Probabilistic Modelling of Classical and Quantum Systems

While probabilistic modelling has been widely used in the last decades, the quantitative prediction in stochastic modelling of real physical problems remains a great challenge and requires sophisticated mathematical models and advanced numerical algorithms. In this study, we developed the mathematical tools for solving three long-standing problems in Polymer Science and Quantum Measurement theory. The question, “Why kinetic models cannot reproduce experimental observations in Controlled Radical Polymerization (CRP)?” has been answered by introducing in the kinetic model a delay and treating CRP as a non-Markovian process. The efficient stochastic simulation (SS) approach allowing for an accurate description of CRP has been formulated, theoretically grounded and tested using experimental data and the less advanced SS algorithms. An accurate prediction of a morphology development in multi-phase polymers is vital for synthesis of new materials but still not feasible due to its complexity. We proposed a Population Balance Equations (PBE)-based model and derived a conceptually new and computationally tractable numerical approach for its solution in order to provide a systematic tool for a morphology prediction in composite polymers. Finally, we designed a stochastic simulation framework for continuous measurements performed on quantum systems of theoretical and experimental interest, which helped us to re-examine the “fuzzy continuous measurements” theory by Audretsch and Mensky (1997) and expose some of its deficiencies, while making amendments where necessary. All developed modelling approaches are general enough to be applied to the broad range of physical applications and thus ultimately to contribute to the understanding and prediction of complex chemical and physical processes.BES-2014-06864, MTM2013-46553-C3-1-

An innovative technique for the investigation of the 4-fold forbidden beta-decay of 50^{50}V

For the first time a Vanadium-based crystal was operated as cryogenic particle detector. The scintillating low temperature calorimetric technique was used for the characterization of a 22 g YVO$_4$ crystal aiming at the investigation of the 4-fold forbidden non-unique $\beta^-$ decay of $^{50}$V. The excellent bolometric performance of the compound together with high light output of the crystal makes it an outstanding technique for the study of such elusive rate process. The internal radioactive contaminations of the crystal are also investigated showing that an improvement on the current status of material selection and purification are needed, $^{235/238}$U and $^{232}$Th are measured at the level of 28 mBq/kg, 1.3 Bq/kg and 28 mBq/kg, respectively. In this work, we also discuss a future upgrade of the experimental set-up which may pave the road for the detection of the rare $^{50}$V $\beta^-$ decay

Reexamination of continuous fuzzy measurement on two-level systems

Imposing restrictions on the Feynman paths of the monitored system has in the past been proposed as a universal model-free approach to continuous quantum measurements. Here we revisit this proposition and demonstrate that a Gaussian restriction, resulting in a sequence of many highly inaccurate (weak) von Neumann measurements, is not sufficiently strong to ensure proximity between a readout and the Feynman paths along which the monitored system evolves. Rather, in the continuous limit, the variations of a typical readout become much larger than the separation between the eigenvalues of the measured quantity. Thus, a typical readout is not represented by a nearly constant curve, correlating with one of the eigenvalues of the measured quantity $\hat{A}$, even when decoherence or Zeno effect is achieved for the observed two-level system, and does not point directly to the system's final state. We show that the decoherence in a ``free'' system can be seen as induced by a Gaussian random walk with a drift, eventually directing the system towards one of the eigenstates of $\hat{A}$. A similar mechanism appears to be responsible for the Zeno effect in a driven system, when its Rabi oscillations are quenched by monitoring. Alongside the Gaussian case, which can only be studied numerically, we also consider a fully tractable model with a ``hard wall'' restriction and show the results to be similar.MINECO, Fondo Europeo de Desarrollo Regional FEDER, Grant No. FIS2015-67161-P (MINECO/FEDER) (D.S.), MINECO Grant No. SVP-2014-068451 (S.R.), MINECO Grant No. MTM2013-46553-C3-1-P (E.A.), SGI/IZOSGIker UPV/EHU, i2BASQUE academic network

Cryogenic light detectors with enhanced performance for rare events physics

We have developed and tested a new way of coupling bolometric light detectors to scintillating crystal bolometers based upon simply resting the light detector on the crystal surface, held in position only by gravity. This straightforward mounting results in three important improvements: (1) it decreases the amount of non-active materials needed to assemble the detector, (2) it substantially increases the light collection efficiency by minimizing the light losses induced by the mounting structure, and (3) it enhances the thermal signal induced in the light detector thanks to the extremely weak thermal link to the thermal bath. We tested this new technique with a 16 cm$^2$ Ge light detector with thermistor readout sitting on the surface of a large TeO$_2$ bolometer. The light collection efficiency was increased by greater than 50\% compared to previously tested alternative mountings. We obtained a baseline energy resolution on the light detector of 20~eV RMS that, together with increased light collection, enabled us to obtain the best $\alpha$ vs $\beta/\gamma$ discrimination ever obtained with massive TeO$_2$ crystals. At the same time we achieved rise and decay times of 0.8 and 1.6 ms, respectively. This superb performance meets all of the requirements for the CUPID (CUORE Upgrade with Particle IDentification) experiment, which is a 1-ton scintillating bolometer follow up to CUORE.Comment: 6 pages, 4 figure