherent_turbulent_structure
Classic entropy of a quantum-mechanical density matrix
for pure states). Wehrl entropy can be defined for other kinds of coherent states. For example, it can be defined for Bloch coherent states, that is,
Wehrl_entropy
Type of quantum state
In physics, a squeezed coherent state is a quantum state that is usually described by two non-commuting observables having continuous spectra of eigenvalues
Squeezed_coherent_state
Range of physical processes in physics
In physics, scattering is a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deflect
Scattering
2006 string theory book by Lee Smolin
quantum gravity. In the book, Smolin claims that string theory makes no new testable predictions; that it has no coherent mathematical formulation; and
The_Trouble_with_Physics
Fundamental principle of physics
linear systems is that they are easier to analyze mathematically; there is a large body of mathematical techniques, frequency-domain linear transform methods
Superposition_principle
Initial estimate or framework to the solution of a mathematical problem
a mathematical or physical problem or solution. It typically provides an initial estimate or framework to the solution of a mathematical problem. In fact
Ansatz
Description of physical properties at the atomic and subatomic scale
World: Science as a Candle in the Dark. Ballantine Books. p. 249. ISBN 0-345-40946-9. "For most physics students, (the "mathematical underpinning" of quantum
Quantum_mechanics
American physicist (b. 1939)
gave the 2002 Andrejewski Lectures in Mathematical Physics at the Max Planck Institute for Mathematics in the Sciences in Leipzig. Daniel Freedman is a professor
Daniel_Z._Freedman
Branch of physics
Theoretical physics is a branch of physics that uses mathematical models and abstractions of physical objects and systems to explain and predict natural
Theoretical_physics
Criterion for evaluating rules for fair division
called coherent if the following holds for every allocation vector ( a i ) i = 1 n ∈ M ( h ; ( t i ) i = 1 n ) {\displaystyle (a_{i})_{i=1}^{n}\in M{\big
Coherence_(fairness)
German mathematician (1862–1943)
understand physics and how physicists were using mathematics, he developed a coherent mathematical theory for what he found – most importantly in the area
David_Hilbert
competition, such as the USA Mathematical Olympiad, or the International Mathematical Olympiad. Students majoring in mathematics, the physical sciences, engineering
Mathematics education in the United States
Mathematics_education_in_the_United_States
American physicist (1932–2024)
Simulations in Minkowski Space - Numerical techniques for simulating quantum field theory. Coherent States - Applications in Physics and Mathematical Physics -
John_R._Klauder
Book by Albert Einstein and Leopold Infeld
book was published in the United States by Simon & Schuster. In the book, Albert Einstein pushed his realist approach to physics in defiance of much of
The_Evolution_of_Physics
Theory of subatomic structure
fundamental physics. String theory has contributed a number of advances to mathematical physics, which have been applied to a variety of problems in black hole
String_theory
American physicist of quantum computing (1930–2022)
2002, pp. 495–509. "Use of mathematical logical concepts in quantum mechanics: an example," Journal of Physics A: Mathematical and General, Vol. 35, 2002
Paul_Benioff
Concept in quantum optics
coherences. Coherent waves have a well-defined constant phase relationship. Coherence functions, as introduced by Roy Glauber and others in the 1960s,
Higher_order_coherence
Danish mathematical physicist
(born 14 June 1961) is a Danish mathematician and mathematical physicist working on the mathematical theory of quantum mechanics. He is a professor at
Jan_Philip_Solovej
Theoretical framework in physics
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines field theory, special relativity and quantum mechanics. QFT
Quantum_field_theory
No spontaneous symmetry breaking in two-dimensional systems at finite temperature
Limitations of the Hohenberg–Mermin–Wagner Theorem". Journal of Physics A: Mathematical and Theoretical. 54 (31): 315001. arXiv:2107.09714. Bibcode:2021JPhA
Mermin–Wagner_theorem
Extended physical object in string theory
branch of mathematics that arose from studies of classical physics. Symplectic geometry studies spaces equipped with a symplectic form, a mathematical tool
Brane
In physics and geometry: conjectured relation between pairs of Calabi–Yau manifolds
symmetry is a major research topic in pure mathematics, and mathematicians are working to develop a mathematical understanding of the relationship based
Mirror symmetry (string theory)
Mirror_symmetry_(string_theory)
Mathematical concept
larger than the number of integers. In this usage, infinity is a mathematical concept, and infinite mathematical objects can be studied, manipulated,
Infinity
Historical development of physics
accumulation and specialization that gave rise to the field of physics. Mathematical advances of the 18th century gave rise to classical mechanics, and
History_of_physics
Hilbert space of square-integrable holomorphic functions of n complex variables
_{j=1}^{n}{\overline {a_{j}}}z_{j}.} The function Fa is called the coherent state (applied in mathematical physics) with parameter a, and the function κ ( a , z ) :=
Segal–Bargmann_space
Russian-American mathematician
Chicago and works on mathematics. His research has spanned representation theory, algebraic geometry and mathematical physics. In 1999, Beilinson was awarded
Alexander_Beilinson
Textbook by Paul Dirac
relativity in order to create a coherent quantum theory of electrodynamics, he resorted to using three-dimensional space in the sense of classical physics. He
The Principles of Quantum Mechanics
The_Principles_of_Quantum_Mechanics
Area of mathematics
is also called dynamical systems, mathematical dynamics, mathematical dynamical systems theory or the mathematical theory of dynamical systems. Dynamical
Dynamical_systems_theory
Polish mathematician and physicist
Odzijewicz, Anatol (1 November 1992). "Coherent states and geometric quantization". Communications in Mathematical Physics. 150 (2): 385–413. Bibcode:1992CMaPh
Anatol_Odzijewicz
Interdisciplinary field of research
Mathematical sociology is an interdisciplinary field of research concerned with the use of mathematics within sociological research. Starting in the early
Mathematical_sociology
Device that emites acoustic radiation
coherent terahertz sound in a Wannier–Stark ladder superlattice has been achieved in 2009 according to a paper publication from the School of Physics
Sound amplification by stimulated emission of radiation
Sound_amplification_by_stimulated_emission_of_radiation
Branch of mathematics
important for foliations, tilings, dynamical systems and examples from mathematical physics. A smooth compact Riemannian manifold can be studied using analytic
Noncommutative_geometry
Foundational principle in quantum physics
(January 2011). "Resonances/decaying states and the mathematics of quantum physics". Reports on Mathematical Physics. 67 (3): 279–303. Bibcode:2011RpMP
Uncertainty_principle
Principle of quantum mechanics
=\sum _{n}a_{i}\psi _{i}.} The states like ψ i {\displaystyle \psi _{i}} are called basis states. Important mathematical operations on quantum system solutions
Quantum_superposition
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern
History_of_mathematics
List of particles in matter including fermions and bosons
hypothesized molecular, atomic, and subatomic particles in particle physics, condensed matter physics and cosmology. Elementary particles are particles with
List_of_particles
Danish physicist and educator (born 1959)
educator. She is the Mallinckrodt Professor of Physics and of Applied Physics at Harvard University. In 1999, she led a Harvard University team that, by
Lene_Hau
Mathematical conjecture
an issue in theoretical physics and mathematics. The original conjecture was proposed by Andrew Strominger, Shing-Tung Yau, and Eric Zaslow in 1996. Along
SYZ_conjecture
Theory of a quantum origin of consciousness
mathematical truths, which relates to Penrose's ideas concerning the three worlds: the physical, the mental, and the Platonic mathematical world. In Shadows
Orchestrated objective reduction
Orchestrated_objective_reduction
Formulation of quantum mechanics
called the "most powerful formula in physics", with Stephen Wolfram also declaring it to be the "fundamental mathematical construct of modern quantum mechanics
Path-integral_formulation
Basic unit of quantum information
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
Qubit
Type of uncertainty of meaning where several interpretations are possible
It is common to define the coherent states in quantum optics with | α ⟩ {\displaystyle ~|\alpha \rangle ~} and states with a fixed number of photons
Ambiguity
South Korean physicist, academic, author and researcher
Space Picture of Quantum Mechanics, Physics of the Lorentz Group, New Perspectives on Einstein's E = mc2, and Mathematical Devices for Optical Sciences. Kim
Young_Suh_Kim
Approximation or recovery of classical mechanics in certain theories
for quantum mechanical correlation functions". Communications in Mathematical Physics. 35 (4): 265–277. Bibcode:1974CMaPh..35..265H. doi:10.1007/BF01646348
Classical_limit
French physicist and mathematician
physicist and mathematician who works in the field of symmetry in quantum physics. His research has focused on coherent states; beta numeration for quasicrystals
Jean-Pierre_Gazeau
Physics phenomenon
in Mathematical Physics. 4 (2): 93–100. Bibcode:1980LMaPh...4...93C. doi:10.1007/BF00417500. S2CID 120680226. Werner, R. F. (1989). "Quantum States with
Quantum_entanglement
American theoretical physicist (1925–2018)
(see coherent state) and light from light bulbs (see blackbody). His theories are widely used in the field of quantum optics. In statistical physics he
Roy_J._Glauber
Computational physics simulation tool
distribution, this similarity may be misleading, because different coherent states are not orthogonal. Two different points α do not represent disjoint
Husimi_Q_representation
American physicist
Anupam (2000). "The semiclassical propagator for spin coherent states". Journal of Mathematical Physics. 41 (12): 8025. arXiv:cond-mat/0004247. Bibcode:2000JMP
Anupam_Garg
Method in physics used to deal with infinities
12, 2002), published in : Duplantier, Bertrand; Rivasseau, Vincent (Eds.); Poincaré Seminar 2002, Progress in Mathematical Physics 30, Birkhäuser (2003)
Renormalization
Relativistic wave equation in quantum mechanics
In particle physics, the Klein–Gordon equation is a relativistic wave equation for spinless particles. It was discovered in 1926 as the relativistic generalization
Klein–Gordon_equation
Physics experiment
In modern physics, the double-slit experiment demonstrates that light and matter can exhibit behavior associated with both classical particles and classical
Double-slit_experiment
Scottish physicist and mathematician (1831–1879)
Cambridge, in 1854, where he earned distinction in mathematics and the Smith's Prize. He remained at Cambridge briefly, publishing early mathematical work and
James_Clerk_Maxwell
Applied mathematician and academic administrator
attended Creighton University in Omaha, Nebraska, majoring in physics and mathematics and graduating summa cum laude in 1966. McLaughlin went on to graduate
David_W._McLaughlin
Austrian mathematician and mathematical physicist
specialized in the study of the Leray–Maslov index and in the theory of the metaplectic group, and their applications to mathematical physics. In 1998 de
Maurice_A._de_Gosson
Fundamental interaction between charged particles
In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force
Electromagnetism
Quantum astrophysicist (born 1968)
moved to the United States in 1986 and enrolled at Wellesley College, where she received a bachelor's degree in physics and astronomy in 1990. She then joined
Nergis_Mavalvala
Quantum feature of condensed-matter systems
conductors. The necessity of pair ODLRO implies that the basic unit of coherent states in superconductors consists of pair of electrons. The Meissner effect
Off-diagonal_long-range_order
any special faculty of mathematical intuition. In this view, logic is the proper foundation of mathematics, and all mathematical statements are necessary
Philosophy_of_mathematics
Natural sciences as described by Aristotle
Aristotelian physics is the form of natural philosophy described in the works of the Greek philosopher Aristotle (384–322 BC). In his work Physics, Aristotle
Aristotelian_physics
Physics award
The Comstock Prize in Physics is awarded by the U.S. National Academy of Sciences "for recent innovative discovery or investigation in electricity, magnetism
Comstock_Prize_in_Physics
particles are proposed subatomic or composite entities arising in theoretical particle physics and cosmology that have not been experimentally confirmed.
List of hypothetical particles
List_of_hypothetical_particles
American physicist
Mechanics. Schumacher is a professor of physics at Kenyon College, a liberal arts college in rural Ohio. He is the lecturer in four courses produced by the Teaching
Benjamin_Schumacher
Quantum states light can be in
In quantum physics, light is in a squeezed state if its electric field strength Ԑ for some phases ϑ {\displaystyle \vartheta } has a quantum uncertainty
Squeezed_states_of_light
BCE, this is one of the oldest mathematical texts. It laid the foundations of Indian mathematics and was influential in South Asia. It was primarily a
List of publications in mathematics
List_of_publications_in_mathematics
Gold medal awarded annually by the Institute of Physics
and T-ray detection of cancer receives highest Institute of Physics accolade — Mathematical, Physical and Life Sciences Division". University of Oxford
Isaac_Newton_Medal
Application of quantum entanglement to high-precision measurement
the limit of classical states represented in coherent states. In atomic ensembles, spin squeezed states can be used for phase measurements. An important
Quantum_metrology
American mathematician
Lawrence Sirovich is mathematical scientist whose research includes, among other topics, applied mathematics, neuroscience and physics. He is recognized
Lawrence_Sirovich
Interpretation of quantum mechanics
Paths" Parallel universes in fiction The Beginning of Infinity Mathematical universe hypothesis Multiverse "Relative states of Everett come to mind. One
Many-worlds_interpretation
Mathematical operation in quantum optics, general relativity and other areas of physics
In theoretical physics, the Bogoliubov transformation, also known as the Bogoliubov–Valatin transformation, was independently developed in 1958 by Nikolay
Bogoliubov_transformation
Elementary particle with extremely low mass
theorized in extensions of the Standard Model of particle physics. In November 2012, American scientists used a particle accelerator to send a coherent neutrino
Neutrino
Academic association dedicated to the use of mathematics in industry
American Mathematical Society 1939-88. American Mathematical Society. ISBN 9780821896761. Scientific and Technical Societies of the United States. National
Society for Industrial and Applied Mathematics
Society_for_Industrial_and_Applied_Mathematics
Coherence (physics) Coherence length Coherence theory (optics) Coherence time Coherent backscattering Coherent control Coherent information Coherent perfect
Index_of_physics_articles_(C)
Procedure of coping with redundant degrees of freedom in physical field theories
In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom
Gauge_fixing
Austrian-American mathematician
and physics. He was born to a Jewish family in Vienna and escaped for England in 1939 via the Kindertransport. He moved to the United States in 1946
Walter_Feit
Truths and principles of the study of matter, space, time and energy
In philosophy, the philosophy of physics deals with conceptual and interpretational issues in physics, many of which overlap with research done by certain
Philosophy_of_physics
French mathematician (1928–2014)
Montpellier and, while still producing relevant mathematical work, he withdrew from the mathematical community and devoted himself to political and religious
Alexander_Grothendieck
Russian physicist
graduated in 1968 from a special school for physics and mathematics in Moscow (School No. 2). In 1968 he also achieved first place in the Moscow Physics Olympiad
Yury_Bunkov
Wigner distribution function in physics as opposed to in signal processing
"Weyl transform in nonrelativistic quantum dynamics". Journal of Mathematical Physics. 9 (5): 769–781. Bibcode:1968JMP.....9..769L. doi:10.1063/1.1664640
Wigner quasiprobability distribution
Wigner_quasiprobability_distribution
French mathematical physicist
Gutzwiller semiclassical trace formula using coherent states decomposition. Communications in mathematical physics, 202(2), 463–480. Combescure, M., Gieres
Monique_Combescure
Lvovsky
its applications in technology. Lvovsky attended Moscow State School 57, a school renowned for its focus on mathematics and physics. He earned his undergraduate
Alexander_Lvovsky
French mathematician and lawyer (1601–1665)
His life besides mathematics". Newsletter of the European Mathematical Society: 12–16. Mahoney, Michael Sean (1994). The mathematical career of Pierre
Pierre_de_Fermat
Elementary particle or quantum of light
mechanical state. This work led to the concept of coherent states and the development of the laser. In the same papers, Einstein extended Bose's formalism
Photon
Formulation of quantum mechanics
pure states, with the unique exception of (optionally squeezed) coherent states, in violation of the first axiom. Regions of such negative value are
Phase-space_formulation
Chinese-American mathematician and poet
the American Mathematical Society, 58 (9), Providence, Rhode Island: American Mathematical Society: 1226–1249, October 2011 Chern's Work in Geometry, by
Shiing-Shen_Chern
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COHERENT STATES-IN-MATHEMATICAL-PHYSICS
COHERENT STATES-IN-MATHEMATICAL-PHYSICS
COHERENT STATES-IN-MATHEMATICAL-PHYSICS
COHERENT STATES-IN-MATHEMATICAL-PHYSICS
COHERENT STATES-IN-MATHEMATICAL-PHYSICS
COHERENT STATES-IN-MATHEMATICAL-PHYSICS
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