On the Adiabatic Theorem of Quantum Mechanics

1950 ◽  
Vol 5 (6) ◽  
pp. 435-439 ◽  
Author(s):  
Tosio Kato
Keyword(s):  
Quantum Mechanics ◽  
Adiabatic Theorem

Extensions of the Adiabatic Theorem in Quantum Mechanics

1970 ◽  
Vol 1 (2) ◽  
pp. 419-429 ◽  
Author(s):  
Ralph H. Young ◽  
Walter J. Deal
Keyword(s):  
Quantum Mechanics ◽  
Adiabatic Theorem

scholarly journals Tosio Kato’s work on non-relativistic quantum mechanics, Part 2

2019 ◽  
Vol 09 (01) ◽  
pp. 1950005 ◽  
Author(s):  
Barry Simon
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Trace Class ◽  
Product Formula ◽  
Relativistic Quantum Mechanics ◽  
Adiabatic Theorem ◽  
Trotter Product Formula ◽  
Embedded Eigenvalues

We review the work of Tosio Kato on the mathematics of non-relativistic quantum mechanics and some of the research that was motivated by this. Topics in this second part include the absence of embedded eigenvalues, trace class scattering, Kato smoothness, the quantum adiabatic theorem and Kato’s ultimate Trotter Product Formula.

On the adiabatic theorem in quantum mechanics

2001 ◽  
Vol 27 (2) ◽  
pp. 93-96 ◽  
Author(s):  
A. G. Chirkov
Keyword(s):  
Quantum Mechanics ◽  
Adiabatic Theorem

scholarly journals Comments on the adiabatic theorem

2018 ◽  
Vol 33 (24) ◽  
pp. 1850140 ◽  
Author(s):  
Dmitrii A. Trunin
Keyword(s):  
Quantum Mechanics ◽  
Quantum System ◽  
Level Population ◽  
Quantum Mechanical ◽  
Mechanical Oscillator ◽  
Adiabatic Theorem ◽  
Diagrammatic Technique ◽  
Energy Pumping

We consider the simplest example of a nonstationary quantum system which is quantum mechanical oscillator with varying frequency and [Formula: see text] self-interaction. We calculate loop corrections to the Keldysh, retarded/advanced propagators and vertices using Schwinger–Keldysh diagrammatic technique and show that there is no physical secular growth of the loop corrections in the cases of constant and adiabatically varying frequency. This fact corresponds to the well-known adiabatic theorem in quantum mechanics. However, in the case of nonadiabatically varying frequency we obtain strong IR corrections to the Keldysh propagator which come from the “sunset” diagrams, grow with time indefinitely and indicate energy pumping into the system. It reveals itself via the change in time of the level population and of the anomalous quantum average.

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