Content deleted Content added
m Open access bot: hdl, arxiv, doi added to citation with #oabot. |
m Various citation & identifier cleanup (Citation bot to follow) |
||
Line 60:
</math>where <math>
k_B
</math> is the Boltzmann constant. Several experiments can test such a spread. They range from cold atom free expansion,<ref name=":6" /><ref name=":7" /> nano-cantilevers cooled to millikelvin temperatures,<ref name=":8" /><ref>{{Cite journal|last=Vinante|first=A.|last2=Mezzena|first2=R.|last3=Falferi|first3=P.|last4=Carlesso|first4=M.|last5=Bassi|first5=A.|date=2017-09-12|title=Improved Noninterferometric Test of Collapse Models Using Ultracold Cantilevers|url=https://link.aps.org/doi/10.1103/PhysRevLett.119.110401|journal=Physical Review Letters|volume=119|issue=11|pages=110401|doi=10.1103/PhysRevLett.119.110401|hdl=11368/2910142|hdl-access=free}}</ref><ref>{{Cite journal|last=Carlesso|first=Matteo|last2=Vinante|first2=Andrea|last3=Bassi|first3=Angelo|date=2018-08-17|title=Multilayer test masses to enhance the collapse noise|url=https://link.aps.org/doi/10.1103/PhysRevA.98.022122|journal=Physical Review A|volume=98|issue=2|pages=022122|doi=10.1103/PhysRevA.98.022122}}</ref> gravitational wave detectors,<ref>{{Cite journal|last=Carlesso|first=Matteo|last2=Bassi|first2=Angelo|last3=Falferi|first3=Paolo|last4=Vinante|first4=Andrea|date=2016-12-23|title=Experimental bounds on collapse models from gravitational wave detectors|url=https://link.aps.org/doi/10.1103/PhysRevD.94.124036|journal=Physical Review D|volume=94|issue=12|pages=124036|doi=10.1103/PhysRevD.94.124036|hdl=11368/2889661|hdl-access=free}}</ref><ref>{{Cite journal|last=Helou|first=Bassam|last2=Slagmolen|first2=B. J. J.|last3=McClelland|first3=David E.|last4=Chen|first4=Yanbei|date=2017-04-28|title=LISA pathfinder appreciably constrains collapse models|url=https://link.aps.org/doi/10.1103/PhysRevD.95.084054|journal=Physical Review D|volume=95|issue=8|pages=084054|doi=10.1103/PhysRevD.95.084054|doi-access=free}}</ref> levitated optomechanics,<ref name=":9" /><ref>{{Cite journal|last=Zheng|first=Di|last2=Leng|first2=Yingchun|last3=Kong|first3=Xi|last4=Li|first4=Rui|last5=Wang|first5=Zizhe|last6=Luo|first6=Xiaohui|last7=Zhao|first7=Jie|last8=Duan|first8=Chang-Kui|last9=Huang|first9=Pu|last10=Du|first10=Jiangfeng|last11=Carlesso|first11=Matteo|date=2020-01-17|title=Room temperature test of the continuous spontaneous localization model using a levitated micro-oscillator|url=https://link.aps.org/doi/10.1103/PhysRevResearch.2.013057|journal=Physical Review Research|volume=2|issue=1|pages=013057|doi=10.1103/PhysRevResearch.2.013057|doi-access=free}}</ref><ref name=":11">{{
== Dissipative and colored extensions ==
The CSL model describes consistently the collapse mechanism as a dynamical process. It has, however, two weak points.
* ''CSL does not conserve the energy of isolated systems''. Although this increase is small, it is an at least unpleasant feature also for a phenomenological model.<ref name=":2" />
E(t)=e^{-\beta t}(E(0)-E_{ as})+E_{ as},
</math>where <math>
E_{ as}=\tfrac32 k_B T_{ CSL}</math>, <math>\beta=4 \chi \lambda /(1+\chi)^5</math> and <math>\chi=\hbar^2/(8 m_0 k_B T_{ CSL}r_C^2)</math>. Assuming that the CSL noise has a cosmological origin (which is reasonable due to its supposed universality), a plausible value such a temperature is <math>T_{ CSL}=1</math> K, although only experiments can indicate a definite value. Several interferometric<ref name=":4" /><ref name=":10" /> and non-interferometric<ref name=":7" /><ref name=":11" /><ref>{{Cite journal|last=Nobakht|first=J.|last2=Carlesso|first2=M.|last3=Donadi|first3=S.|last4=Paternostro|first4=M.|last5=Bassi|first5=A.|date=2018-10-08|title=Unitary unraveling for the dissipative continuous spontaneous localization model: Application to optomechanical experiments|url=https://link.aps.org/doi/10.1103/PhysRevA.98.042109|journal=Physical Review A|volume=98|issue=4|pages=042109|doi=10.1103/PhysRevA.98.042109|hdl=11368/2929989|hdl-access=free}}</ref> tests bound the CSL parameter space for different choices of <math>T_{CSL}</math>.
* ''The CSL noise spectrum is white''. If one attributes a physical origin to the CSL noise, then its spectrum cannot be white, but colored. In particular, in place of the white noise <math>w_t({\bf x})</math>, whose correlation is proportional to a Dirac delta in time, a non-white noise is considered, which is characterized by a non-trivial temporal correlation function <math>f(t)</math>. The effect can be quantified by a rescaling of <math>F_{{ CSL}}(k,q,t)</math>, which becomes<math display="block">
F_{{cCSL}}(k,q,t)=F_{{ CSL}}(k,q,t) \exp\left[ \frac{\lambda \bar\tau}{2}\left( e^{-(q-k t/m)^2/4r_C^2}-e^{-q^2/4r_C^2} \right) \right],
</math>where <math> \bar\tau=\int_0^t\operatorname{d}\! s\,f(s)</math>. As an example, one can consider an exponentially decaying noise, whose time correlation function can be of the form<ref name=":12">{{Cite journal|last=Carlesso|first=Matteo|last2=Ferialdi|first2=Luca|last3=Bassi|first3=Angelo|date=2018-09-18|title=Colored collapse models from the non-interferometric perspective|url=https://doi.org/10.1140/epjd/e2018-90248-x|journal=The European Physical Journal D|language=en|volume=72|issue=9|pages=159|doi=10.1140/epjd/e2018-90248-x|issn=1434-6079|doi-access=free}}</ref> <math>f(t)=\tfrac12\Omega_{ C}e^{-\Omega_{ C}|t|}</math>. In such a way, one introduces a frequency cutoff <math>\Omega_{C}</math>, whose inverse describes the time scale of the noise correlations. The parameter <math>\Omega_{ C}</math> works now as the third parameter of the colored CSL model together with <math>\lambda</math> and <math>r_C</math>. Assuming a cosmological origin of the noise, a reasonable guess is<ref>{{Cite journal|last=Bassi|first=A.|last2=Deckert|first2=D.-A.|last3=Ferialdi|first3=L.|date=2010-12-01|title=Breaking quantum linearity: Constraints from human perception and cosmological implications|url=https://iopscience.iop.org/article/10.1209/0295-5075/92/50006|journal=EPL (Europhysics Letters)|language=en|volume=92|issue=5|pages=50006|doi=10.1209/0295-5075/92/50006|issn=0295-5075|arxiv=1011.3767}}</ref> <math>\Omega_{ C}=10^{12}\,</math>Hz. As for the dissipative extension, experimental bounds were obtained for different values of <math>\Omega_{ C}</math>: they include interferometric<ref name=":4" /><ref name=":10" /> and non-interferometric<ref name=":7" /><ref name=":12" /> tests.
== References ==
| |||