Arrival times in quantum mechanics

Seidel D.

Table of contents :
Introduction……Page 7
Classical arrival time……Page 11
Quantum arrival times for free motion……Page 13
Quantum mechanical flux……Page 14
Kijowski’s distribution……Page 15
Aharonov-Bohm arrival-time operator and POVMs……Page 16
Arrival-time distributions and the relation to local densities……Page 18
Phase times, tunneling times, transmission times……Page 19
Classical dwell time……Page 21
Classical flux-flux correlation function……Page 22
Quantum dwell times……Page 23
Quantum dwell-time operator……Page 24
Dwell-time distribution for free motion……Page 25
Moments of the dwell-time distribution……Page 26
An alternative proposal for free dwell times……Page 28
Operational approaches to quantum arrival times……Page 30
Conditional time evolution……Page 31
The reset operation and the Bloch equation……Page 32
Exclusive and non-exclusive detection probability……Page 34
Example: Two-level system with quantized cm motion……Page 35
Corrections to the conditional time evolution……Page 38
Laser-based approach to quantum arrival-time distributions……Page 39
The probability density for the first photon……Page 41
Detection delay and reflection……Page 43
Deconvolution and ideal distributions……Page 45
Normalized arrival-time distributions……Page 47
Galilean invariance of the first-photon distribution……Page 50
The probability density for the first photon……Page 51
Parameter regimes for the narrow laser model……Page 53
Arrival-time measurement with absorbing potentials……Page 55
Absorbing potentials as a limiting case of the laser model……Page 56
Deconvolution of the absorption rate……Page 58
The reset state for absorption……Page 59
Position-dependent decay rate……Page 60
Local kinetic energy densities……Page 61
Measurement-based approach to kinetic energy densities……Page 62
The case of fixed decay rate……Page 64
Expansion of Kijowski’s distribution……Page 67
Operational approach to mean dwell times……Page 69
Quantum flux-flux correlations……Page 70
First moment……Page 72
Second moment……Page 73
Photon-photon correlations……Page 75
Normalization on the level of operators……Page 77
Connection to Kijowski’s arrival-time distribution……Page 79
Fixed decay rate……Page 81
Operator normalization and connection with the flux……Page 83
Alternative derivation of the operator normalization……Page 84
Operator normalization for narrow laser fields……Page 85
Operator normalization for absorbing potentials……Page 86
Operator normalization and filtering……Page 88
Real-valued filter potentials……Page 90
Arrival times in the presence of interactions……Page 99
Operator-normalized absorption rate……Page 100
Generalized free arrival-time distributions……Page 102
Left incidence……Page 103
Symmetric and antisymmetric incidence……Page 104
General incidence……Page 105
Generalized arrival-time distribution in the presence of interactions……Page 106
Arrival time behind a potential barrier……Page 107
Mean arrival times and the Hartman effect……Page 110
Arrival time inside a potential barrier……Page 113
Arrival time in front of a potential barrier……Page 114
Example: Linear potentials……Page 116
Example: Reflectionless potentials……Page 119
Conclusion……Page 124
The classical case……Page 128
The quantum case……Page 129
One-channel case……Page 131
Potential barrier……Page 132
Potential step……Page 133
Continuous potentials……Page 134
Two-channel case……Page 135
Half-space laser field……Page 136
Dirac delta laser field……Page 137
One-dimensional scattering……Page 138
Relation between transmission and reflection coefficients……Page 139
Marchenko equations with bound states……Page 140
Bibliography……Page 141