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\"Over the last 25 years, dynamical mean-field theory (DMFT) has emerged as one of the most powerful new developments in many-body physics. Written by one of the key researchers in the field, this book presents the first comprehensive treatment of this ever-developing topic. Transport in Mutlilayered Nanostructures is varied and modern in its scope, and: Develops the formalism of many-body Green's functions using the equation-of-motion approach Applies DMFT to study transport in multilayered nanostructures, which is likely to be one of the most prominent applications of nanotechnology in the coming years Develops formalism first for the bulk and then for the inhomogeneous multilayered systems Describes in great detail the science behind the metal-insulator transition, electronic charge reconstruction, strongly correlated contributions to capacitance, and superconductivity Includes complete derivations and emphasizes how to carry out numerical calculations, including discussions of parallel programming algorithms Provides descriptions of the crossover from tunneling to thermally activated transport, of the properties of Josephson junctions with barriers tuned near the metal-insulator transition of thermoelectric coolers and power generators and of nonequilibrium extensions to determine current-voltage characteristics as applications of the theory A series of over 40 problems help develop the skills to allow readers to reach the level of being able to contribute to research. This book is suitable for an advanced graduate course in DMFT, and for individualized study by graduate students, postdoctoral fellows and advanced researchers wishing to enter the field\"-- Provided by publisher.

We develop a real space cluster extension of the typical medium theory (cluster-TMT) to study Anderson localization. By construction, the cluster-TMT approach is formally equivalent to the real space cluster extension of the dynamical mean field theory. Applying the developed method to the 3D Anderson model with a box disorder distribution, we demonstrate that cluster-TMT successfully captures the localization phenomena in all disorder regimes. As a function of the cluster size, our method obtains the correct critical disorder strength for the Anderson localization in 3D, and systematically recovers the re-entrance behavior of the mobility edge. From a general perspective, our developed methodology offers the potential to study Anderson localization at surfaces within quantum embedding theory. This opens the door to studying the interplay between topology and Anderson localization from first principles.

Experiments have shown that the families of cuprate superconductors that have the largest transition temperature at optimal doping also have the largest oxygen hole content at that doping [D. Rybicki et al., Nat. Commun. 7, 1–6 (2016)]. They have also shown that a large charge-transfer gap [W. Ruan et al., Sci. Bull. (Beijing) 61, 1826–1832 (2016)], a quantity accessible in the normal state, is detrimental to superconductivity. We solve the three-band Hubbard model with cellular dynamical mean-field theory and show that both of these observations follow from the model. Cuprates play a special role among doped charge-transfer insulators of transition metal oxides because copper has the largest covalent bonding with oxygen. Experiments [L. Wang et al., arXiv [Preprint] (2020). https://arxiv.org/abs/2011.05029 (Accessed 10 November 2020)] also suggest that superexchange is at the origin of superconductivity in cuprates. Our results reveal the consistency of these experiments with the above two experimental findings. Indeed, we show that covalency and a charge-transfer gap lead to an effective short-range superexchange interaction between copper spins that ultimately explains pairing and superconductivity in the three-band Hubbard model of cuprates.

We study the stochastic dynamics of an arbitrary number of noise-activated cyclic processes, or oscillators, that are all coupled to each other via a dissipative coupling. The N coupled oscillators are described by N phase coordinates driven in a tilted washboard potential. At low N and strong coupling, we find synchronization as well as an enhancement in the average speed of the oscillators. In the large N regime, we show that the collective dynamics can be described through a mean-field theory, which predicts a great enhancement in the average speed. In fact, beyond a critical value of the coupling strength, noise activation becomes irrelevant and the dynamics switch to an effectively deterministic ‘running’ mode. Finally, we study the stochastic thermodynamics of the coupled oscillators, in particular their performance with regards to the thermodynamic uncertainty relation.

In frictionless jammed packings, existing evidence suggests a picture in which localized physics dominates in low spatial dimensions, d = 2, 3, but quickly loses relevance as d rises, replaced by spatially extended mean-field behavior. For example, quasilocalized low-energy vibrational modes and low-coordination particles associated with deviation from mean-field behavior (rattlers and bucklers) all vanish rapidly with increasing d. These results suggest that localized rearrangements, which are associated with low-energy vibrational modes, correlated with local structure, and dominant in low dimensions, should give way in higher d to extended rearrangements uncorrelated with local structure. Here, we use machine learning to analyze simulations of jammed packings under athermal, quasistatic shear, identifying a local structural variable, softness, that correlates with rearrangements in dimensions d = 2 to d = 5. We find that softness—and even just the local coordination number Z—is essentially equally predictive of rearrangements in all d studied. This result provides direct evidence that local structure plays an important role in higher d, suggesting a modified picture for the dimensional cross-over to mean-field theory.

We present a fully comprehensive multi-mode quantum treatment based on the truncated Wigner approximation (TWA) to study many-body effects and effects of quantum fluctuations on the formation of a discrete time crystal (DTC) in a Bose–Einstein condensate (BEC) bouncing resonantly on a periodically driven atom mirror. Zero-range contact interactions between the bosonic atoms are assumed. Our theoretical approach avoids the restrictions both of mean-field theory, where all bosons are assumed to remain in a single mode, and of time-dependent Bogoliubov theory, which assumes boson depletion from the condensate mode is small. We show that the mean-field and time-dependent Bogoliubov approaches can be derived as approximations to the TWA treatment. Differing initial conditions, such as a finite temperature BEC, can also be treated. For realistic initial conditions corresponding to a harmonic trap condensate mode function, our TWA calculations performed for period-doubling agree broadly with recent mean-field calculations for times out to at least 2000 mirror oscillations, except at interaction strengths very close to the threshold value for DTC formation where the position probability density differs significantly from that determined from mean-field theory. For typical attractive interaction strengths above the threshold value for DTC formation and for the chosen trap and driving parameters, the TWA calculations indicate a quantum depletion due to quantum many-body fluctuations of less than about two atoms out of a total of 600 atoms at times corresponding to 2000 mirror oscillations, in agreement with time-dependent Bogoliubov theory calculations. On the other hand, for interaction strengths very close to the threshold value for DTC formation, the TWA calculations predict a large quantum depletion—as high as about 260 atoms out of 600. We also show that the mean energy per particle of the DTC does not increase significantly for times out to at least 2000 mirror oscillations and typically oscillates around an average value close to its initial value; so TWA theory predicts the absence of thermalisation. Finally, we find that the dynamical behaviour of our system is largely independent of whether the boson–boson interaction is attractive or repulsive, and that it is possible to create a stable DTC based on repulsive interactions.

Recent works have shown that the contact process running on the top of highly heterogeneous random networks is described by the heterogeneous mean-field theory. However, some important aspects such as the transition point and strong corrections to the finite-size scaling observed in simulations are not quantitatively reproduced in this theory. We develop a heterogeneous pair-approximation, the simplest mean-field approach that takes into account dynamical correlations, for the contact process. The transition points obtained in this theory are in very good agreement with simulations. The proximity with a simple homogeneous pair-approximation is elicited showing that the transition point in successive homogeneous cluster approximations moves away from the simulation results. We show that the critical exponents of the heterogeneous pair-approximation in the infinite-size limit are the same as those of the one-vertex theory. However, excellent matches with simulations, for a wide range of network sizes, are obtained when the sub-leading finite-size corrections given by the new theory are explicitly taken into account. The present approach can be suited to dynamical processes on networks in general providing a profitable strategy to analytically assess and fine-tune theoretical corrections.

Current theoretical studies of electronic correlations in transition metal oxides typically only account for the local repulsion between d-electrons even if oxygen ligand p-states are an explicit part of the effective Hamiltonian. Interatomic interactions such as \\({{U}_{pd}}\\) between d- and (ligand) p-electrons, as well as the local interaction between p-electrons, are neglected. Often, the relative d–p orbital splitting has to be adjusted ‘ad hoc’ on the basis of the experimental evidence. By applying the merger of local density approximation and dynamical mean field theory to the prototypical case of the three-band Emery dp model for the cuprates, we demonstrate that, without any ‘ad hoc’ adjustment of the orbital splitting, the charge transfer insulating state is stabilized by the interatomic interaction \\({{U}_{pd}}\\). Our study hence shows how to improve realistic material calculations that explicitly include the p-orbitals.

The superfluid weight is an important observable of superconducting materials since it is related to the London penetration depth of the Meissner effect. It can be computed from the change in the grand potential (or free energy) in response to twisted boundary conditions in a torus geometry. Here we review the Bardeen–Cooper–Schrieffer mean-field theory emphasizing its origin as a variational approximation for the grand potential. The variational parameters are the effective fields that enter in the mean-field Hamiltonian, namely the Hartree–Fock potential and the pairing potential. The superfluid weight is usually computed by ignoring the dependence of the effective fields on the twisted boundary conditions. However, it has been pointed out in recent works that this can lead to unphysical results, particularly in the case of lattice models with flat bands. As a first result, we show that taking into account the dependence of the effective fields on the twisted boundary conditions leads in fact to the generalized random phase approximation. Our second result is providing the mean-field grand potential as an explicit function of the one-particle density matrix. This allows us to derive the expression for the superfluid weight within the generalized random phase approximation in a transparent manner. Moreover, reformulating mean-field theory as a well-posed minimization problem in terms of the one-particle density matrix is a first step towards the application to superconducting systems of the linear scaling methods developed in the context of electronic structure theory.

This paper presents a theoretical description of the magnetocaloric effect in Pr 0.67 Sr 0.33 MnO 3 manganite. The mean-field theory has been used around the Curie temperature to simulate the temperature dependence of the magnetic entropy change under several applied magnetic fields. The obtained results were compared with experimental data computed from the Maxwell relation. The excellent agreement between the two methods confirms the validity of the mean-field theory for modeling the magnetocaloric properties of the Pr 0.67 Sr 0.33 MnO 3 manganite. The validity of this theory suggests the presence of negligible critical fluctuations near the Curie temperature T C . The magnetocaloric study indicates that our sample can be used as a magnetic refrigerant near room temperature.