Thermal transport in dielectric, non-magnetic crystals is mediated by quantized lattice vibrations, which drift and interact when driven out of equilibrium by a temperature gradient. This phenomenon can be described at multiple theoretical levels, ranging from fully quantum descriptions to semiclassical and mesoscopic continuum approaches. This review rigorously discusses the theoretical steps and approximations connecting these levels, bridging quantum phonon Dyson and Kadanoff-Baym equations and semiclassical Boltzmann transport formalism, and discussing the coarse-graining procedures that yield mesoscopic viscous heat equations for non-diffusive, hydrodynamic heat transport in devices. We show how the Guyer-Krumhansl and dual-phase-lag equations emerge as special linear-isotropic-band and inviscid limits of the viscous heat equations, respectively; most importantly, we demonstrate that these equations predict not only Poiseuille flow and second sound, but also more exotic effects such as negative thermal resistance, steady-state thermal backflow and vortices. We highlight how combining these frameworks with first-principles simulations connects microscopic phonon physics to observable non-diffusive heat-transport phenomena and guides their detection, amplification, and control. We recast the viscous heat equations in terms of Helmholtz and biharmonic equations solved analytically, and use this to discuss similarities and differences between the macroscopic behavior of the phonon fluid and other hydrodynamic systems, such as classical and electron fluids, focusing on compressibility, vorticity, and their influence on phonon hydrodynamics. We conclude with a roadmap to generalize the tools used to describe phonon hydrodynamics to other quasiparticles, motivating future advances in collective quantum transport phenomena in solids.
We highlight recent progress in the study of artificial flat band systems with a threefold focus. First, we discuss single-particle flat band physics, which has advanced through the design of various flat band generators. These generators rely on the classification of flat bands in terms of compact localized states - their fundamental building blocks. A related development is the complete real-space description of flat band projectors. Next, we review studies on perturbations of flat bands, which provide new insights into the effects of disorder and, more importantly, the intricate interplay between many-body interactions and flat band physics. Finally, we survey the growing number of experimental realizations of flat bands across diverse physical platforms.
In this review, we first present compelling evidence from resonant inelastic x-ray scattering data that highlights the significance of the long-range Coulomb interaction in cuprate charge dynamics, particularly around the in-plane momentum q=(0,0). We show that these experimental observations are well-captured by the layered t-J-V model, which extends the standard t-J framework to include the long-range Coulomb interaction V and the layered structure. This new perspective elucidates how charge dynamics renormalizes one-particle excitation properties, leading to several profound and often counterintuitive consequences. We demonstrate that the electron dispersion does not exhibit a sharp kink, and Landau quasiparticles persist in the low-energy limit despite a significant suppression of their spectral weight. We further show that while charge fluctuations alone cannot fully account for the pseudogap, they are a crucial component for understanding its formation. Additionally, we reveal that optical plasmon excitations generate fermionic quasiparticles, known as plasmarons, which give rise to a distinct, incoherent replica band. We argue that accurately describing these plasmonic effects requires a three-dimensional theoretical approach. This perspective on plasmon excitations may offer a critically new clue to a long-standing puzzle: why multi-layer cuprate superconductors, containing more than two CuO2 layers per unit cell, consistently exhibit a higher critical temperature Tc than their single-layer counterparts. Finally, we review the spin-fluctuation mechanism of superconductivity suffers from the "self-restraint effect" and show how important the screened Coulomb interaction is in the spin-fluctuation mechanism to realize high-Tc superconductivity.
We review the theoretical modelling of moiré materials, focusing on various aspects of magic-angle twisted bilayer graphene (MA-TBG) viewed through the lens of Hartree-Fock mean-field theory. We first provide an elementary introduction to the continuum modelling of moiré bandstructures, and explain how interactions are incorporated to study correlated states. We then discuss how to implement mean-field simulations of ground state structure and collective excitations in this setting. With this background established, we rationalize the power of mean-field approximations in MA-TBG, by discussing the idealized "chiral-flat" strong-coupling limit, in which ground states at electron densities commensurate with the moiré superlattice are exactly captured by mean-field ansätze. We then illustrate the phenomenological shortcomings of this limit, leading us naturally into a discussion of the intermediate-coupling incommensurate Kekulé spiral (IKS) order and its origins in ever-present heterostrain. IKS and its placement within an expanded Hartree-Fock manifold form our first "case study". Our second case study involves time-dependence, and focuses on the collective modes of various broken-symmetry insulators in MA-TBG. As a third and final case study, we return to the strong-coupling picture, which can be stabilized by aligning MA-TBG to an hBN substrate. In this limit, we show how mean field theory can be adapted to the translationally non-invariant setting in order to quantitatively study the energetics of domain walls in orbital Chern insulating states. We close with a discussion of extensions and further applications. Used either as a standalone reference or alongside the accompanying open-source code, this review should enable readers with a basic knowledge of band theory and many-body physics to systematically build and analyze detailed models of generic moiré systems.
High-order harmonic generation (HHG) in solids has emerged as a versatile platform for exploring ultrafast and quantum-coherent phenomena in condensed matter. Recent advances reveal Berry-phase and topological effects in harmonic emission, strong-field control of excitons and lattice motion, the generation of nonclassical light states driven by quantum and squeezed fields, and the emergence of orbital-angular-momentum transfer in solid-state high-harmonic generation. Nanostructured and hybrid plasmonic-semiconductor platforms enable enhanced and spectrally tunable HHG, while interferometric and cryogenic setups allow attosecond-resolved phase measurements. On the theoretical side, multiband and topological models incorporating dephasing, propagation, and electron-hole coherence effects have deepened our understanding of the interplay between interband and intraband dynamics. These developments establish solid-state HHG as a bridge between ultrafast spectroscopy, quantum optics, and material science, paving the way toward quantum-engineered attosecond sources and coherent control of light-matter interactions in solids.
A briefly formulated update of the recently published review [1] on the topic of multidimensional solitons (chiefly, in nonlinear optics and atomic Bose-Einstein condensates (BECs)) is presented. The update briefly summarizes some notable results on this topic that have been reported very recently, and offers a compact outline of the directions of the current experiment and theoretical work in this and related fields. In particular, as concerns newest experimental findings, included are the creation of multiple quantum droplets in prolate BEC, and the observation of expanding toroidal light structures in linear optics. The update of theoretical results includes the analysis of 2D solitons in the optical system with the quadratic nonlinearity and fractional diffraction, and the prediction of stable 3D vortex solitons in various BEC schemes with long-range interactions.
These lecture notes provide an introduction to Langevin processes and briefly discuss some interesting properties and simple applications. They compile material presented at the "School of Physics and Mathematics Without Frontiers" (ZigZag), held at La Havana, Cuba, in March 2024, the School "Information, Noise and Physics of Life" held at Niš, Serbia, in June 2024, both sponsored by ICTP, the PEBBLE summer camp at Westlake University, China, in August 2024, the Barcelona school on "Non-equilibrium Statistical Physics", in April 2025, and the 2012-2016 course "Out of Equilibrium Dynamics of Complex Systems" for the Master 2 program "Physics of Complex Systems" in the Paris area.
We review the theory of martingales as applied to stochastic thermodynamics and stochastic processes in physics more generally.
The study on the electronic state of muon as pseudo-hydrogen (represented by the elemental symbol Mu) has long been appreciated as one of the few methods to experimentally access the electronic state of dilute hydrogen (H) in semiconductors and dielectrics. Meanwhile, theoretical predictions on the electronic state of H in these materials by first-principles calculations using density functional theory (DFT) do not always agree with the observed states of Mu, standing as an obstacle to integrating the findings of both Mu and H. In this paper, we provide resolution to this problem by a semi-quantitative model that enables systematic understanding of the electronic states of Mu in most oxides.
These notes are based on lectures serving the advanced graduate education of the Delta Institute of Theoretical Physics in the Netherlands in autumn 2021. The goal is to explain in a language that can be understood by non-specialists very recent advances in quantum information and especially string theory suggesting the existence of entirely new forms of matter. These are metallic states characterized by an extremely dense many body entanglement, requiring the supremacy of the quantum computer to be completely enumerated. The holographic duality discovered in string theory appears to be a mathematical machinery capable of computing observable properties of such matter, suggesting the presence of universal general principles governing its phenomenology. The case is developing that these principles may well apply to the highly mysterious physical properties observed in the high temperature superconductors and other strongly interacting electron systems of condensed matter physics.
Thin films based on silicon and transition-metal elements dominate the semiconducting industry and are ubiquitous in all modern devices. Films have also been produced in the rare-earth series of elements for both research and specialized applications. Thin films of uranium and uranium dioxide were fabricated in the 1960s and 1970s, but there was little sustained effort until the early 2000s. Significant programmes started at Oxford University (transferring to Bristol University in 2011), and Los Alamos National Laboratory (LANL) in New Mexico, USA. In this review we cover the work that has been published over the last ~20 years with these materials. Important breakthroughs occurred with the fabrication of epitaxial thin films of initially uranium metal and UO2, but more recently of many other uranium compounds and alloys. These have led to a number of different experiments that are reviewed, as well as some important trends. The interaction with the substrate leads to differing strain and hence changes in properties. An important advantage is that epitaxial films can often be made of materials that are impossible to produce as bulk single crystals. Examples are U3O8, U2N3 and alloys of U-Mo, which form in a modified bcc structure. Epitaxial films may also be used in applied research. They represent excellent surfaces, and it is at the surfaces that most of the important reactions occur in the nuclear fuel cycle. For example, the fuel-cladding interactions, and the dissolution of fuel by water in the long-term storage of spent fuel. To conclude, we discuss possible future prospects, examples include bilayers containing uranium for spintronics, and superlattices that could be used in heterostructures. Such applications will require a more detailed knowledge of the interface interactions in these systems, and this is an important direction for future research.
"To David Sherrington, Editor-in-Chief of Advances in Physics." Advances in Physics, ahead-of-print(ahead-of-print), pp. 1–2
Path integrals are a ubiquitous tool in theoretical physics. However, their use is sometimes hindered by the lack of control on various manipulations–such as performing a change of the integration path–one would like to carry out in the light-hearted fashion that physicists enjoy. Similar issues arise in the field of stochastic calculus, which we review to prepare the ground for a proper construction of path integrals. At the level of path integration, and in arbitrary space dimension, we not only report on existing Riemannian geometry-based approaches that render path integrals amenable to the standard rules of calculus, but also bring forth new routes, based on a fully time-discretized approach, that achieve the same goal. We illustrate these various definitions of path integration on simple examples such as the diffusion of a particle on a sphere.
Fundamental physical constants play a profound role in physics. For example, they govern nuclear reactions, formation of stars, nuclear synthesis and stability of biologically vital elements. These are high-energy processes discussed in particle physics, astronomy and cosmology. More recently, it was realised that fundamental physical constants extend their governing reach to low-energy processes and properties operating in condensed matter systems, often in an unexpected way. These properties are those we experience daily and can routinely measure, including viscosity, thermal conductivity, elasticity and sound. Here, we review this work. We start with the lower bound on liquid viscosity, its origin and show how to relate the bound to fundamental physical constants. The lower bound of kinematic viscosity represents the global minimum on the phase diagram. We show how this result answers the long-standing question considered by Purcell and Weisskopf, namely why viscosity never falls below a certain value. An accompanying insight is that water viscosity and water-based life are well attuned to fundamental constants, adding another higher-level layer to the anthropic principle. We then discuss viscosity minima in liquid He above and below the λ-point. We subsequently consider a very different property, thermal diffusivity, and show that it has the same minimum fixed by fundamental physical constants as viscosity. We also discuss bounds related to elastic properties, elastic moduli and their analogues in low-dimensional systems, and show how these bounds are related to the upper bound for the speed of sound. We conclude with listing ways in which the discussion of fundamental constants and bounds advance physical theories.
This review addresses resistive switching devices operating according to the bipolar valence change mechanism (VCM), which has become a major trend in electronic materials and devices over the last decade due to its high potential for non-volatile memories and future neuromorphic computing. We will provide detailed insights into the status of understanding of these devices as a fundament for their use in the different fields of application. The review covers the microscopic physics of memristive states and the switching kinetics of VCM devices. It is shown that the switching of all variants of VCM cells relies on the movement of mobile donor ions, which are typically oxygen vacancies or cation interstitials. VCM cells consist of three parts: an electronically active electrode (AE), often a metal with a high work function, in front of which the switching occurs, a mixed ionic-electronic conducting (MIEC) layer consisting of a nanometer-scale metal oxide or a stack of different metal oxides, and an ohmic counter electrode (OE). After an introduction to definitions and classification, the fundamentals of solid-state physics and chemistry associated with VCM cells are described, including redox processes and the role of electrodes. The microscopic changes induced by electroforming, a process often required prior to resistive switching, are described in terms of electronic initialization and subsequent changes in chemistry, structure, and conductivity. The switching process is discussed in terms of switching polarity, geometry of the switching region, and spectroscopic detection of the valence changes. Emphasis is placed on the extreme nonlinearity of switching kinetics described by physics-based multiscale modeling, ranging from ab initio methods to kinetic Monte Carlo and finite element models to compact models that can be used in circuit simulators. The review concludes with a treatment of the highly relevant reliability issues and a description of the failure mechanisms, including mutual trade-offs.
In this article, we review the recent significant progress in the theoretical studies of the electronic states by mainly focusing on Fe-based and cuprate superconductors. These superconductors are “unconventional” in that strong electron-electron correlation mediates the pairing; they are different from conventional phonon-mediated BCS superconductors. To seek the high- pairing mechanism, many scientists have focused on the mysterious spontaneous rotational symmetry breaking above , such as nematic order at and smectic order at . Such exotic correlation-driven symmetry breaking in metals has become a central issue in condensed matter physics. We demonstrate the emergence of the nematic and smectic orders due to orbital polarization ( ) and the symmetry breaking in the correlated inter-site hopping (= bond order ) in Fe-based and cuprate superconductors. In addition, we discuss exotic spontaneous loop current orders driven by the pure imaginary . These interesting “unconventional density-waves” originate from the quantum interference between different spin fluctuations that is described by the vertex correction (VC) in the field theory. In the next stage, we discuss electron-correlation-driven superconductivity due to the fluctuations of unconventional density-waves. For this purpose, we suggest the beyond-Migdal–Eliashberg gap equation by including the VCs into the equation. In Fe-based superconductors, high- s-wave superconductivity can be mediated by nematic and smectic fluctuations because the pairing interaction is magnified by the VCs. We also discuss the multipolar fluctuation pairing mechanism in heavy fermion systems, owing to the cooperation between the strong spin-orbit interaction and the strong electron correlation. To summarize, we suggest that the quantum interference mechanism described by the VCs plays essential roles in not only various unconventional density-waves but also exotic superconducting states in many strongly correlated metals. We finally discuss some interesting future issues with respect to the quantum interference mechanism.
We review the recent developments and the current status in the field of quantum-gas cavity QED. Since the first experimental demonstration of atomic self-ordering in a system composed of a Bose–Einstein condensate coupled to a quantized electromagnetic mode of a high-Q optical cavity, the field has rapidly evolved over the past decade. The composite quantum-gas-cavity systems offer the opportunity to implement, simulate, and experimentally test fundamental solid-state Hamiltonians, as well as to realize non-equilibrium many-body phenomena beyond conventional condensed-matter scenarios. This hinges on the unique possibility to design and control in open quantum environments photon-induced tunable-range interaction potentials for the atoms using tailored pump lasers and dynamic cavity fields. Notable examples range from Hubbard-like models with long-range interactions exhibiting a lattice-supersolid phase, over emergent magnetic orderings and quasicrystalline symmetries, to the appearance of dynamic gauge potentials and non-equilibrium topological phases. Experiments have managed to load spin-polarized as well as spinful quantum gases into various cavity geometries and engineer versatile tunable-range atomic interactions. This led to the experimental observation of spontaneous discrete and continuous symmetry breaking with the appearance of soft-modes as well as supersolidity, density and spin self-ordering, dynamic spin-orbit coupling, and non-equilibrium dynamical self-ordered phases among others. In addition, quantum-gas-cavity setups offer new platforms for quantum-enhanced measurements. In this review, starting from an introduction to basic models, we pedagogically summarize a broad range of theoretical developments and put them in perspective with the current and near future state-of-art experiments.
