Bose-glass phase **in** a **quantum** magnet. We have first fully determined the microscopic model of the DTNX compound based on nuclear magnetic resonance experiments which can be interpreted **and** understood via single impurity physics. This made it possible to perform analytical as well as exact diagonalization calculations on large systems from which a unique set of coupling parameters could be determined for the impurity degrees of freedom. This simple description provided fruitful insights on the microscopic picture of DTNX at high magnetic field with a strong localization of isolated impurity states **and** the fact that the clean background polarizes at a smaller magnetic field than the impurities. Thus, a simple picture of DTNX at high magnetic field consists **in** a frozen (clean) background with a collection of impurities spatially randomly distributed, yet to be polarized upon increasing the magnetic field. By studying the mutual effect of two impurities we revealed that, despite the strong localization of the impurity states, there exists an effective unfrustrated pairwise interaction between impurity degrees of freedom. This paved the way to a resurgence of global phase coherence **in** DTNX, **in** sharp contrast with the many-body localized Bose-glass phase reported previously. Indeed, using large scale **quantum** Monte Carlo simulations, we showed that the **disorder** itself is actually getting ordered, forming a Bose-Einstein condensation through a novel order-by-**disorder** mechanism. Moreover, we determined a complete picture of the phase diagram “high magnetic fields vs. doping concentrations vs. temperatures”. At low doping there is still room for a Bose-glass phase **and** we studied the critical properties of the Bose-Einstein condensation to Bose-glass transition. We found critical exponents compatible with previous studies confirming the universal character of the transition, although we could not be conclusive regarding the “φ-crisis” raised by conflicting numerics. The theoretically predicted **disorder**-induced revival of Bose-Einstein condensation **in** “DTN” was afterwards experimentally observed **and** verified by nuclear magnetic

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Key-words: semiconductor laser, **quantum** dots, carrier **dynamics**, rate equation
Introduction
While optics has proven to be the most practical response to the high traffic rate demand for long-haul transmission, its extension to the metropolitan networks down to the home remains an open challenge. The implementation of optics at transmission rate where other technical solutions exist requires cost reduction. As a consequence, semiconductor lasers based on low dimensional heterostructures such as **quantum** dots (QDs) laser are very promising. Indeed, QDs structures have attracted a lot of attention **in** the last decade since they exhibit many interesting **and** useful properties such as low threshold current, temperature insensitivity, chirpless behavior **and** optical feedback resistance. As a result, thanks to QDs lasers, several steps toward cost reduction can be reached such as: improving the laser resistance to temperature fluctuation **in** order to remove temperature control elements, or designing feedback resistant laser for isolator-free **and** optics-free module. Most investigations reported **in** the literature deal with **In**(Ga)As QDs grown on GaAs substrates (Tan et al. 2004, Mukai et al. 1999). It is however important to stress that **In**(Ga)As / GaAs QDs devices do not allow a laser emission above 1.35 µm which is detrimental for optical transmission. **In** order to reach

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we do **in** this paper. We shall see that the complete **dynamics**, including the color degrees of freedom, can still be described by Fokker-Plack **and** Langevin equations, but only **in** very specific circumstances.
This paper focusses on conceptual issues. It is organized as follows. **In** Sect. 2 we derive the **quantum** master equation for the reduced density ma- trix of a system of heavy quarks **and** antiquarks immersed **in** a quark-gluon plasma, **in** thermal equilibrium. This equation, whose structure is close to that of a Lindblad equation, is used as a starting point of all later developments. **In** Sect. 3 we rederive from it the results that we had previously obtained for the abelian plasma [24] using a path integral formalism. **In** particular we re- cover, after performing a semi-classical approximation, the Fokker-Planck **and** Langevin equations that describe the random walks of center of mass **and** rela- tive coordinates of a quark-antiquark pair. This section on the abelian plasma paves the way for the treatment of the non abelian case discussed **in** Sect. 4. The equations that we present there, before we do the semi-classical approxi- mation, are fully **quantum** equations. But they are difficult to solve **in** general. Thus, **in** Sect. 5 we look for additional approximations that allow us to obtain solutions **in** some particular regimes, **in** order to start getting insight into the general solution. **In** particular, we explore two ways of implementing the semi- classical approximation. **In** the first case, we restrict the **dynamics** to stay close to a maximum entropy color state, where the colors of the heavy quarks are random. **In** this case the **dynamics** is described by a Langevin equation with a new random color force. The method used **in** this case is easily extended to the case of an arbitrary number of quark-antiquark pairs, **and** allows us to address the question of recombination. However, it is based on a perturbative approach that breaks down for some values of the parameters. Another strategy focuses on the case of a single quark-antiquark pair. The transition between singlets **and** octets are treated as “collisions” **in** a kinetic equation that we solve using Monte Carlo techniques. The last section summarizes our main results, **and** presents a brief outlook. Several appendices at the end gather various technical material.

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[ 6 , 7 ].But informations on the carrier **dynamics** **and** energy relaxation processes **in** such InAs/InP QDs are still lacking. Recently, the growth of self-organized InAs QDs on misoriented InP(113)B substrates has been proposed to get QDs with both **quantum** sizes **and** a high surface density [8]. **In** the optimized structures, the control of the maximum QD height of the sample yields the control of their wavelength emission [9]. These structures are named double-cap **quantum** dots (DC-QDs) **and** emit at 1.55 µm at room temperature [10]. The optical properties of a single DC-QDs layer have been analyzed [10,11,12], **and** lasing structures were obtained with such nanostructures with low threshold current densities [13,14]. **In** a previous study, we managed to dissociate the two capture (or relaxation) mechanisms described **in** literature: phonon **and** Auger assisted relaxations [15]. Nevertheless, a complete dynamic analysis, necessary to give us useful information for the description of the properties of a InAs/InP laser emitting at 1,55 µm, was still lacking.

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The magnetization relaxations of three different types of geometrically frustrated magnetic systems have been studied with the same experimental procedures as previously used **in** spin glasses. The materials investigated are Y 2 Mo 2 O 7 (pyrochlore system), SrCr 8 .6 Ga 3 .4 O 19 (piled pairs of Kagom´e layers) **and** (H 3 O )Fe 3 (SO 4 ) 2 (OH) 6 (jarosite compound). Despite a very small amount of **disorder**, all the samples exhibit many characteristic features of spin glass **dynamics** below a freezing temperature T g , much smaller than their Curie–Weiss temperature θ. The ageing properties of their thermoremanent magnetization can be well accounted for by the same scaling law as **in** spin glasses, **and** the values of the scaling exponents are very close. The effects of temperature variations during ageing have been specifically investigated. **In** the pyrochlore **and** the bi-Kagom´e compounds, a decrease of temperature after some waiting period at a certain temperature T p reinitializes ageing, **and** the evolution at the new temperature is the same as if the system were just quenched from above T g . However, as the temperature is raised back to T p , the sample recovers the state it had previously reached at that temperature. These features are known **in** spin glasses as rejuvenation **and** memory effects. They are clear signatures of the spin glass **dynamics**. **In** the Kagom´e compound, there is also some rejuvenation **and** memory, but much larger temperature changes are needed to observe the effects. **In** that sense, the behaviour of this compound is quantitatively different from that of spin glasses.

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is well-suited to investigate o ﬀ-equilibrium criticality, which **in** my opinion is a topic underdeveloped **and** full of promises.
The third part of the thesis is dealing with equilibrium aspects of the physics of disordered **quantum** systems. Like **in** our previous studies, the disordered Bose-Hubbard model that we consider could be soon investigated **in** cold atoms experiments. This work is an extension of the powerful method developed by Io ﬀe, Mézard [228], which is based on the cavity method **and** on a clever scheme, which allows to extract fine properties of the distribution functions of susceptibility **and** superfluid order analytically. Our results raise new ques- tions about the Bose glass to superfluid transition. Within the cavity method, we find that the transition is either of infinite **disorder**, far from the insulating lobes or conventional otherwise, which is a completely unheard of scenario. On the qualitative level, the replica symmetry breaking transition bears simi- larities with the percolation transition found **in** real-space renormalization. We also find that the conventional transition has continuously varying critical ex- ponents, which again was not suspected but is not **in** direct contradiction with any previous study. Finally, we relate all these properties to the large tails of the distribution of susceptibility, which is accessible within various other meth- ods **and** could be used as a benchmark to compare the cavity results with other approaches. Qualitatively, the approach stresses the consequences of rare re- alizations of **disorder** on the transition, an argument that is often evoked about the Mott insulator to Bose glass Gri ﬃths-like transition, but less often about the superfluid to Bose glass transition. Conversely, these predictions about the Bose-Hubbard model can be used as a testing ground for this approximate treat- ment of the **quantum** cavity, which has not yet been much compared against other methods. To put our prediction of varying critical exponents **and** of **in**- finite **disorder** fixed points to the test, one could for example apply the real- space renormalization group method [212] on di ﬀerent points of the superfluid to insulator transition. We also plan to approach the problem using Migdal- Kadano ﬀ decimation, which yields good approximates for critical exponents on lattices **in** small dimensions, **and** thus is a good complement to the Bethe lattice analysis which is valid **in** the limit of a large number of dimensions 19 .

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Describing the interaction of particles with isolated vortex lines or complex **quantum** vortex tangles is not an easy task. Depending on the scale of interest, there are different theoretical **and** numerical models that can be adopted. A big effort has been made **in** adapting the standard **dynamics** of particles **in** classical fluids to the case of superfluids described by two-fluid models [ 13 , 14 ]. This is a macroscopic model **in** which vorticity is a coarse-grained field **and** therefore there is no notion of quantized vortices. A medium-scale description is given by the vortex filament model, where the superfluid is modeled as a collection of lines that evolve following Biot- Savart integrals. **In** this approximation, circulation of vortices is by construction quantized but reconnections are absent **and** have to be implemented via some ad hoc mechanism. Finite- size particles can be studied **in** the vortex filament frame- work but the resulting equations are numerically costly **and** limited [ 15 ]. A microscopic approach consists **in** describing each impurity by a classical field **in** the framework of the Gross-Pitaevskii model [ 16 – 18 ]. **In** principle, such method is valid for weakly interacting BECs, **and** is numerically **and** theoretically difficult to handle if one wants to consider more than just a few particles. **In** the same context, an alternative possibility is to assume classical degrees of freedom for the particles, while the superfluid is still a complex field obeying the Gross-Pitaevskii equation. This idea of modeling parti- cles as simple classical hard spheres has been shown to be both numerically **and** analytically very powerful [ 19 – 22 ]. **In** particular, such minimal **and** self-consistent model allows for simulating a relatively large number of particles, **and** describes well the particle-vortex interaction [ 22 ]. Although formally valid for weakly interacting BECs, it is expected to give a good qualitative description of superfluid helium.

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∂t T race(ρ(t)) = 0 (4)
The first advantage of this formulation of the **dynamics** as a **Quantum** Markovian Master Equation is that the relaxation properties can be studied from the spectrum of the Lindblad operator [17–19] with possible metastability phenomena [20]. This spectral analysis also allows to make some link with the Random Matrix Theory of eigenvalues statistics [21]. The second advantage is that this framework is very convenient to study the non-equilibrium transport properties [23–31] with many exact solutions [32–37]. **In** addition, many important ideas that have been developed **in** the context of classical non-equilibrium systems (see the review [38] **and** references therein) have been adapted to the Lindblad description of non-equilibrium dissipative **quantum** systems, **in** particular the large deviation formalism to access the full-counting statistics [39–46], the additivity principle [47] **and** the fluctuation relations [48].

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than-ballistic (quasi-ballistic) for D < α < D + 1, **and** (iii) instantaneous for D > α. The existence of the last two of them is associated to second **and** first order divergences **in** the many-body excitation spectrum.
We then focus on a different model: lattice bosons interacting via a long-range poten- tials (long-range Bose-Hubbard model) **in** one dimension. We aim to understand if the previous results which determine a connection between the regime of propagation **and** the energy spectrum of excitations are universal. We start from the density-density cor- relations **and** their time evolution that presents a ballistic spreading for every value of α. This is completely unexpected from the general bounds **and** the analysis of the Ising model, where a transition from a bounded to an unbounded propagation occurs at α = 1. We then use again the analytic approach to explain these data. The bosonic model allows again long-lived excitations known as Bogoliubov quasi-particles. They are created fol- lowing the **quantum** quench **and** they spread **in** the system creating correlations **and** other observables. For α > 1, the excitation spectrum has a finite maximum group velocity. This is compatible with a ballistic propagation **and** it explains the data of the numeric for these values of α. **In** turns, for α < 1 the maximum group velocity is infinite **and** one may expect non-ballistic spreading. Studying carefully the observable it is anyway possible to see that not all the modes contribute the same way to the time evolution. Due to the long-range interactions, some parts of the spectrum have a vanishing contribution to the **dynamics**. Using the quasi-particle picture **and** the stationary-phase approximation we quantified this contribution **and** we concluded that the modes with infinite velocity have a completely negligible effect on the **dynamics**. To prove this argument we compare the velocity of the light-cone extracted from time-dependent Monte Carlo data to the one of the quasi-particles with the largest contribution, finding a perfect agreement.

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Scientific context of vibrational excitation of the CO stretch mode **in** carboxyhemoglobin
Conformational **dynamics** **in** proteins is known to be essential for understanding the protein functions. It relies on local elementary structural changes that occur on the ultrashort timescale of vibrations, **and** cannot be observed by usual structural determination techniques like Nuclear Magnetic Resonance (NMR) or X-ray crystallography. Since it allows to probe the fast vibrational **dynamics** of molecules during chemical or biological processes, ultrafast 2D infrared spectroscopy has become a powerful technique during the last decade. At the same time, methods for shaping pulses **in** the mid-infrared have been developed **and** can also bring useful information on the dy- namics behavior of the molecules by directly controlling their vibrational motions [36, 37]. The number of atoms, the diversity of interaction involved **and** the eﬀects of the environment make the theoretical description of such systems very complex, but novel methods mixing **quantum** **and** classical calculations give now access to dynamic processes with high precision **and** eﬃciency. There is a general interest to achieve vibrational coherent control of a diatomic ligand such as carbon monoxide (CO) **in** various hemoproteins for investigating yet unexplored regions of the potential energy surface **and** thus gain new information on the vibrational **dynamics**. To achieve this goal, diﬀerent theoretical, experimental **and** technological aspects need to be considered. One of the speciﬁcally interesting features is that ligands **in** heme proteins can be impulsively photodissociated using visible pulses, so that CO can be used as a probe of the protein environ- ment **in** other interesting places such as the docking site **in** the heme pocket [38]. Furthermore, another very interesting application of IR pulse shaping is to excite speciﬁc high-lying levels of selected vibrational modes, **and** to follow their temporal evolution. By this method, state- speciﬁc relaxation times are directly accessible to experimental measurements, a very promising technique [36].

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However, the large width of Dirac surface states (arising due to their slow decay into the bulk) can strongly reduce their overlap with the atomic-scale disorder at [r]

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In order to obtain electroluminescence from the QDs, there must be efficient exciton formation from injected charges in a device. This requires both facile injection[r]

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Unconventional spin dynamics is further revealed by NMR and μSR in the low-T , correlated, spin-liquid regime, where a broad distribution of spin-lattice relaxation times is observed.. W[r]

The exact reason for this non-uniform distribution of the two Si isotopes within a NW is not well understood at the moment. The best we have at this point is to hypothesize that this distribution might be related to the atomistic processes taking place at the catalyst-NW interface. It has been long assumed that during the VLS growth, the catalyst-NW interface always remains planar **and** the NW growth take place by nucleation **and** step-flow at this planar interface. However, recent **in** situ TEM experiments demonstrated that for a wide variety of catalyst-semiconductor systems, the planar main facet truncates into oblique facets at the vapor-liquid-solid triple phase boundary (TPB) [228]–[230], as shown schematically **in** Figure 7.3(a). The existence of this truncated facets depends on the balance of the capillary forces [230]. For 〈111〉 oriented Si NWs, it has been confirmed by both **in** situ experiments **and** theoretical simulations that the {111} main facet truncates into {113} **and**/or {120} inclined facets [229], [231], [232], with the nucleation kinetics of atoms on the main facet being markedly different from that on the truncated oblique facets. On the closely-packed {111} main facet, growth takes place by first forming a critical nucleus followed by a 2D step propagation. Molecular **dynamics** show that a considerable amount of supersaturation (often called a critical supersaturation which depends on the growth conditions) is required to overcome the energy barrier for the formation of the critical nucleus [229]. On the other hand, the less densely packed oblique facets have a high density of terrace steps **and** kinks. This special morphology reduces nucleation barrier **and** with it the critical supersaturation required for nucleation on these oblique facets. **In** fact, it was argued that if these oblique facets can get an atomic scale roughness, then the nucleation on these facets can occur with any finite supersaturation, that is without any nucleation barrier [229]. The molecular dynamic simulations also showed that Si atoms from an Au catalyst droplet are first incorporated at these oblique facets, due to their proximity to the Si rich contact line. When growth take place on these oblique facets, several small nuclei form **and** dissolve on the main {111} facet, **in** an attempt to overcome its large nucleation barrier. Even after the growth of a complete layer on the oblique facets, growth on the main facet remains virtually non-existent. It is only when all nucleation sites on the oblique facets are exhausted, that the crystallization is driven on to the main facet [231]. The same conclusion was reached during **in** situ TEM annealing experiments on VLS grown Au-catalyzed Ge NWs [233].

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Ground state energy per site as obtained from finite size extrapolation using equation (9). In the intermediate region 0A < J2 < 0.65 the extrapolation can not be used reliably, an[r]

, so that we obtain L diff ≈ 50 nm . This value is similar to the sample thickness (≈ 100 nm) **and** has to be compared with the transit length of the photoconductive channel, which **in** our devices was 20 μm. Thus, the difference **in** fall times between photocurrent **and** the SPV measurement can be attributed to the relevant dimension of the photoconductor being 200 times larger than that **in** the time-resolved photoemission measurement. This suggests that response times can be fast if the device size is similar to the diffusion length. Reducing the size of the device down to the 100 nm range to achieve a fast photoresponse 42 with gain 43–45 is an promising future direction for this work. It is also worth noting that sulfide capping results **in** a shorter SPV lifetime compared to EDT. This contributes to its weaker photoresponse, as a shorter minority carrier lifetime leads to a lower gain. When the light is turned-off, the majority carriers now flow from the bulk of the film to refill the surface traps **and** restore the band bending as depicted **in** Figure 7b. The turn-off time, which is related to the majority carrier transport, is **in** the 200 to 500 ns range. This is longer than the on-time **and** this difference is consistent with the photoconduction measurements which similarly show decays which are slower than the rise times. Both the rise **and** fall times are nevertheless fast, suggesting deep traps are not involved **in** transport. This contrasts with observations with small PbS CQD, for which much longer SPV **dynamics** are observed 46 by both time resolved photoemission (ms range) **and** transient photovoltage (µs to ms range). 30 Indeed for small PbS CQD, traps are known to play a key role **in** the optoelectronic properties 12,13 . It is also useful to note that the measured SPV off time (majority carrier relaxation time) is below the RC time which has been measured to be around 30 µs **in** our samples (see figure S4). This confirms that not only do HgTe NPL present better optical properties than alternative nanocrystal emitters (PbS, CuInGaS(e)) **in** the near IR, with narrower **and** faster PL, but also that the transport properties are less affected by traps. Figure 7c summarizes the different **dynamics** involved **in** this material, which appears promising for the design of photodetectors with high bandwidth (>MHz).

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ever, the ordering of the triplet states **in** these molecular
systems appears to be sometimes inverted with respect to bare acetophenone.
The kinetics of the intersystem crossing of acetophe- none have not been reported to the best of our knowledge, but there are reports on the closely related benzaldehyde molecule [5, 6] . Ultrafast electron diffraction experiments by Zewail **and** co-workers showed a lifetime of the ﬁrst singlet excited state of 42 ps [5] , whereas theoretical Mar- cus theory estimates by Ou **and** Subotnik predicted a four times faster process [6] . Accordingly, the dynamical mechanism of the acetophenone populated triplet states remains an open question **and** the central aim of the pre- sent contribution.

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The absence of the polarization fields normal to the QW plane **in** non-polar structures makes it possible to eliminate the excitation density dependence of the luminescence peak energy **and** variation of radiative lifetime with well thick- ness. Moreover, the eliminated separation of electrons **and** holes **in** non-polar QWs provides an ideal realm for studies of exciton recombination **dynamics** **and** excitonic recombi- nation selection rules. So far, most of the studies **in** this field have focused on InGaN QWs widely utilized as active regions **in** blue/UV LEDs **and** laser diodes. It has been shown that, **in** this case, excitonic recombination **dynamics** are gov- erned by localized states, rather than reflecting the intrinsic properties of the material. 11 , 12 Only few works so far have been dedicated to detailed investigation of excitonic recom- bination **in** non-polar GaN 13 , 14 **and** GaN/AlGaN QWs. 15 Therefore, it is imperative to study the optical anisotropy **and** exciton **dynamics** **in** non-polar GaN/AlGaN QWs.

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MSRJD formalism. It is possible to give a field theory representation of the stochastic
Langevin **dynamics** by use of the Martin-Siggia-Rose-Janssen-deDominicis (MSRJD) for-
malism [ 81 – 86 ]. **In** a nutshell, the generating functional is obtained by first upgrading the
physical degrees of freedom of the system **and** the random noise into fields. The Langevin equation of motion **and** its initial conditions are turned into a path integral **and** the action of the corresponding field theory is evaluated on-shell, thanks to the introduction of one extra Lagrange multiplier field for each physical degree of freedom. Since it is Gaussian, the noise field appears quadratically **in** the action **and** can thus be integrated out. One is left with a path integral over twice as many fields as number of physical degrees of freedom. The MSRJD formalism is particularly well suited to treating the **dynamics** of disordered systems following a quench. Indeed, provided that the initial conditions are uncorrelated with **disorder** (e.g. for very high temperature initial conditions), the generating functional evaluated at zero sources is equal to one **and** can therefore be trivially averaged over the

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