, , (. 1.32):
, 0 ≤ t ≤ NT
ψk - , φ 0.
.1.32. N .
rN (τ) (.1.33)
.
.1.33. .
, | τ | ≤ NT .
S 0(ω) SN (ωT ), , F = 1 / T , SN (ω) (.1.34):
, .
, . NT :
.
.1.34. .
Δ f 0, Δ f 0 T .
τ, F. , τ
.
, , ρ (τ,0) :
.
F ,
.
. 1.35.
.1.35. .
ρ (τ, F) . , . , T , F . τ NT , F 1/ T .
|
|
( 0 = T ) τ, F τ, , ,
.
.1.36.
.1.36. .
, , , , ρ (τ, F) , -, Δ tr = Δ τ = 1/Δ f 0 Δ F = Δ FN = 1/ NT -, tr = T F = 1/ T . 0= T F → ∞.
(U (t)=1) (.1.37):
.1.37. .
, () , .
,
C (τ) = 1 (.1.38).
.1.38. .
,
ω 0 (.1.39).
.1.39. .
, (.1.40).
.1.40. .
U (t) = | U (t)|e iψ ( t ), , , .
|
|
- ( ) :
.
M (t), ( ), , () . , . M (t) , . . (. 1.41.):
,
.
τ ( , , , , .) .
.1.41. .
, :
.
r 0(τ). rN (τ) rC (τ) :
rNC (τ) = rN (τ) rC (τ).
,
, , :
, .
, .. , , -, , ( ) , -, :
.
. , , , , .
x (t). (x 1, x 2,, xN). p (x 1, x 2,, xN).
dx 1 × dx 2×× dxN, : x 1 x 1 + dx 1, - x 2 x 2 + dx 2 :
|
|
x 1 < x (t 1) < x 1 + dx 1;
x 2 < x (t 2) < x 2 + dx 2;
x N < x (tN) < xN + dxN.
x 1, x 2,, xN ,
p (x 1, x 2,, xN) dx 1× dx 2×× dxN
x (t) "", xk (.1.42):
xk < x (tk) < xk + dxk.
. 1.42. .
, (t) ( , , ), ( ) (t)
,
( ) , , - , - , , - () .
N = 1, 1 1* ( ):
.
x y ( 1, 1*) → (x, y).
, 1 = x + iy, 1* = x iy, :
.
(. 1.43).
.1.43. .
()
,
.
φ
( 1, 1*) → ( , φ ).
, ,
.
.
, , :
,
, -π π (.1.44).
.1.44. .
, -π π ,
, E c ≥ 0,
(.1.45).
.1.45. .
:
|
|
,
.
:
.
, , →
.
:
, Pc ≥ 0.
(. 1.46).
.1.46.
(, -, ) . 3 ; , . , , . , , - .
, , , . ( ) :
,
- , xh (t), yh (t) - .
. 1.47.
. 1.47. .
,
- , r (τ) - .
, , :
(. 1.48):
,
τ - .
ω0 :
.
. 1.48. .
(. 1.49):
.
. 1.49. .
:
.
:
.
, Δ f >> Δ f 0. , , :
.
. , (. 1.50).
. 1.50. .
, ,
,
.. -, (. 1.51):
. 1.51. .
, , .
, Δ t >> τ . δkl:
,
.
:
|
|
L .
:
,
.
, , .