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 Curvature Tensor > see energy-momentum tensor [for gravity].
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 AJP(18)jan-a1704 [two examples of applications];
Bartolotta & Deffner PRX(18)-a1710 [for driven quantum field theories].
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.
@ General references: Kiessling AAM(03)ap/99;
Ershkovich a1108 [the Jeans model is self-consistent];
Falco et al MNRAS(13)-a1210 [formal justification].
@ Modified theories: Arbuzova et al PLB(14)-a1406 [in classical and modified gravity];
Moradpour et al MNRAS(19)-a1907 [with GUP];
> s.a. Modified Gravity.
> Online resources:
see Wikipedia page.
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)
@ 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];
Parfrey et al PRL(19)
+ Penna Phy(19) [first-principles simulations].
> 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,
∂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-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.
Jones Polynomial > see knot invariants.
Jordan Algebra > s.a. geometric
formulations of quantum mechanics; lie algebras [invariants].
* Idea: An algebra in which the product
satisfies [a, b, a2] = 0 for all
a, b, with [a, b, c]:= (ab)c
− a(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 LA&A(16)-a1401 [5D nilpotent, classification];
Carotenuto et al LMP(19)-a1803 [differential calculus];
> 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];
Farnsworth a2003
[in the standard model of particle physics];
in Baez a2006;
> s.a. entangled quantum systems.
@ And gravity, cosmology: Ambjørn & Watabiki a2003 [as model for the universe].
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 Operator Algebras > see operator theory.
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.
Jordan-Wigner Transformations
* Idea: A mapping between
spin chains and fermionic systems in one dimension.
@ References: Backens et al a1810 [extension to arbitrary tree structures].
Josephson Effect / Junction
> 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.
* Josephson junction: A device
based on this effect, which has become an important technology in its own
right, for example in superconducting quantum interference devices (SQUIDs).
* Related physics: Analysis of
heavy-ion collision experiments uncovers evidence that two colliding nuclei
behave like a Josephson junction
[@ Phys(21)feb].
* 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 backwards 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 the 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.
main page
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send feedback and suggestions to bombelli at olemiss.edu – modified 1 mar 2021