Hamiltonian

See also: hamiltonian

English

Pronunciation

• Rhymes: -əʊniən

Etymology 1

From Hamilton (“a surname”) +‎ -ian.

Adjective

Hamiltonian (not comparable)

1. (mathematics) Of, attributed to or inspired by the Irish mathematician, astronomer and physicist William Rowan Hamilton (1805–1865).
2. (mathematics, graph theory, of a cycle/path) That visits each vertex exactly once.
3. (mathematics, graph theory, of a graph) Containing a Hamiltonian cycle.
   • 2016, Jacky Cresson, Jordy Palafox, “Isochronous centers of polynomial Hamiltonian systems and a conjecture of Jarque and Villadelprat”, in arXiv‎^[1]:

     Using the correction of a vector field to characterize isochronicity and explicit computations of this quantity for polynomial vector fields, wa are able to describe a very large class of nonisochronous Hamiltonian system of even degree of degree arbitrary large.

4. (historical, chiefly US, of certain fiscal policies) Advocated by American politician Alexander Hamilton (1755-1804).
5. Relating to James Hamilton (1769-1831), or his method of teaching languages without grammar, by a literal interlinear word-for-word translation.
6. Of, relating to, or in the literary style of Edmond Hamilton (1904–1977), American science fiction writer.
7. Relating to Sir William Hamilton, 9th Baronet (1788–1856), Scottish metaphysician.

Derived terms

Derived terms

• Hamiltonian constraint
• Hamiltonian cycle
• Hamiltonianness
• Hamiltonian path
• Hamiltonian spite
• hypohamiltonian
• pseudohamiltonian

Noun

Hamiltonian (plural Hamiltonians)

1. (physics, Hamiltonian mechanics) A function (of time), denoted H, that corresponds to the total energy of the system.
   • 2016, Edward Farhi, Aram W Harrow, “Quantum Supremacy through the Quantum Approximate Optimization Algorithm”, in arXiv‎^[2]:

     We contrast this with the case of sampling from the output of a quantum computer running the Quantum Adiabatic Algorithm (QADI) with the restriction that the Hamiltonian that governs the evolution is gapped and stoquastic.

   • 2016, R. Barends et al., “Digitized adiabatic quantum computing with a superconducting circuit”, in Nature, 534, 222-226, 9 June 2016:

     As stoquastic problems we use frustrated Ising Hamiltonians, having random local X and Z fields, and random σ_zσ_z couplings.

2. (physics, quantum mechanics) The observable, denoted H, that corresponds to the total energy of the system.
3. (historical, chiefly US) A member of the faction of the US government in the George Washington administration led by Alexander Hamilton.

Derived terms

• H
• Kamiltonian

Translations

(quantum mechanics)

• Danish: Hamiltonoperator c
• Persian: هامیلتونی (hâmiltoni)
• Portuguese: hamiltoniano m

Etymology 2

From Hamilton (“a place name”) +‎ -ian.

Adjective

Hamiltonian (comparative more Hamiltonian, superlative most Hamiltonian)

1. Of or relating to any city named Hamilton.

Noun

Hamiltonian (plural Hamiltonians)

1. A native or inhabitant of any city named Hamilton.