The meaning of "adiabatic"

Abstract

This paper is dedicated to Professor John C. Polanyi or1 the occasiorl ofhis 65th birtlldcryKEITH J. LAIDLER Can. J. Chem. 72, 936 (1 994). In chemical kinetics the word "adiabatic" has come to refer to a process in which there is no change of quantum state, a meaning that has no connection with the thermodynamic meaning or with the etymology of the word. This usage is traced to early discussions of reversible adiabatic processes in classical and quantum mechanics, processes that came to be referred to simply as adiabatic.KEITH J. LAIDLER Can. J. Chem. 72,936 (1994). En cinktique chimique, le mot adiabatiques se refkre aujourd'hui a un processus dans lequel il n'y a pas de changement d'ktat quantique, une signification qui n'a aucune relation avec le sens thermodynamique ou avec l'itymologie du mot. On peut retracer I'origine de ce nouvel usage dans les premieres discussions des processus adiabatiques re'versibles de la micanique classique ou quantique auxquels on a fini parse rifkrer simplement adiabatiques.[Traduit par la ridaction] Introduction In chemical kinetics the word "adiabatic" has long been used to refer to a chemical reaction in which the products remain in the same quantum state as the reactants. This usage has created some puzzlement as it does not seem to have, and indeed does not in fact have, any connection with the etymology of the word adiabatic, or with the appropriate use of the word in thermodynamics. The word adiabatic means "not passing through," and in thermodynamics refers to a condition imposed on a system, a condition that prevents any passage of heat into or out of the system. In its kinetic usage the word relates not to a condition imposed on the system, but rather to an inherent property of a chemical process, namely its tendency under certain conditions to occur without any change in quantum states.A consideration of how the kinetic meaning of adiabatic developed is of some interest in the history of science, and is also instructive in leading to a better understanding of some of the fundamental principles of statistical mechanics and quantum mechanics. The trail begins with a paper (1) published in 1866 by Ludwig Boltzmann, in which he mistakenly claimed to have derived the second law of thermodynamics on the basis of classical mechanics. Within a few years, thanks to his study of Clerk Maxwell's papers, he had realized that his argument was invalid, and that the second law must be explained along statistical lines. In his 1868 paper, however, he had considered a reversible adiabatic process, and it is from that argument that the winding and sometimes indistinguishable trail eventually led, through several false turns, to the inappropriate use of the word adiabatic in modern kinetics.

General conditions for quantum adiabatic evolution

“…(13) itself can be seen as a generalization of the Eq. (12) which itself generalizes the standard condition (1). Indeed, if we add to the condition (13) the, fortunately common condition of negligible coupling within the space orthogonal to |n , i.e.…”

“…This result simply highlight the fact that the standard mathematical technique (so called asymptotic analysis) to study the adiabaticity consists in extracting, form the global solution of the Schroedinger equation, a set of local solutions which individually covers a region (let say between time 0 and T ), with a controlled behavior of the coefficients in the equation. This means that the criterion (1) is local and that in order to study the adiabatic behavior of a given hamiltonian, one should cut its evolution in part where we could apply safely the criterion (1), namely in part with single branching point or with single crossing between pairs of levels. Globally we shall add each local non-adiabatic amplitude to get the global non-adiabatic amplitude [16,17,18,19,43].…”

“…The "adiabatic" process, from the Greek α− (a-), not, δια (dia), through, βαινιν (bainen), to pass, was introduced by Carnot (in 1824) and W. J. M. Rankine (in 1858) in thermodynamics, then by Boltzmann (in 1866) in classical mechanics [1]. In 1928, Fritz London applied adiabatic process in chemical kinetics.…”

Microwave Effect in Chemical Reactions

“…The adiabatic theorem, 15,20,21 which is sometimes referred to as Ehrenfest's theorem 22,23 essentially says that if a perturbation changes in time slowly enough, the probability amplitudes do not change even though the overall energy changes over time. In other words, if a system is in its ground state in it ially , it remains in the instantaneous ground state as the perturbation changes slowly in time.…”

Breaking the quantum adiabatic speed limit by jumping along geodesics

“…Besides important applications in quantum state engineering (2,3), quantum simulation (4)(5)(6), and quantum computation (7)(8)(9)(10)(11), the quantum adiabatic evolution itself also provides interesting properties such as Abelian (12) or non-Abelian geometric phases (13), which can be used for the realization of quantum gates. However, the conventional quantum adiabatic theorem (14,15), which dates back to the idea of extremely slow and reversible change in classical mechanics (14,16), imposes a speed limit on the quantum adiabatic methods, that is, for a quantum process to remain adiabatic the changes to the system Hamiltonian at all times must be much smaller than the energy gap of the Hamiltonian. On the other hand, in order to avoid perturbations from the environment high rates of change are desirable.…”