Property of physical systems that stays somewhat constant through slow changes
This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations.(February 2023) (Learn how and when to remove this message)
A property of a physical system, such as the entropy of a gas, that stays approximately constant when changes occur slowly is called an adiabatic invariant. By this it is meant that if a system is varied between two end points, as the time for the variation between the end points is increased to infinity, the variation of an adiabatic invariant between the two end points goes to zero.
In thermodynamics, an adiabatic process is a change that occurs without heat flow; it may be slow or fast. A reversible adiabatic process is an adiabatic process that occurs slowly compared to the time to reach equilibrium. In a reversible adiabatic process, the system is in equilibrium at all stages and the entropy is constant. In the 1st half of the 20th century the scientists that worked in quantum physics used the term "adiabatic" for reversible adiabatic processes and later for any gradually changing conditions which allow the system to adapt its configuration. The quantum mechanical definition is closer to the thermodynamical concept of a quasistatic process and has no direct relation with adiabatic processes in thermodynamics.
In mechanics, an adiabatic change is a slow deformation of the Hamiltonian, where the fractional rate of change of the energy is much slower than the orbital frequency. The area enclosed by the different motions in phase space are the adiabatic invariants.
In quantum mechanics, an adiabatic change is one that occurs at a rate much slower than the difference in frequency between energy eigenstates. In this case, the energy states of the system do not make transitions, so that the quantum number is an adiabatic invariant.
The old quantum theory was formulated by equating the quantum number of a system with its classical adiabatic invariant. This determined the form of the Bohr–Sommerfeld quantization rule: the quantum number is the area in phase space of the classical orbit.
and 22 Related for: Adiabatic invariant information
stays approximately constant when changes occur slowly is called an adiabaticinvariant. By this it is meant that if a system is varied between two end points...
the quantum numbers. The quantum mechanical concept of adiabatic is related to adiabaticinvariant, it is often used in the old quantum theory and has no...
complexity A result in classical mechanics for adiabaticinvariants A theorem of algorithmic probability Invariant (mathematics) This disambiguation page lists...
true constants of motion, such as energy, reducing it to merely an "adiabaticinvariant." For most plasmas in the magnetosphere, the deviation from constancy...
relates closely to the second adiabaticinvariant J{\displaystyle {\cal {J}}} (often called the parallel or longitudinal invariant). One can show that the radial...
{\displaystyle \mu =mv_{\perp }^{2}/2B} is the magnetic moment (first adiabaticinvariant). The direction in the subscript indicates parallel or perpendicular...
Ehrenfest's most important contribution from 1912 to 1933 is the theory of adiabaticinvariants. It is a concept derived from classical mechanics that, on the one...
Wissenschaften zu Berlin: 548–568. Ehrenfest, P. (June 1917). "XLVIII. Adiabaticinvariants and the theory of quanta". The London, Edinburgh, and Dublin Philosophical...
analysis and developed fundamental ideas about asymptotic expansions, adiabaticinvariants, and numerous related topics. His Ph.D. dissertation, written under...
Littlejohn. At University of California, Berkeley, Jarzynski studied adiabaticinvariants in chaotic classical systems. After graduating with a PhD, he spent...
Planck satellite gives a constraint of r < 0.11 {\displaystyle r<0.11} . Adiabatic fluctuations are density variations in all forms of matter and energy...
Shortcuts to adiabaticity (STA) are fast control protocols to drive the dynamics of system without relying on the adiabatic theorem. The concept of STA...
principle, is the only one possible, since the quantum numbers are adiabaticinvariants. The Bohr–Sommerfeld model was fundamentally inconsistent and led...
quantum mechanics, the Berry phase arises in a cyclic adiabatic evolution. The quantum adiabatic theorem applies to a system whose Hamiltonian H ( R )...
physical observation that the quantities which are quantized must be adiabaticinvariants. Given Planck's quantization rule for the harmonic oscillator, either...
conditions, such as complete combustion under adiabatic conditions (i.e., no heat loss or gain), the adiabatic combustion temperature can be determined. The...
Tennyson, J. L.; Cary, John R.; Escande, D. F. (1986). "Change of the AdiabaticInvariant due to Separatrix Crossing". Physical Review Letters. 56 (20): 2117–2120...
cannot be cancelled; it is invariant and becomes an observable property of the system. By reviewing the proof of the adiabatic theorem given by Max Born...
Antonio; Paleari, Simone; Penati, Tiziano (2015). "An extensive adiabaticinvariant for the Klein-Gordon model in the thermodynamic limit". Annales Henri...
linked the postulate proposed three years earlier to the theory of adiabaticinvariants. Around the same time, analogous rules for quantizing systems of...
Global Information