Haut PDF Dynamics and disorder in quantum antiferromagnets

Dynamics and disorder in quantum antiferromagnets

Dynamics and disorder in quantum antiferromagnets

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
En savoir plus

238 En savoir plus

Carrier dynamics and saturation effect in (113)B InAs/InP quantum dot lasers

Carrier dynamics and saturation effect in (113)B InAs/InP quantum dot lasers

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
En savoir plus

21 En savoir plus

Quantum and Classical Dynamics of Heavy Quarks in a Quark-Gluon Plasma

Quantum and Classical Dynamics of Heavy Quarks in a Quark-Gluon Plasma

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.
En savoir plus

63 En savoir plus

Electronic structure and carrier dynamics in InAs/InP double-cap quantum dots

Electronic structure and carrier dynamics in InAs/InP double-cap quantum dots

[ 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.
En savoir plus

17 En savoir plus

The relative influences of disorder and of frustration on the glassy dynamics in magnetic systems

The relative influences of disorder and of frustration on the glassy dynamics in magnetic systems

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.
En savoir plus

8 En savoir plus

Out of equilibrium quantum dynamics and disordered systems in bosonic ultracold atoms

Out of equilibrium quantum dynamics and disordered systems in bosonic ultracold atoms

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 .
En savoir plus

175 En savoir plus

Dynamics of active particles in superfluids and their interaction with quantum vortices

Dynamics of active particles in superfluids and their interaction with quantum vortices

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.
En savoir plus

240 En savoir plus

Boundary-driven Lindblad dynamics of random quantum spin chains : strong disorder approach for the relaxation, the steady state and the current

Boundary-driven Lindblad dynamics of random quantum spin chains : strong disorder approach for the relaxation, the steady state and the current

∂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].
En savoir plus

19 En savoir plus

Out-Of-Equilibrium Dynamics and Locality in Long-Range Many-Body Quantum Systems

Out-Of-Equilibrium Dynamics and Locality in Long-Range Many-Body Quantum Systems

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.
En savoir plus

182 En savoir plus

Dynamics and control of open quantum systems : applications to exciton dynamics in quantum dots and vibrational dynamics in carboxyhemoglobin

Dynamics and control of open quantum systems : applications to exciton dynamics in quantum dots and vibrational dynamics in carboxyhemoglobin

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].
En savoir plus

141 En savoir plus

Boundaries, disorder and noise in quantum-coherent systems

Boundaries, disorder and noise in quantum-coherent systems

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]

143 En savoir plus

Charge and exciton dynamics in quantum dot light-emitting diodes

Charge and exciton dynamics in quantum dot light-emitting diodes

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]

174 En savoir plus

Spin dynamics and disorder effects in the S = 1/2 kagome Heisenberg spin liquid phase of kapellasite

Spin dynamics and disorder effects in the S = 1/2 kagome Heisenberg spin liquid phase of kapellasite

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]

14 En savoir plus

Isotope Engineering and Lattice Disorder in Group IV Nanoscale and Quantum Semiconductors

Isotope Engineering and Lattice Disorder in Group IV Nanoscale and Quantum Semiconductors

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].
En savoir plus

237 En savoir plus

Magnetic Order and Disorder in the Frustrated Quantum Heisenberg Antiferromagnet in Two Dimensions

Magnetic Order and Disorder in the Frustrated Quantum Heisenberg Antiferromagnet in Two Dimensions

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]

30 En savoir plus

Charge Dynamics and Optolectronic Properties in HgTe Colloidal Quantum Wells

Charge Dynamics and Optolectronic Properties in HgTe Colloidal Quantum Wells

, 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).
En savoir plus

15 En savoir plus

Disorder and $c$-axis quasiparticle dynamics in underdoped Bi2Sr2CaCu2O8

Disorder and $c$-axis quasiparticle dynamics in underdoped Bi2Sr2CaCu2O8

HAL Id: hal-00288477 https://hal.archives-ouvertes.fr/hal-00288477 Submitted on 17 Jun 2008 HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

5 En savoir plus

Population of triplet states in acetophenone: A quantum dynamics perspective

Population of triplet states in acetophenone: A quantum dynamics perspective

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.
En savoir plus

8 En savoir plus

Excitonic recombination dynamics in non-polar GaN/AlGaN quantum wells

Excitonic recombination dynamics in non-polar GaN/AlGaN quantum wells

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.
En savoir plus

11 En savoir plus

Classical and quantum out-of-equilibrium dynamics. Formalism and applications.

Classical and quantum out-of-equilibrium dynamics. Formalism and applications.

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
En savoir plus

196 En savoir plus

Show all 10000 documents...