Photoelectron holography constitutes a powerful tool for the ultrafast imaging of matter, as it combines high electron currents with subfemtosecond resolution, and gives information about transition amplitudes and phase shifts. Similarly to light holography, it uses the phase difference between the probe and the reference waves associated with qualitatively different ionization events for the reconstruction of the target and for ascertaining any changes that may occur. These are major advantages over other attosecond imaging techniques, which require elaborate interferometric schemes in order to extract phase differences. For that reason, ultrafast photoelectron holography has experienced a huge growth in activity, which has led to a vast, but fragmented landscape. The present review is an organizational effort towards unifying this landscape. This includes a historic account in which a connection with laser-induced electron diffraction is established, a summary of the main holographic structures encountered and their underlying physical mechanisms, a broad discussion of the theoretical methods employed, and of the key challenges and future possibilities. We delve deeper in our own work, and place a strong emphasis on quantum interference, and on the residual Coulomb potential.
In the first part we present the number theoretical properties of the Riemann zeta function and formulate the Riemann hypothesis. In the second part we review some physical problems related to this hypothesis: the Polya-Hilbert conjecture, the links with random matrix theory, relation with the Lee-Yang theorem on the zeros of the partition function and phase transitions, random walks, billiards etc.
We present here a review of the most significant recent achievements in the field of HAXPES (hard x-ray photoelectron spectroscopy) on isolated atoms and molecules, and related spectroscopies. The possibility of conducting hard x-ray photoexcitation and photoionization experiments under state-of-the art conditions in terms of photon and electron kinetic energy resolution has become available only in the last few years. HAXPES has then produced structural and dynamical information at the level of detail already reached in the VUV and soft-x-ray ranges. The much improved experimental conditions have allowed extending to the hard x-ray range some methods well established in soft x-ray spectroscopies. Investigations of electron and nuclear dynamics in the femtosecond (fs, 10-15 s) and even attosecond (as, 10-18 s) regime have become feasible. Complex relaxation phenomena following deep-core ionization can now be enlightened in great detail. Other phenomena like e.g. recoil-induced effects are much more important in fast photoelectron emission, which can be induced by hard x-rays. Furthermore, a new kind of ionic states with double core holes can be observed by x-ray single-photon absorption. Future perspectives are also discussed.
This review presents a survey of, and guide to, new materials physics (NMP) research. It begins with an overview of the goals of NMP and then presents important ideas and techniques for the design and growth of new materials. An emphasis is placed on the use of compositional phase diagrams to inform and motivate solution growth of single crystals. The second half of this review focuses on the vital process of generating actionable ideas for the growth and discovery of new materials and ground states. Motivations ranging from (1) wanting a specific compound, to (2) wanting a specific ground state to (3) wanting to explore for known and unknown unknowns, will be discussed and illustrated with abundant examples. The goal of this review is to inform, inspire, an even entertain, as many practitioners of this field as possible.
In this paper we give an overview of some recent progress in using holography to study various far-from-equilibrium condensed matter systems. Non-equilibrium problems are notoriously difficult to deal with, not to mention at strong coupling and when including quantum effects. Remarkably, using holographic duality one can describe and follow the real-time evolution of far-from-equilibrium systems, including those which are spatially inhomogeneous and anisotropic, by solving partial differential gravity equations. We sample developments in two broad classes of question which have recently been of much interest to the condensed matter community: non-equilibrium steady states, and quantum systems undergoing a global quench. Our discussion focuses on the main physical insights obtained from the gravity approaches, rather than comprehensive treatment of each topic or detailed descriptions of gravity calculations. The paper also includes an overview of current numerical techniques, as well as the holographic Schwinger-Keldysh approach to real-time correlation functions.

