DICTIONARY OF MATERIAL SCIENCE AND HIGH ENERGY PHYSICS
A SPHERE (THE SIMPLEST CASE TO ANALYZE), THE DRAG FORCE IN AN IDEAL (FRICTIONLESS) ?OW DUE TO ACCEL- ERATION IS D = 3?R3? DU DT WHICH IS EQUIVALENT TO INCREASING THE VOLUME OF THE SPHERE BY EXACTLY 1/2 THUS, THE INCREASED DRAG FORCE MAY BE NEGLECTED IF THE ADDED MASS IS INCLUDED IN THE SPHERE TO GIVE A TOTAL MASS OF (? + V ?P ?V S ADIABATIC INVARIANT CHARACTERISTIC PARAME- TER THAT DOES NOT CHANGE AS A PHYSICAL SYSTEM SLOWLY EVOLVES; THE MOST COMMONLY USED ADIA- BATIC INVARIANT IN PLASMA PHYSICS IS THE MAGNETIC MOMENT OF A CHARGED PARTICLE THAT IS SPIRALING AROUND A MAGNETIC ?ELD LINE ADIABATIC PLASMA COMPRESSION COMPRES- SION OF A GAS AND/OR PLASMA THAT IS NOT ACCOM- PANIED BY GAIN OR LOSS OF HEAT FROM OUTSIDE THE PLASMA CON?NEMENT SYSTEM FOR EXAMPLE, PLAS- MA IN AN INCREASING MAGNETIC ?ELD THAT RESULTS IN PLASMA COMPRESSION SLOW ENOUGH THAT THE MAG- NETIC MOMENT, OR OTHER ADIABATIC INVARIANTS OF THE PLASMA PARTICLES, MAY BE TAKEN AS CONSTANT ADIABATIC PROCESS A PROCESS IN WHICH NO HEAT ENTERS OR LEAVES A SYSTEM ADIABATIC THEOREM DESCRIBES THE BEHAVIOR OF THE WAVE FUNCTION FOR A SYSTEM UNDERGOING ADI- ABATIC EVOLUTION CONSIDER A QUANTUM SYSTEM WHOSE TIME EVOLUTION IS GOVERNED BY A HAMIL- TONIAN H(R(T)), WHERE R(T) IS A NON-QUANTUM MECHANICAL PARAMETER AND T IS THE TIME PARAME- TER INTHELIMITOFSLOWEVOLUTION, SOTHATTHETIME DERIVATIVEOFH(T)CANBENEGLECTED, M BORNAND V FOCK SHOWED THAT |(T) >= EXP(?I ¯H T E(T) DT)|(0) >, WHERE E(T) IS THE INSTANTANEOUS EN- ERGYEIGENVALUEFORSTATE|(T) >, ISASOLUTIONTO THE TIME DEPENDENT SCHRÖDINGER EQUATION THIS IS A STATEMENT OF THE QUANTUM ADIABATIC THEOREM THAT WAS GENERALIZED IN 1984 BY M V BERRY SEE BERRY’S PHASE ADJOINT EQUATION A CORRESPONDING RELATION- SHIP THAT RESULTS FROM REPLACING OPERATORS BY THEIR HERMITIAN CONJUGATE, ORDINARY NUMBERS BY THEIR COMPLEX CONJUGATE, CONJUGATING BRAS INTO KETS (AND KETS INTO BRAS), AND REVERSING WITHIN EACH INDIVIDUAL TERM THE ORDER OF THESE SYMBOLS ADJOINT OPERATOR PROPERTY ASSOCIATED WITH A PAIR OF OPERATORS FOR OPERATOR A THAT HAS THE PROPERTY A|? >= |?? >, WHERE |? >, |?? > ARE VECTORS IN HILBERT SPACE, THE OPERATOR A† IS CALLED THE ADJOINT OPERATOR OF A IT HAS THE FOL- LOWING PROPERTY < ?|A† =< ??|, WHERE < ?| IS THE DUAL TO VECTOR |? > IF A IS A SQUARE MA- TRIX, THEN A† IS THE MATRIX OBTAINED BY TAKING