EXPONENTIAL DECAY AND GEOMETRIC ASPECT OF TRANSITION-PROBABILITIES IN THE ADIABATIC LIMIT

被引：82

作者：

JOYE, A ^{[1
]}

KUNZ, H ^{[1
]}

PFISTER, CE ^{[1
]}

机构：

[1] ECOLE POLYTECH FED LAUSANNE,DEPT MATH,CH-1015 LAUSANNE,SWITZERLAND

来源：

ANNALS OF PHYSICS | 1991年 / 208卷 / 02期

关键词：

D O I：

10.1016/0003-4916(91)90297-L

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider a quantum mechanical system whose hamiltonian is a time-dependent analytic n × n matrix. For n = 2 we establish a generalization of Dykhne formula which gives the transition probability from one energy level to the other in the adiabatic limit. We discuss in particular the geometric nature of this formula. In the general case, n ≥ 2, we prove an upper bound for the probability of such transitions which shows that they are exponentially small. © 1991.

引用

页码：299 / 332

页数：34

共 17 条

[1]

Berry M. V., 1989, GEOMETRIC PHASES PHY

[2] QUANTAL PHASE-FACTORS ACCOMPANYING ADIABATIC CHANGES [J].

BERRY, MV .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1984, 392 (1802) :45-57

[3] GEOMETRIC AMPLITUDE FACTORS IN ADIABATIC QUANTUM TRANSITIONS [J].

BERRY, MV .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1990, 430 (1879) :405-411

[4] Proof of Adiabatic law [J].

Born, M. ;

Fock, V. .

ZEITSCHRIFT FUR PHYSIK, 1928, 51 (3-4) :165-180

[5] NONADIABATIC TRANSITIONS INDUCED BY A TIME-DEPENDENT HAMILTONIAN IN SEMICLASSICAL ADIABATIC LIMIT - 2-STATE CASE [J].

DAVIS, JP ;

PECHUKAS, P .

JOURNAL OF CHEMICAL PHYSICS, 1976, 64 (08) :3129-3138

[6]

DYKHNE AM, 1962, ZH EKSP TEOR FIZ, V14, P941

[7]

Fedoriouk M., 1987, METHODES ASYMPTOTIQU

[8] ADIABATIC THEOREM IN COMPLEX PLANE AND SEMICLASSICAL CALCULATION OF NONADIABATIC TRANSITION AMPLITUDES [J].

HWANG, JT ;

PECHUKAS, P .

JOURNAL OF CHEMICAL PHYSICS, 1977, 67 (10) :4640-4653

[9]

JOYE A, 1989, EXPONENTIAL DECAY TO

[10]

JOYE A, IN PRESS COMMUN MATH

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