In United States federal courts, this is referred to as an assignment "by designation" of the Chief Justice of the United States (for inter-circuit assignments) or the Circuit Chief Judge (for intra-circuit assignments), and is authorized by 28 U.S.C.
[1][2] In many United States Courts of Appeals it is not uncommon for a district judge to sit on a panel as a visiting judge; less frequently it is a judge from another circuit (in active service or, more commonly, in senior status).
Retired Supreme Court justices have done the same, including Justices Sandra Day O'Connor,[3] David Souter, and Stephen Breyer,[4] and very unusually, sitting justices (in 1984, for example, Justice William Rehnquist served as a visiting judge for a jury trial in the United States District Court for the Eastern District of Virginia).
[5] This is sometimes done to ease caseload pressures, and sometimes (as in Rehnquist's case) for experience.
[6] In other cases, notably those of some judges in senior status, the individual may sit in a different court for personal reasons (such as sitting in areas popular with retirees such as Florida or in a person's hometown).