Schwinger effect verified by Unruh temperature?
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According to https://arxiv.org/abs/1407.4569, equation.(2.15), the Schwinger electron-positron pair production rate in Minkowski space,
N
S
NS
, is given in natural units by
N
S
∼exp(−
m
2
T
U
)
NS∼exp(−m2TU)
where the `Unruh temperature for the accelerating charge',
T
U
TU
, is given by
T
U
=
1
2π
qE
m
TU=12πqEm
where
q
q
is the electron charge,
m
m
is the electron mass and
E
E
is the applied electric field.
In principle, could the Schwinger effect be confirmed by measuring the temperature
T
U
TU
rather than trying to detect electron-positron pairs?
In SI Units:
T
U
=
1
2π
ℏ
c
k
B
qE
m
TU=12πℏckBqEm
If the static electric field
E=1
E=1
MV/m then the Unruh temperature
T
U
∼
10
−3
TU∼10−3
K.
Could one use laser cooling to cool atoms down to the millikelvin range and then apply a large electric field of say
10
6
106
V/m? The atoms should warm up due to the Unruh temperature,
T
U
∼
10
−3
TU∼10−3
N
S
NS
, is given in natural units by
N
S
∼exp(−
m
2
T
U
)
NS∼exp(−m2TU)
where the `Unruh temperature for the accelerating charge',
T
U
TU
, is given by
T
U
=
1
2π
qE
m
TU=12πqEm
where
q
q
is the electron charge,
m
m
is the electron mass and
E
E
is the applied electric field.
In principle, could the Schwinger effect be confirmed by measuring the temperature
T
U
TU
rather than trying to detect electron-positron pairs?
In SI Units:
T
U
=
1
2π
ℏ
c
k
B
qE
m
TU=12πℏckBqEm
If the static electric field
E=1
E=1
MV/m then the Unruh temperature
T
U
∼
10
−3
TU∼10−3
K.
Could one use laser cooling to cool atoms down to the millikelvin range and then apply a large electric field of say
10
6
106
V/m? The atoms should warm up due to the Unruh temperature,
T
U
∼
10
−3
TU∼10−3
Answered by
0
Unruh temperature, as a purely geometric effect, is protected ..... the worldline satisfies a Kubo-Martin-Schwinger ( KMS) .... This can be checked by taking p ...
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