4.3 Predictions
39
4.3 Predictions
With the tools we have developed in this chapter and the calculations of S B z (ω, T )
from MC, it was now possible to predict the structure of magnetic monopole noise
coming from a Dy 2 Ti 2 O 7 sample that is studied in our experiment.
1. Analytic form
Monopole number fluctuations arising out of slight differences in generation and
recombination rates of these particles will manifest as fluctuations in flux through
a superconducting coil. We predict that S N (ω, T ) (as shown in Figs. 4.2 and 4.3)
will embody itself in S (ω, T ) measured by our detector.
S (ω, T ) ∝
τ (T )
1 + ω 2 τ 2 (T )
(4.10)
Fig. 4.2 Predicted spectral
density of fluctuations in
monopole number S N (ω, T )
from Eq. (4.5), for several
monopole GR time constants
τ , in a range that one might
expect to achieve by cooling
Dy 2 Ti 2 O 7 from 4K to ∼1K.
The GR plateau in S N (ω, T )
is clear as ω → 0 as is the
ω −2 falloff expected of free
monopole motion for
frequencies ωτ > 1
Fig. 4.3 Normalized spectral
density S N (ω, T )/S N (0, T )
shows variation of
microscopic time constant τ
with temperature
39
4.3 Predictions
With the tools we have developed in this chapter and the calculations of S B z (ω, T )
from MC, it was now possible to predict the structure of magnetic monopole noise
coming from a Dy 2 Ti 2 O 7 sample that is studied in our experiment.
1. Analytic form
Monopole number fluctuations arising out of slight differences in generation and
recombination rates of these particles will manifest as fluctuations in flux through
a superconducting coil. We predict that S N (ω, T ) (as shown in Figs. 4.2 and 4.3)
will embody itself in S (ω, T ) measured by our detector.
S (ω, T ) ∝
τ (T )
1 + ω 2 τ 2 (T )
(4.10)
Fig. 4.2 Predicted spectral
density of fluctuations in
monopole number S N (ω, T )
from Eq. (4.5), for several
monopole GR time constants
τ , in a range that one might
expect to achieve by cooling
Dy 2 Ti 2 O 7 from 4K to ∼1K.
The GR plateau in S N (ω, T )
is clear as ω → 0 as is the
ω −2 falloff expected of free
monopole motion for
frequencies ωτ > 1
Fig. 4.3 Normalized spectral
density S N (ω, T )/S N (0, T )
shows variation of
microscopic time constant τ
with temperature