A → quantum walk taking place entirely in
the position space. Continuous-time quantum walk was introduced by E. Farhi & S. Gutmann
(1998, Phys. Rev. A 58, 915).

A → quantum walk involving a probabilistic
→ operator that changes the direction while leaving the position
fixed, and a shift operator that changes the position. Discrete-time quantum walk
was introduced by J. Watrous (2001, Journal of Computer and System Sciences 62, 376)

A generalization of the classical concept of → random walk
using quantum mechanical laws such as the → superposition principle
and → interference of quantum amplitudes. In the classical
version the particle moves in the
position space with a certain probability. In contrast, in the quantum counterpart
the particle moves by exploring multiple
possible paths simultaneously with the amplitudes corresponding to the
influence of different paths.
The concept of quantum walk is studied in two
standard forms: → continuous-time quantum walk
and → discrete-time quantum walk.
Quantum walk was first introduced by Aharonov et al.
(1993, Phys. Rev. A, 48, 1687).

The mathematical description of the interval (→ space-time
separation) between → events ("points" in space-time)
in a → homogeneous and
→ isotropic → Universe.
It results from an exact solution of
→ Einstein's field equations
of → general relativity.
Under the assumptions, the
Robertson-Walker interval is expressed by:
ds^{2} = c^{2}dt^{2} -
R^{2}(t) [dr^{2}/(1 - kr^{2}) +
r^{2}dθ^{2} +
r^{2}sin^{2}θ dθ^{2})].
Same as Friedmann-Lemaître-Robertson-Walker metric.
Compare → Minkowski metric.

Named after Howard Percy Robertson (1903-1961), American mathematician and physicist, and
Arthur Geoffrey Walker (1909-2001), British mathematician and physicist, for their
contributions to physics and physical cosmology; → metric.

walk

۱) چمیدن، گامیدن؛ ۲) چم، پویش

1) camidan (#), gâmidan (#); 2) cam; puyeš (#)

Fr.: 1) marcher; 2) marche

1) To move along on foot at a moderate pace; advance by steps.
2a) An act or instance of walking.
2b) Physics: A moving of a particle among particles.
→ random walk;
→ quantum walk.