Topics, J

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, mp/05 [in superspace]; Langmann mp/05-in [and review].

Jackiw-Pi Theory
* Idea: A 3D non-Abelian gauge model.
@ References: Dayi MPLA(98) [Hamiltonian formulation]; Del Cima JPA(11) [symmetries].

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.

Jaynes-Cummings Model > see atomic physics.

Jeans Instability, Model, Swindle > s.a. Instability.
@ References: Kiessling AAM(03)ap/99; Ershkovich a1108 [the Jeans model is self-consistent].

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

Jericho Effect > see locality [quantum localization].

Jerk
$ 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) > see astrophysics; matter and radiation around black-holes; Acceleration and bianchi-I spacetimes [cosmic jets].

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, ∂_i∂_j 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-in [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 > see algebra.

Jordan Curve Theorem
* Idea: Every simple closed curve divides the plane into exactly two components.

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.

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).
@ References: in Tinkham 75; Anandan & Pati PLA(97) [geometry]; news pw(07)oct [in atomic gas]; news pw(12)apr [magnetic version].

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

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

Julia Set > see fractals.

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

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

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