Exact Spin Coherent State Path Integral for a Damped Two-Level Atom in an Electromagnetic Wave

2013 ◽  
Vol 52 (10) ◽  
pp. 3662-3675 ◽  
Author(s):  
Farida Halimi ◽  
Mekki Aouachria
Keyword(s):  
Electromagnetic Wave ◽  
Coherent State ◽  
Path Integral ◽  
Spin Coherent State ◽  
Level Atom ◽  
State Path

Exact spin coherent state path integral for a two-level atom in gravitational fields

2011 ◽  
Vol 89 (11) ◽  
pp. 1141-1148 ◽  
Author(s):  
Mekki Aouachria
Keyword(s):  
Electromagnetic Wave ◽  
Path Integral ◽  
Standard Form ◽  
Unit Vector ◽  
Wave Functions ◽  
Integral Formalism ◽  
Gravitational Fields ◽  
Spin Coherent State ◽  
Level Atom ◽  
State Path

The movement of a two-level atom interacting with an electromagnetic wave while subject to gravity is studied using path-integral formalism. The propagator is first written in a standard form, ∫[Formula: see text](path) exp(i/ℏ)S(path), by replacing the spin with a unit vector aligned along the polar and azimuthal directions to determine the propagator exactly. Thus, the exact wave functions of the system are deduced.

scholarly journals A NOTE ON (SPIN-) COHERENT-STATE PATH INTEGRAL

1999 ◽  
Vol 13 (02) ◽  
pp. 107-140 ◽  
Author(s):  
JUNYA SHIBATA ◽  
SHIN TAKAGI
Keyword(s):  
Coherent State ◽  
Path Integral ◽  
Continuous Time ◽  
Classical Level ◽  
Classical Action ◽  
Single Spin ◽  
Spin Coherent State ◽  
Classical Path ◽  
Time Formalism ◽  
State Path

It is pointed out that there are some fundamental difficulties with the frequently used continuous-time formalism of the spin-coherent-state path integral. They arise already in a single-spin system and at the level of the "classical action" not to speak of fluctuations around the "classical path". Similar difficulties turn out to be present in the case of the (boson-)coherent-state path integral as well; although partially circumventable by an ingenious trick (Klauder's ∊-prescription) at the "classical level", they manifest themselves at the level of fluctuations. Detailed analysis of the origin of these difficulties makes it clear that the only way of avoiding them is to work with the proper discrete-time formalism. The thesis is explicitly illustrated with a harmonic oscillator and a spin under a constant magnetic field.

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