Topics, J

j-Function > see finite groups.

Jack Polynomials
* Remark: Related to the eigenfunctions of a well-known exactly solvable quantum many-body system of the Calogero-Sutherland type.
@ Generalizations: Desrosiers et al CMP(03)ht/02, AiM(07)mp/05 [in superspace]; Langmann mp/05-proc [and review]; Lapointe & Mathieu Sigma(15)-a1503 [double Jack polynomials].

Jackiw-Pi Theory
* Idea: A 3D non-Abelian gauge model for massive vector fields.
@ References: Dayi MPLA(98) [Hamiltonian formulation]; Del Cima JPA(11) [symmetries]; Nikoofard & Abreu AdP(16)-a1601 [BV quantization].

Jackiw-Rebbi Model
* Idea: A (1+1)-dimensional model that Jackiw and Rebbi considered to show that half-integral fermion numbers are possible due to the presence of an isolated self charge conjugate zero mode.
@ References: Charmchi & Gousheh PRD(14)-a1402 [complete spectral analysis], NPB(14)-a1404 [massive].

Jackiw-Teitelboim Theory > see 2D gravity; 2D quantum gravity.

Jacobi Algebra / Bracket / Manifold / Structure > see poisson structure.

Jacobi Conjecture
@ References: Abdesselam AHP(03)m.CO/02 [perturbative quantum field theory approach].

Jacobi Elliptic Functions > see Elliptic Functions.

Jacobi Equation, Field > see geodesics.

Jacobi Metric, Hamiltonian > s.a. variational principles in physics [Jacobi principle].

Jacobi Principal Function
@ In quantum mechanics: Ferraro JPA(99)qp/96.

Jamiolkowski Criterion > see operator theory.

Jamming > a phase transition in granular metamaterials.

Janis-Newman Algorithm > see under Newman-Janis Algorithm.

Java, Javascript > see programming languages.

Jarzynski Equality
* Idea: A statement relating transient irreversible processes to infinite-time free energy differences.
@ References: Gittes a1704 [two examples of applications].

Jaynes-Cummings Model > see atomic physics.

Jeans Instability, Model, Swindle > s.a. Instability.
* Idea: An instability in astrophysics, which causes the gravitational collapse of interstellar gas clouds and star formation; The name "Jeans swindle" alludes to the fact that Jean's original model and analysis contained a flawed assumption.
@ References: Kiessling AAM(03)ap/99; Ershkovich a1108 [the Jeans model is self-consistent]; Falco et al MNRAS(13)-a1210 [formal justification]; Arbuzova et al PLB(14)-a1406 [Jeans instability in classical and modified gravity]; > s.a. Modified Gravity.
> Online resources: see Wikipedia page.

Jebsen-Birkhoff Theorem > see under Birkhoff's Theorem.

Jericho Effect > see locality [quantum localization].

$ Def: The time rate of change of acceleration, d3x/dt3.
* And chaos: Jerk is the lowest order effect in particle motion that can give rise to chaos.
@ References: Schot AJP(78)nov; Sandin TPT(90)jan; Leen AJP(94)may [letter]; Gottlieb AJP(96)may [question], von Baeyer ThSc(98)jan [and chaos].
> Online resources: see John Baez's page [including names for further derivatives: snap, etc].

Jet (in astrophysics and cosmology)
@ References: Gralla et al PRD(16)-a1504 [force-free solutions modeling rotating stars and black holes immersed in the magnetic field of a thin disk]; Pian a1512-proc [recent progress].
> Related topics: see matter and radiation around black-holes; acceleration and bianchi-I spacetimes [cosmic jets]; star formation and evolution.

Jet (in differential geometry)
$ Def: The n-th jet of a function g defined on a manifold M is the function itself together with all its partial derivatives up to the n-th order, or j(n)g = (g, ∂i g, ∂ij g, ..., up to n-th derivatives).
* Idea: Whereas the n-th derivatives of a function by themselves are not a geometrical object, the n-th jet is geometrical; given its values in some coordinate system, one can calculate its values in any other.
@ Jet bundle: in Mather AM(69); Saunders 89; Sardanashvily mp/02-ln [in classical and quantum field theory]; Tulczyjew mp/06-proc [modification of Ehresmann's jet theory]; Sardanashvily a0908-ln [and fiber bundles and Lagrangian theory]; > s.a. field theory.

Jet (in particle physics) > see QCD phenomenology.

Johnson-Mehl Model > see random tilings.

Join > s.a. lattice.

Jones Polynomial > see knot invariants.

Jordan Algebra > s.a. formulations of quantum mechanics [Jordan geometry]; lie algebras [invariants].
* Idea: An algebra in which the product satisfies [a, b, a2] = 0 for all a, b, with [a, b, c]:= (ab)ca(bc) (the "associator"); This property is weaker than associativity.
@ General references: Raptis mp/01 [Jordan-Lie superalgebras]; Rios mp/05 [exceptional, spectrum]; Bremner a1008, & Peresi a1008 [quasi-Jordan algebras]; Iordanescu a1106 [in mathematics and physics]; Hegazi & Abdelwahab a1401 [5D nilpotent, classification]; > s.a. Jordan-Lie-Banach Algebra.
@ And quantum mechanics: Townsend proc(85)-a1612 [rev]; Niestegge IJTP(04)-a1001, FP(09) [and quantum observables]; Wilce a1110 [from operational or physical principles]; > s.a. entangled quantum systems.

Jordan Curve
* Idea: A simple closed curve, i.e., a non-self-intersecting continuous loop in the plane.
Jordan curve theorem: Every simple closed curve divides the plane into exactly two components, an "interior" and an "exterior" region.
> Online resources: see Wikipedia page.

Jordan Frame > see scalar-tensor theories of gravitation.

Jordan Normal Form of a Matrix > see matrices.

Jordan Theory > see higher-dimensional gravity; kaluza-klein theory; scalar-tensor theories.

Jordan Triple > see spin.

Jordan-Lie Superalgebra > see algebra.

Jordan-Lie-Banach Algebra > see Algebraic Quantum Theory.

Josephson Effect > s.a. superconductivity.
* Idea: The tunneling effect proposed in 1962 by Brian Josephson of Cooper pairs between two superconductors separated by a thin insulator, maintaining phase coherence between the two superconductors; The difference δ between the phases on the two sides is related to the supercurrent I through the barrier by sin δ = I/I0, where I0 is the critical current, the maximum current that the junction can sustain; This was quickly verified in the lab and Josephson was awarded the 1973 Nobel Prize for Physics
* Applications: A device based on this effect is now called a Josephson junction and it has become an important technology in its own right, for example in superconducting quantum interference devices (SQUIDs).
* Thermal Josephson effect: Heat transport across a gap between two superconductors; Predicted in 1965 and measured in the lab for the first time.
@ References: in Tinkham 75; Anandan & Pati PLA(97) [geometry]; news pw(07)oct [in atomic gas]; news pw(12)apr [magnetic version]; Williams et al PRL(12) + Moore Phy(12) [in hybrid superconductor-topological insulator devices, and Majorana fermions].
@ Thermal Josephson effect: Giazotto & Martínez-Pérez Nat(12)dec + news pw(13)jan [measurement, and heat flow from colder to hotter].

Jost Functions
@ References: Damanik & Simon IMRN-m.SP/05 [for Jacobi matrices].

Joule Expansion
* Idea: The free adiabatic expansion of a gas against a vacuum.
@ References: Camalet PRL(08) [from the principles of quantum mechanics].

Joule's Law
* Joule's first law: The amount of heat generated by an electric current I flowing through a conductor of resistance R for a time t is \(Q = I^2R\,t\).
* Joule's second law: The internal energy of an ideal gas does not change if volume and pressure change, but does change if temperature changes.
> Online resources: see Wikipedia page.

Joule-Thomson Effect / Process
* Idea: The temperature change of a gas or liquid when it is forced through a valve or porous plug while kept insulated, so that no heat is exchanged with the environment (throttling process); The effect was discovered in 1852 by Lord Kelvin (William Thomson), following earlier work by Joule on Joule expansion; it is applied in refrigerators, air conditioners, heat pumps, and liquefiers.
> Online resources: see Wikipedia page.

Julia Set > see fractals.

Junction Conditions > see boundaries in field theory; metric matching.

JUNO (Jiangmen Underground Neutrino Observatory) > see neutrinos.

JWKB Approximation (for Jeffreys, Brillouin, Wentzel and Kramers) > see under WKB Approximation.

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