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Phase of a cycle
quantum mechanics, the geometric phase (also known as the Pancharatnam–Berry phase, Pancharatnam phase, or Berry phase) is a phase difference acquired over
Geometric_phase
Method of digital signal processing
Geometric phase analysis is a method of digital signal processing used to determine crystallographic quantities such as d-spacing or strain from high-resolution
Geometric_phase_analysis
Indian physicist
optics. He is noted for his discovery of a type of geometric phase sometimes known as Pancharatnam phase for polarized beams passing through crystals. He
S._Pancharatnam
Mechanics analogue of the geometric phase
mechanics, the Hannay angle is a mechanics analogue of the geometric phase (or Berry phase). It was named after John Hannay of the University of Bristol
Hannay_angle
Ancient Greek temple on Aegina
Sub-Mycenaean period and into the Geometric where cult activity is once more reasonably certain. Furtwängler proposes three phases of building at the sanctuary
Temple_of_Aphaia
Electromagnetic quantum-mechanical effect in regions of zero magnetic and electric field
connected regions, but this has been argued to be a different kind of geometric phase as it is "neither nonlocal nor topological", depending only on local
Aharonov–Bohm_effect
Concept in physics
associated with the Berry phase or geometric phase. The concept was first introduced by S. Pancharatnam as geometric phase and later elaborately explained
Berry connection and curvature
Berry_connection_and_curvature
Quantum computing implementation
be used to induce a geometric phase on one of the computational states of the qubits. This leads to an entangling conditional phase shift of the relevant
Superconducting quantum computing
Superconducting_quantum_computing
Free crystallographic software
for geometric phase analysis. It allows to generate 2D maps of various crystallographic quantities using high-resolution images. Since the geometric phase
CrysTBox
Kurtosis of the order parameter in statistical physics
cumulant scheme in cases in which the relevant physical quantity is a geometric phase, which happens in many systems which are inherently quantum mechanical
Binder_parameter
Ratio of a celestial body's brightness to that of a Lambertian ideal
astronomy, the geometric albedo of a celestial body is the ratio of its actual brightness as seen from the light source (i.e. at zero phase angle) to that
Geometric_albedo
Device to demonstrate Earth's rotation
rotating reference frame Eötvös experiment – Physics experiment Geometric phase – Phase of a cycle Gyroscope – Device for measuring or maintaining orientation
Foucault_pendulum
mathematical lens, but it has the drawbacks of the hologram (diffraction). Geometric phase lenses, also known as polarization-directed flat lenses are made by
Flat_lens
Aspect of theoretical physics
periodic solid. It provides a geometric language for how a band wavefunction changes across parameter space and how its phase twists under parallel transport
Quantum geometry (condensed matter)
Quantum_geometry_(condensed_matter)
Location of a discrete degeneracy between two electronic states
coupling at conical intersections is responsible for the existence of Geometric phase, which was discovered by Longuet-Higgins in this context. Degenerate
Conical_intersection
Mechanism of spontaneous symmetry breaking
of geometric phase by Berry (or Berry phase as it is also known) provided a general background to aid understanding of the rotation-dependent phase associated
Jahn–Teller_effect
Type of angular momentum in light
recently, the geometric phase concept has been adopted for OAM generation. The geometric phase is modulated to coincide with the spatial phase dependence
Orbital angular momentum of light
Orbital_angular_momentum_of_light
Type of reflective prism
In a roof prism without a phase-correcting coating, s-polarized and p-polarized light each acquire a different geometric phase as they pass through the
Roof_prism
Phase of Greek art, characterized largely by geometric motifs in vase painting
Geometric art is a phase of Greek art, characterized largely by geometric motifs in vase painting, that flourished towards the end of the Greek Dark Ages
Geometric_art
System for defining and representing engineering tolerances
Geometric dimensioning and tolerancing (GD&T) is a system for defining and communicating engineering tolerances via a symbolic language on engineering
Geometric dimensioning and tolerancing
Geometric_dimensioning_and_tolerancing
Concept in quantum mechanics
dynamical phase θ m ( t ) = − 1 ℏ ∫ 0 t E m ( t ′ ) d t ′ {\displaystyle \theta _{m}(t)=-{\frac {1}{\hbar }}\int _{0}^{t}E_{m}(t')dt'} and geometric phase γ m
Adiabatic_theorem
Topological bound state of an electron
their own geometric phases which partly cancel the Aharonov–Bohm phase due to the external magnetic field to generate a net geometric phase that can be
Composite_fermion
Mathematical Physics professor
74.032326. S2CID 32704515. Fuentes-Schuller, Ivette (2003-04-23). "Geometric phase in open systems". Physical Review Letters. 90 (16) 160402. arXiv:quant-ph/0301037
Ivette_Fuentes
Topics referred to by the same term
Party of Alberta Guam Power Authority Generalized Procrustes analysis Geometric phase analysis Gigapascal (GPa), a unit of pressure Glenopolar angle Gradient
GPA_(disambiguation)
Physical function
Bohm, A Mostafazadeh, H Koizumi, Q Niu and J Zqanziger (2003). The Geometric Phase in Quantum Systems. Springer. pp. §12.5, p. 292 ff. doi:10.1007/978-3-662-10333-3
Wannier_function
Indian family, several of whom are notable in physics
discovered the properties of what is now known as the geometric phase (sometimes known as the Pancharatnam phase) for polarized beams passing through crystals
Chandrasekhar_family
Type of artificial sheet material
convert between linear and circular polarization states, often via geometric-phase (Pancharatnam–Berry) elements. By mechanism Passive metasurfaces –
Electromagnetic_metasurface
Chinese science award
state-resolved reaction dynamics studies, revealing quantum resonances and geometric phase effects in chemical reactions." Jie Zhang Shanghai Jiao Tong University
Future_Science_Prize
Material which alters light reflection or transmission on optics
In a roof prism without a phase-correcting coating, s-polarized and p-polarized light each acquire a different geometric phase as they pass through the
Optical_coating
Search algorithm
In computer science, geometric hashing is a method for efficiently finding two-dimensional objects represented by discrete points that have undergone
Geometric_hashing
Indian theoretical physicist
Kac's ring. His work in neutrino physics pioneered in calculation of geometric phases in neutrinos. Among other contributions, Jain made significant developments
Sudhir_Ranjan_Jain
British chemist and cognitive scientist (1923–2004)
prize for his work. Among the most important were his discovery of geometric phase at the conical intersection of potential energy surfaces, his introduction
Christopher_Longuet-Higgins
Optical phenomenon
angle by only half a round. This is an early example of the geometric phase. This geometric phase of π {\displaystyle \pi } is observable in the difference
Conical_refraction
Recipe for constructing a quantum analog of a classical physical theory
the classical phase space. This led him to discover the phase-space star-product of a pair of functions. The modern theory of geometric quantization was
Geometric_quantization
Indian theoretical physicist (1926–2005)
processes of elementary particles based on unitarity and analyticity, geometric phases of wave function in quantum mechanics and quantum optics, equation
Samarendra_Nath_Biswas
Perpetual motion device
sustaining their rotation. Quantum stirring, ratchets, and pumping Geometric phase § Stochastic pump effect M. von Smoluchowski (1912) Experimentell nachweisbare
Brownian_ratchet
Plot of a dynamical system's trajectories in phase space
In mathematics, a phase portrait is a geometric representation of the orbits of a dynamical system in the phase plane. Each set of initial conditions
Phase_portrait
Space of all possible states that a system can take
composition. In mathematics, a phase portrait is a geometric representation of the orbits of a dynamical system in the phase plane. Each set of initial conditions
Phase_space
State of a physical system in phase space
{\displaystyle (\xi _{1},\xi _{2},-\xi _{1}-\xi _{2})} in phase space, acquires a geometric phase factor D ^ [ − ξ 1 − ξ 2 ] D ^ ( ξ 2 ) D ^ ( ξ 1 ) | α
Phase_space_crystal
Indian physicist and cosmologist (1957–2021)
in understanding the primordial, pre-geometric phase of the universe, from which the classical, geometric phase described by Einstein's equations emerges
Thanu_Padmanabhan
Problem of determining if a Boolean formula could be made true
undergoes a geometric phase transition, namely that it shatters into exponentially many, well-separated clusters. The onset of this phase transition coincides
Boolean satisfiability problem
Boolean_satisfiability_problem
Mathematics problem
"Indistinguishability for quantum particles: spin, statistics and the geometric phase", Proceedings of the Royal Society of London. Series A: Mathematical
Berry–Robbins_problem
Oscillating dynamical system with nonlinear damping
of the Van der Pol oscillator. Such a Hamiltonian also connects the geometric phase of the limit cycle system having time dependent parameters with the
Van_der_Pol_oscillator
Rotation of the plane of linearly polarized light as it travels through a chiral material
Cryptochirality Specific rotation Circular dichroism Birefringence Geometric phase Polarization Chirality (chemistry) Chirality (electromagnetism) Polarization
Optical_rotation
Fundamental principle of physics
Press, p. 17. Solem, J. C.; Biedenharn, L. C. (1993). "Understanding geometrical phases in quantum mechanics: An elementary example". Foundations of Physics
Superposition_principle
Topics referred to by the same term
temple architecture. Pancharatnam-Berry phase In classical and quantum mechanics, geometric phase is a phase difference acquired over the course of a
Panchayatana
Optical filter device
sphere (optics) Edwin Land Polariscope Polarized light microscope Geometric Phase Lens Wolf, Mark J. P. (2008). The Video Game Explosion: A History from
Polarizer
Trapped-ion quantum gate
ions. In 2003, Wineland's group produced better results by using a geometric phase gate, which is a specific case of the more general formalism put forward
Mølmer–Sørensen_gate
Type of order at absolute zero
topological orders and non-Abelian topological orders) and the non-Abelian geometric phase of degenerate ground states, were introduced to characterize and define
Topological_order
Type of microscope with electrons as a source of illumination
electron microscopy - the use of electron microscopy in immunology Geometric phase analysis - a method to analyze high-resolution images Serial block-face
Electron_microscope
Metric on a smooth statistical manifold
\right]\end{aligned}}} The imaginary term is a symplectic form, it is the Berry phase or geometric phase. In index notation, the metric is: h j k = h ( ∂ ∂ θ j , ∂ ∂ θ
Fisher_information_metric
Mathematical theory on behavior of connected clusters in a random graph
behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network
Percolation_theory
Quantum physics and chemistry phenomenon
crossings between electronic states of the same symmetry are not avoided. Geometric phase Christopher Longuet-Higgins Conical intersection Vibronic coupling
Avoided_crossing
Thin layer of material
strained and unstrained regions in a crystal yields the strain value. Geometric phase analysis (GPA), analyzes local variations in the Fourier components
Thin_film
Branch of mathematics
Geometric mechanics is a branch of mathematics applying particular geometric methods to many areas of mechanics, from mechanics of particles and rigid
Geometric_mechanics
Angle between the light incident on, and reflected from, an astronomical object
approaches 180°. This relationship is referred to as the phase curve. Illumination angle – Angle in geometric opticsPages displaying short descriptions of redirect
Phase_angle_(astronomy)
Type of probability distribution
The discrete phase-type distribution is a probability distribution that results from a system of one or more inter-related geometric distributions occurring
Discrete phase-type distribution
Discrete_phase-type_distribution
Mathematical approach to quantum physics
Mostafazadeh, A. (1997). "Quantum adiabatic approximation and the geometric phase". Physical Review A. 55 (3): 1653–1664. arXiv:hep-th/9606053. Bibcode:1997PhRvA
Perturbation theory (quantum mechanics)
Perturbation_theory_(quantum_mechanics)
Field used in the dynamics of ultracold quantum gases
force and the Coriolis force) or by imprinting a spatially varying geometric phase through an atom-laser interaction scheme. Recently, some attention
Synthetic_gauge_field
phase transitions. Topological phases are quantum phases of matter that are characterized by robust ground state degeneracy and quantized geometric phases
Curvature renormalization group method
Curvature_renormalization_group_method
Relation of wavelength/wavenumber as a function of a wave's frequency
wave propagation and attenuation. Dispersion may be caused either by geometric boundary conditions (waveguides, shallow water) or by interaction of the
Dispersion_relation
American theoretical physicist (born 1949)
Computation in Chemistry (NRCC). His renormalization group work focused on geometric phase transitions such as percolation and their connection to disordered
Peter_Reynolds_(physicist)
Riemannian metric on the space of mixed states of a quantum system
ISSN 2469-9926. Uhlmann, A. (1992). "The Metric of Bures and the Geometric Phase". In Gielerak, R.; Lukierski, J.; Popowicz, Z. (eds.). Groups and Related
Bures_metric
Research university in England
Sir Michael Berry, one of the discoverers of quantum mechanics' "geometric phase", John Rarity international expert on quantum optics, quantum cryptography
University_of_Bristol
Product of geometric length and refractive index
refractive index over the path C of geometric length |C|. An electromagnetic wave propagating along a path C has the phase shift over C as if it was propagating
Optical_path_length
Fraction of incident light reflected by an astronomical body
albedo (A) is related to the geometric albedo (p) by the expression A = p q {\displaystyle A=pq} where q is termed the phase integral and is given in terms
Bond_albedo
Israeli physicist and activist (born 1963)
experimental test of the geodesic rule proposition for the noncyclic geometric phase, Science & AAAS What time does Schrödinger's clock show? | Vikki Academy
Ron_Folman
Indian physicist
Vlatko Vedral and other scientists have introduced the concept of geometric phase for mixed states. This has been experimentally measured by several
Arun_K._Pati
"Fresnel–Arago fifth law of interference: the first description of a geometric phase in optics". Journal of Modern Optics. 68 (6): 350–356. doi:10.1080/09500340
Fresnel–Arago_laws
ratchet Geometric phase § Stochastic pump effect Adiabatic quantum motor N. A. Sinitsyn (2009), "Stochastic pump effect and geometric phases in dissipative
Quantum stirring, ratchets, and pumping
Quantum_stirring,_ratchets,_and_pumping
battles, presumably representing those fought by the deceased. The Geometric phase was followed by an Orientalizing period in the late 8th century, when
Ancient_Greek_art
Complex structures in matter physics
In condensed matter physics, geometrical frustration (or in short, frustration) is a phenomenon where the combination of conflicting inter-atomic forces
Geometrical_frustration
State of matter with insulating bulk but conductive boundary
are band indices. Its integral over a path gives the geometric phase, which corresponds to the phase gained by a state during adiabatic evolution that is
Topological_insulator
Archaeological culture in the Eastern Mediterranean
Kebaran is the first phase of the Epipalaeolithic in the Levant. Kebaran stone tool assemblages are characterized by small, geometric microliths, and are
Kebaran_culture
System of moving vectors in differential geometry
parallel transport (or parallel translation) is a way of transporting geometrical data along smooth curves in a manifold. If the manifold is equipped with
Parallel_transport
applications, though it does play an important role when considering geometric phase. In the notation of Reck et al., the 2 × 2 {\textstyle 2\times 2} beam
Universal multiport interferometer
Universal_multiport_interferometer
Interaction between electronic and nuclear vibrational motion in a molecule
coupling at conical intersections is responsible for the existence of Geometric phase, which was discovered by Longuet-Higgins in this context. Although
Vibronic_coupling
Method of microscopic imaging
(May 2020). "Ptychography retrieval of fully polarized holograms from geometric-phase metasurfaces". Nature Communications. 11 (1) 2651. Bibcode:2020NatCo
Ptychography
American physicist
time). He also was the first to measure the topological Berry's Phase (Geometric phase). As of 2006, he accepted a faculty position at UC Merced and turned
Raymond_Chiao
dimension at the same point. UTD is an extension of Joseph Keller's geometrical theory of diffraction (GTD) and was introduced by Robert Kouyoumjian
Uniform_theory_of_diffraction
Topics referred to by the same term
Carnatic classical music Pancharatnam-Berry phase or geometric phase (classical and quantum mechanics), a phase difference acquired over the course of a
Pancharatna
He was Sir C V Raman's nephew, and brother of Pancharatnam of the geometric phase fame, and cousin of Subrahmanyam Chandrasekhar. Discotic liquid crystals
Discotic_liquid_crystal
Type of optimization problem
corresponds to a geometric structure with nontrivial holonomy. Similarly, the concept of non/holonomy in mechanics is related to geometric phases, since those
Nonholonomic_system
Croatian artist (1947–2001)
an unusual painterly expression. In the mid-1980s, she shifted to a geometric phase. In these works, she used acrylic on paper with specific blue and red
Edita_Schubert
Concept in differential geometry
around closed loops fails to preserve the geometrical data being transported. Holonomy is a general geometrical consequence of the curvature of the connection
Holonomy
Building in Trajan Square, Timișoara
whose petals are inscribed in a square, typical of the last phase, the "geometric" phase, the most evolved of the 1900s style. Wikimedia Commons has media
Mercury_Palace
One of six awards of the Wolf Foundation
discovery of quantum topological and geometrical phases, specifically the Aharonov-Bohm effect, the Berry phase, and their incorporation into many fields
Wolf_Prize_in_Physics
Indian Physicist
Nirmalya (2019). "Experimental probe of weak value amplification and geometric phase through the complex zeros of the response function". Physical Review
Nirmalya_Ghosh
Israeli-born American chemist (1945–2024)
iterative maps for pulse sequences and quantum control, and the quantum geometric phase. His combination of optical pumping and cross-polarization made it
Alexander_Pines
theater, opera and ballet performances. The geometric phase was his most characteristic phase. In this phase, he synchronized dialogue with Byzantine and
Dimitar_Kondovski
Optical term
dictionary. In geometric optics, stigmatism refers to the image-formation property of an optical system which focuses a single point source in one phase optics
Stigmatism
characterized by geometrical ornaments, swastikas, diamonds, and horizontal and vertical lines. These samples were mainly in the Late Geometric phase of ceramics
Culture_of_ancient_Illyria
Vector field describing the density of electric dipole moments in a dielectric material
(1994). "Macroscopic polarization in crystalline dielectrics: the geometric phase approach" (PDF). Rev. Mod. Phys. 66 (3): 899–915. Bibcode:1994RvMP
Polarization_density
Topics referred to by the same term
(Jega album), a 2000 album by English musician Jega Geometric art, a phase of ancient Greek art Geometric (typeface classification), a class of sans-serif
Geometry_(disambiguation)
American planetary scientist (born 1953)
Interpretation of Classical Mechanics. His 2003 paper in Science on a new geometric phase effect which Wisdom calls "spacetime swimming" has attracted considerable
Jack_Wisdom
Model of optics describing light as geometric rays
Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of rays. The ray in geometrical optics is an abstraction
Geometrical_optics
Apparent center of radio emission from an antenna
The phase center may vary, depended on the beamforming algorithm. It produces the weight vector, that may vary over time depending on the geometrical setup
Phase_center
Scientific research institute in Bengaluru, India
of RRI at that time." This discovery proved for the first time that geometric phase exists in optics. But this work was not known to the world until similar
Raman_Research_Institute
Type of representation of molecular wave functions
\left(\mathbf {q'} \mid \Gamma \right)\cdot d\mathbf {q'} \right)} (see also Geometric phase). Here P ^ {\displaystyle {\hat {P}}} is an ordering operator, the
Diabatic_representation
Mathematical structures that allow quantum mechanics to be explained
simple special cases. Path integral formulation Phase-space formulation of quantum mechanics & geometric quantization quantum field theory in curved spacetime
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
GEOMETRIC PHASE
GEOMETRIC PHASE
Girl/Female
Tamil
Kala Devi | கலா தேவீ
Art, Phases of Moon
Kala Devi | கலா தேவீ
Girl/Female
Assamese, Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
The Phase of Moon Two Nights After New Moon; Ray of Moon
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Telugu, Traditional
Moon Light; Brightness of Moon; Phases of Moon
Boy/Male
Tamil
One who shows different phases
Girl/Female
Hindu
Art, Phases of Moon
Boy/Male
Greek
Greek surname. Euclid was an early developer of geometry theories.
Girl/Female
Tamil
Art, Phases of Moon
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Marathi, Mythological, Sanskrit, Tamil, Telugu, Traditional
Good Character; An Precious Angel; The Chant of Salvation; Goddess Durga; Phased; Verse; Angle the Chant of Salvation
Girl/Female
Tamil
Shashikala | ஷஷிகலா
Phases of Moon
Shashikala | ஷஷிகலா
Male
German
Old German name, GOMERIC means "man-power."
Boy/Male
Hindu
Symbolizing the phases of Moon
Girl/Female
Tamil
Phase, Time of day
Boy/Male
Tamil
Symbolizing the phases of Moon
Girl/Female
Hindu
Art, Phases of Moon
Girl/Female
Hindu
Phases of Moon
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
Phase; Time of Day
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
One who Shows Different Phases
Girl/Female
Indian, Telugu
A Phase of Life; Childhood
Girl/Female
Hindu, Indian, Tamil
Full Phase of Mooon; Bright Drop; Fair; Attracted by Lord Krishna
Girl/Female
American, Arabic, Bengali, British, English, Greek, Gujarati, Hawaiian, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Tamil, Telugu
The Fine Arts; Art; Miracle; Phases of Moon; Princess; Most Beautiful
GEOMETRIC PHASE
GEOMETRIC PHASE
Boy/Male
Muslim
Thrower
Girl/Female
Hindu
Loving
Boy/Male
British, English, German, Swedish
Wood; Wide
Boy/Male
Welsh American
Rock.
Boy/Male
Indian, Sanskrit
Free from Disease; Well
Girl/Female
Hindu
Meeting, Remembrance, Memory, Wisdom
Boy/Male
Hindu, Indian, Traditional
Lord Shiva
Girl/Female
Muslim
Welfare, Benefit
Boy/Male
Tamil
Samadarshi | ஸமதரà¯à®·à¯€
Lord Vishnu
Male
Hebrew
Short form of Hebrew Elazar, EZAR means "my god has helped."
GEOMETRIC PHASE
GEOMETRIC PHASE
GEOMETRIC PHASE
GEOMETRIC PHASE
GEOMETRIC PHASE
a.
Pertaining to geometry.
a.
Alt. of Geometrical
imp. & p. p.
of Geometrize
a.
Same as Isometric.
v. i.
To investigate or apprehend geometrical quantities or laws; to make geometrical constructions; to proceed in accordance with the principles of geometry.
a.
Same as Isometric.
pl.
of Geometry
a.
Isometric.
a.
Alt. of Pedometrical
a.
Of or pertaining to aerometry; as, aerometric investigations.
n.
One of numerous genera and species of moths, of the family Geometridae; -- so called because their larvae (called loopers, measuring worms, spanworms, and inchworms) creep in a looping manner, as if measuring. Many of the species are injurious to agriculture, as the cankerworms.
a.
Alt. of Isometrical
adv.
In a geocentric manner.
n.
The larva of any species of geometrid moths. See Geometrid.
n.
The larva of any geometrid moth. See Geometrid.
n.
Any geometrid moth of the genus Eupithecia.
a.
Pertaining or belonging to the Geometridae.
a.
Pertaining to, or according to the rules or principles of, geometry; determined by geometry; as, a geometrical solution of a problem.
n.
Any species of geometrid moth; a geometrid.
p. pr. & vb. n.
of Geometrize