- Optical atomic clocks

Author(s): Andrew D. Ludlow, Martin M. Boyd, Jun Ye, E. Peik, and P. O. SchmidtSince 1967 the primary time standard is the cesium atomic clock, based on a hyperfine transition in the microwave domain. … - Macroscopic fluctuation theory

Author(s): Lorenzo Bertini, Alberto De Sole, Davide Gabrielli, Giovanni Jona-Lasinio, and Claudio LandimThe statistical mechanics of systems out of equilibrium provides a formidable challenge. This re … - Neutrino electromagnetic interactions: A window to new physics

Author(s): Carlo Giunti and Alexander StudenikinWith the observation of neutrino masses and mixings, the study of their electromagnetic interactions has assumed greater relevance both as verification … - Lévy walks

Author(s): V. Zaburdaev, S. Denisov, and J. KlafterLévy walks are random walks in which the distribution of step length does not decay exponentially and the velocity of the moving particle is finite. … - Colloquium: Theory of intertwined orders in high temperature superconductors

Author(s): Eduardo Fradkin, Steven A. Kivelson, and John M. TranquadaUnderstanding high temperature superconductors is a central problem in condensed matter physics. Many experiments have uncovered or … - Asymmetries in top quark pair production at hadron colliders

Author(s): J. A. Aguilar-Saavedra, D. Amidei, A. Juste, and M. Pérez-VictoriaSeveral years ago measurements at the Fermilab Tevatron proton-antiproton collider showed top quarks to be produced prefera … - Colloquium: Geometry and optimal packing of twisted columns and filaments

Author(s): Gregory M. GrasonThis Colloquium presents recent progress in understanding constraints and consequences of close-packing geometry of filamentous or columnar materials possessing nontrivial … - Interfacing single photons and single quantum dots with photonic nanostructures

Author(s): Peter Lodahl, Sahand Mahmoodian, and Søren StobbeQuantum dots embedded in photonics nanostructures provide unprecedented control over the interaction between light and matter. This review g … - Quantum error correction for quantum memories

Author(s): Barbara M. TerhalIt may seem inevitable that highly entangled quantum states are susceptible to disturbance through interaction with a decohering environment. However, certain multiqubit en … - Plasma and trap-based techniques for science with positrons

Author(s): J. R. Danielson, D. H. E. Dubin, R. G. Greaves, and C. M. SurkoIn recent years, there has been a wealth of new science involving low-energy antimatter (i.e., positrons and antiprotons) at e … - Baryon resonances in large N_{c} QCD

Author(s): N. Matagne and Fl. StancuThe current status and open challenges of large N_{c} QCD baryon spectroscopy are reviewed. After introducing the 1/N_{c} expansion method, the latest achievements … - Colloquium: Random first order transition theory concepts in biology and physics

Author(s): T. R. Kirkpatrick and D. ThirumalaiThe routine transformation of a liquid, as it is rapidly cooled, resulting in glass formation, is remarkably complex. A theoretical explanation of the dyn … - Colloquium: Time-reversal violation with quantum-entangled B mesons

Author(s): J. Bernabéu and F. Martínez-VidalSymmetry transformations have been proven a bedrock tool for understanding the nature of particle interactions, formulating, and testing fundamental theorie … - Colloquium: Majorana fermions in nuclear, particle, and solid-state physics

Author(s): Steven R. Elliott and Marcel FranzEttore Majorana (1906–1938) disappeared while traveling by ship from Palermo to Naples in 1938. His fate has never been fully resolved and several articles … - Colloquium: 100 years of mass spectrometry: Perspectives and future trends

Author(s): Simon Maher, Fred P. M. Jjunju, and Stephen TaylorMass spectrometry (MS) is widely regarded as the most sensitive and specific general purpose analytical technique. More than a century has … - Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics

Author(s): Hui Cao and Jan WiersigThis is a review on theoretical and experimental studies on dielectric microcavities, which play a significant role in fundamental and applied research. The basic con … - Compass models: Theory and physical motivations

Author(s): Zohar Nussinov and Jeroen van den BrinkCompass models are theories of matter in which the couplings between the internal spin (or other relevant field) components are inherently spatially ( … - Erratum: Bose-Einstein condensation in quantum magnets [Rev. Mod. Phys. 86, 563 (2014)]

Author(s): Vivien Zapf, Marcelo Jaime, and C. D. Batista[Rev. Mod. Phys. 86, 1453] Published Wed Dec 31, 2014 - Cavity optomechanics

Author(s): Markus Aspelmeyer, Tobias J. Kippenberg, and Florian MarquardtThe field of cavity optomechanics is reviewed. This field explores the interaction between electromagnetic radiation and nanome … - Dielectric laser accelerators

Author(s): R. Joel England et al.The use of infrared lasers to power optical-scale lithographically fabricated particle accelerators is a developing area of research that has garnered increasing inter … - Hidden symmetries of dynamics in classical and quantum physics

Author(s): Marco CarigliaThis article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of curre … - Colloquium: Quantum root-mean-square error and measurement uncertainty relations

Author(s): Paul Busch, Pekka Lahti, and Reinhard F. WernerRecent years have witnessed a controversy over Heisenberg’s famous error-disturbance relation. Here the conflict is resolved by way of an anal … - Quantum channels and memory effects

Author(s): Filippo Caruso, Vittorio Giovannetti, Cosmo Lupo, and Stefano ManciniAny physical process can be represented as a quantum channel mapping an initial state to a final state. Hence it can be … - Colloquium: Emergent properties in plane view: Strong correlations at oxide interfaces

Author(s): Jak Chakhalian, John W. Freeland, Andrew J. Millis, Christos Panagopoulos, and James M. RondinelliFinding new collective electronic states in materials is one of the fundamental goals of co … - Colloquium: Fractional calculus view of complexity: A tutorial

Author(s): Bruce J. WestThe fractional calculus has been part of the mathematics and science literature for 310 years. However, it is only in the past decade or so that it has drawn the attention of m … - Editorial: PRX Takes on a New Role

Author(s): Gene D. Sprouse[Rev. Mod. Phys. 86, 1187] Published Thu Oct 09, 2014 - Spin-polarized quantum confinement in nanostructures: Scanning tunneling microscopy

Author(s): Hirofumi Oka, Oleg O. Brovko, Marco Corbetta, Valeri S. Stepanyuk, Dirk Sander, and Jürgen KirschnerExperimental investigations of spin-polarized electron confinement in nanostructures by s … - Erratum: Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems [Rev. Mod. Phys. 81, 1665 (2009)]

Author(s): Massimiliano Esposito, Upendra Harbola, and Shaul Mukamel[Rev. Mod. Phys. 86, 1125] Published Mon Sep 22, 2014 - Colloquium: Nonlinear metamaterials

Author(s): Mikhail Lapine, Ilya V. Shadrivov, and Yuri S. KivsharThis Colloquium presents an overview of the research on nonlinear electromagnetic metamaterials. The developed theoretical approaches a … - The hadronic final state at HERA

Author(s): Paul R. Newman and Matthew WingThe hadronic final state in electron-proton collisions at HERA has provided a rich testing ground for development of the theory of the strong force, QCD. In t … - Modeling semiflexible polymer networks

Author(s): C. P. Broedersz and F. C. MacKintoshThis is an overview of theoretical approaches to semiflexible polymers and their networks. Such semiflexible polymers have large bending rigidities that … - Colloquium: Graphene spectroscopy

Author(s): D. N. Basov, M. M. Fogler, A. Lanzara, Feng Wang, and Yuanbo Zhang (张远波)Spectroscopic studies of electronic phenomena in graphene are reviewed. A variety of methods and techniques are surve … - Colloquium: Biophysical principles of undulatory self-propulsion in granular media

Author(s): Daniel I. GoldmanBiological locomotion, movement within environments through self-deformation, encompasses a range of time and length scales in an organism. These include the electrophysiol … - Beam by design: Laser manipulation of electrons in modern accelerators

Author(s): Erik Hemsing, Gennady Stupakov, Dao Xiang, and Alexander ZholentsAccelerator-based light sources such as storage rings and free-electron lasers use relativistic electron beams to produce in … - Spin-dependent phenomena and device concepts explored in (Ga,Mn)As

Author(s): T. Jungwirth, J. Wunderlich, V. Novák, K. Olejník, B. L. Gallagher, R. P. Campion, K. W. Edmonds, A. W. Rushforth, A. J. Ferguson, and P. NěmecOver the past two decades, the research of (Ga … - Nobel Lecture: The BEH mechanism and its scalar boson

Author(s): François Englert[Rev. Mod. Phys. 86, 843] Published Thu Jul 03, 2014 - Nobel Lecture: Evading the Goldstone theorem

Author(s): Peter W. Higgs[Rev. Mod. Phys. 86, 851] Published Thu Jul 03, 2014 - Publisher’s Note: Bell nonlocality [Rev. Mod. Phys. 86, 419 (2014)]

Author(s): Nicolas Brunner, Daniel Cavalcanti, Stefano Pironio, Valerio Scarani, and Stephanie Wehner[Rev. Mod. Phys. 86, 839] Published Mon Jun 30, 2014 - Publisher’s Note: Phonon-glass electron-crystal thermoelectric clathrates: Experiments and theory [Rev. Mod. Phys. 86, 669 (2014)]

Author(s): Toshiro Takabatake, Koichiro Suekuni, Tsuneyoshi Nakayama, and Eiji Kaneshita[Rev. Mod. Phys. 86, 841] Published Mon Jun 30, 2014 - Nonequilibrium dynamical mean-field theory and its applications

Author(s): Hideo Aoki, Naoto Tsuji, Martin Eckstein, Marcus Kollar, Takashi Oka, and Philipp WernerThe study of nonequilibrium phenomena in correlated lattice systems has developed into one of the mos … - Phonon-glass electron-crystal thermoelectric clathrates: Experiments and theory

Author(s): Toshiro Takabatake, Koichiro Suekuni, Tsuneyoshi Nakayama, and Eiji KaneshitaType-I clathrate compounds have attracted a great deal of interest in connection with the search for efficient t … - Insect flight dynamics: Stability and control

Author(s): Mao SunInsects can hover, fly forward, climb, and descend with ease while demonstrating amazing stability, and they can also maneuver in impressive ways as no other organisms can. Is their … - Real-space renormalization in statistical mechanics

Author(s): Efi Efrati, Zhe Wang, Amy Kolan, and Leo P. KadanoffThis review compares the conceptualization and practice of early real-space renormalization group methods with the conceptualization of m … - Bose-Einstein condensation in quantum magnets

Author(s): Vivien Zapf, Marcelo Jaime, and C. D. BatistaThis article reviews experimental and theoretical work on Bose-Einstein condensation in quantum magnets. These magnets are natural realizations … - Crystalline color superconductors

Author(s): Roberto Anglani, Roberto Casalbuoni, Marco Ciminale, Nicola Ippolito, Raoul Gatto, Massimo Mannarelli, and Marco RuggieriInhomogeneous superconductors and inhomogeneous superfluids appear i … - Standard model Higgs boson searches through the 125 GeV boson discovery

Author(s): Gregorio Bernardi and Matthew HerndonThe experimental searches for the standard model Higgs boson are reviewed from the 2 TeV run of the Tevatron with ≃10 fb−1 of recorded data, and from t … - Bell nonlocality

Author(s): Nicolas Brunner, Daniel Cavalcanti, Stefano Pironio, Valerio Scarani, and Stephanie WehnerBell’s 1964 theorem, which states that the predictions of quantum theory cannot be accounted for by … - 1/f noise: Implications for solid-state quantum information

Author(s): E. Paladino, Y. M. Galperin, G. Falci, and B. L. AltshulerThe efficiency of the future devices for quantum information processing is limited mostly by the finite decoherence rates of the in … - First-principles calculations for point defects in solids

Author(s): Christoph Freysoldt, Blazej Grabowski, Tilmann Hickel, Jörg Neugebauer, Georg Kresse, Anderson Janotti, and Chris G. Van de WallePoint defects and impurities strongly affect the physical pr … - Colloquium: Understanding quantum weak values: Basics and applications

Author(s): Justin Dressel, Mehul Malik, Filippo M. Miatto, Andrew N. Jordan, and Robert W. BoydSince its introduction 25 years ago, the quantum weak value has gradually transitioned from a theoretical … - Recent developments in heavy-ion fusion reactions

Author(s): B. B. Back, H. Esbensen, C. L. Jiang, and K. E. RehmIn this review the main advances in heavy-ion fusion research that have taken place over the last decade are addressed. During this perio … - Dilute ferromagnetic semiconductors: Physics and spintronic structures

Author(s): Tomasz Dietl and Hideo OhnoThis review compiles results of experimental and theoretical studies on thin films and quantum structures of semiconductors with randomly distributed Mn ions, whi … - Quantum simulation

Author(s): I. M. Georgescu, S. Ashhab, and Franco NoriSimulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficult … - Gravitational radiation detection with laser interferometry

Author(s): Rana X. AdhikariGravitational-wave detection has been pursued relentlessly for over 40 years. With the imminent operation of a new generation of laser interferometers, it is expected that d … - Galaxy masses

Author(s): Stéphane Courteau, Michele Cappellari, Roelof S. de Jong, Aaron A. Dutton, Eric Emsellem, Henk Hoekstra, L. V. E. Koopmans, Gary A. Mamon, Claudia Maraston, Tommaso Treu, and Lawrence M. Wi … - Secular evolution in disk galaxies

Author(s): J. A. SellwoodDisk galaxies evolve over time through processes that may rearrange both the radial mass profile and the metallicity distribution within the disk. This review of such slow cha … - Quantum-Bayesian coherence

Author(s): Christopher A. Fuchs and Rüdiger SchackIn the quantum-Bayesian interpretation of quantum theory (or QBism), the Born rule cannot be interpreted as a rule for setting measurement-outcome pro … - Fermi gases in one dimension: From Bethe ansatz to experiments

Author(s): Xi-Wen Guan, Murray T. Batchelor, and Chaohong LeeThis article reviews theoretical and experimental developments for one-dimensional Fermi gases. Specifically, the experimentally realized t … - Defect identification in semiconductors with positron annihilation: Experiment and theory

Author(s): Filip Tuomisto and Ilja MakkonenPositron annihilation spectroscopy is particularly suitable for studying vacancy-type defects in semiconductors. Combining state-of-the-art experimental and … - Colloquium: Annual modulation of dark matter

Author(s): Katherine Freese, Mariangela Lisanti, and Christopher SavageDirect detection experiments, which are designed to detect the scattering of dark matter off nuclei in detectors, are a critical … - Colloquium: Beta-delayed fission of atomic nuclei

Author(s): Andrei N. Andreyev, Mark Huyse, and Piet Van DuppenThis Colloquium reviews the studies of exotic type of low-energy nuclear fission, the β-delayed fission (βDF). Emphasis is made on the new … - Colloquium: Laser probing of neutron-rich nuclei in light atoms

Author(s): Z.-T. Lu, P. Mueller, G. W. F. Drake, W. Nörtershäuser, Steven C. Pieper, and Z.-C. YanThe neutron-rich He6 and He8 isotopes exhibit an exotic nuclear structure that consists of a tightly b … - Colloquium: Multimessenger astronomy with gravitational waves and high-energy neutrinos

Author(s): Shin’ichiro Ando et al.Many of the astrophysical sources and violent phenomena observed in our Universe are potential emitters of gravitational waves and high-energy cosmic radiation, inclu … - Single-electron current sources: Toward a refined definition of the ampere

Author(s): Jukka P. Pekola, Olli-Pentti Saira, Ville F. Maisi, Antti Kemppinen, Mikko Möttönen, Yuri A. Pashkin, and Dmitri V. AverinThe control of electrons at the level of the elementary charge e wa … - Colloquium: Artificial spin ice: Designing and imaging magnetic frustration

Author(s): Cristiano Nisoli, Roderich Moessner, and Peter SchifferFrustration, the presence of competing interactions, is ubiquitous in the physical sciences and is a source of degeneracy and disorder … - Life at the interface of particle physics and string theory

Author(s): A. N. SchellekensIf the results of the first LHC run are not betraying us, many decades of particle physics are culminating in a complete and consistent theory for all nongravitational phys … - Physics of adherent cells

Author(s): Ulrich S. Schwarz and Samuel A. SafranOne of the most unique physical features of cell adhesion to external surfaces is the active generation of mechanical force at the cell-material interf … - Thermal conduction phenomena in carbon nanotubes and related nanostructured materials

Author(s): Amy M. Marconnet, Matthew A. Panzer, and Kenneth E. GoodsonThe extremely high thermal conductivities of carbon nanotubes have motivated a wealth of research. Progress includes innovative co … - White organic light-emitting diodes: Status and perspective

Author(s): Sebastian Reineke, Michael Thomschke, Björn Lüssem, and Karl LeoWhite organic light-emitting diodes (OLEDs) are ultrathin, large-area light sources made from organic semiconductor materials … - Spinor Bose gases: Symmetries, magnetism, and quantum dynamics

Author(s): Dan M. Stamper-Kurn and Masahito UedaSpinor Bose gases form a family of quantum fluids manifesting both magnetic order and superfluidity. This article reviews experimental and theoretical p … - Hydrodynamics of soft active matter

Author(s): M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, Madan Rao, and R. Aditi SimhaThis review summarizes theoretical progress in the field of active matter, placing it in … - Principles of maximum entropy and maximum caliber in statistical physics

Author(s): Steve Pressé, Kingshuk Ghosh, Julian Lee, and Ken A. DillThe variational principles called maximum entropy (MaxEnt) and maximum caliber (MaxCal) are reviewed. MaxEnt originated in the stati … - The molecular universe

Author(s): A. G. G. M. TielensMolecular absorption and emission bands dominate the visible, infrared, and submillimeter spectra of most objects with associated gas. These observations reveal a surpris … - Nobel Lecture: Controlling photons in a box and exploring the quantum to classical boundary

Author(s): Serge HarocheMicrowave photons trapped in a superconducting cavity constitute an ideal system to realize some of the thought experiments imagined by the founding fathers of quantum physics. … - Nobel Lecture: Superposition, entanglement, and raising Schrödinger’s cat

Author(s): David J. Wineland[Rev. Mod. Phys. 85, 1103] Published Fri Jul 12, 2013 - Silicon quantum electronics

Author(s): Floris A. Zwanenburg, Andrew S. Dzurak, Andrea Morello, Michelle Y. Simmons, Lloyd C. L. Hollenberg, Gerhard Klimeck, Sven Rogge, Susan N. Coppersmith, and Mark A. ErikssonThis review descr … - Colloquium: Cluster growth on surfaces: Densities, size distributions, and morphologies

Author(s): Mario Einax, Wolfgang Dieterich, and Philipp MaassUnderstanding and control of cluster and thin-film growth on solid surfaces is a subject of intensive research to develop nanomaterials wit … - Colloquium: Coherent diffusion of polaritons in atomic media

Author(s): O. Firstenberg, M. Shuker, A. Ron, and N. DavidsonCoherent diffusion pertains to the motion of atomic dipoles experiencing frequent collisions in vapor while maintaining their coherence. Re … - Erratum: Hidden variables and the two theorems of John Bell [Rev. Mod. Phys. 65, 803 (1993)]

Author(s): N. David Mermin[Rev. Mod. Phys. 85, 919] Published Fri Jun 28, 2013 - Leaking chaotic systems

Author(s): Eduardo G. Altmann, Jefferson S. E. Portela, and Tamás TélThere are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can ha … - Colloquium: The unexpected properties of alkali metal iron selenide superconductors

Author(s): Elbio DagottoThe iron-based superconductors that contain FeAs layers as the fundamental building block in the crystal structures have been rationalized in the past using ideas based on the … - Colloquium: New physics search with flavor in the LHC era

Author(s): Tobias Hurth and Farvah MahmoudiA status report on quark flavor physics in view of the latest data from the B factories and the LHC is given, and the impact of the latest experimental resul … - Pregalactic metal enrichment: The chemical signatures of the first stars

Author(s): Torgny Karlsson, Volker Bromm, and Joss Bland-HawthornThe emergence of the first sources of light at redshifts of z∼10–30 signaled the transition from the simple initial state of the Univer … - Ion acceleration by superintense laser-plasma interaction

Author(s): Andrea Macchi, Marco Borghesi, and Matteo PassoniIon acceleration driven by superintense laser pulses is attracting an impressive and steadily increasing effort. Motivations can be found in … - Theory and application of explicitly correlated Gaussians

Author(s): Jim Mitroy, Sergiy Bubin, Wataru Horiuchi, Yasuyuki Suzuki, Ludwik Adamowicz, Wojciech Cencek, Krzysztof Szalewicz, Jacek Komasa, D. Blume, and Kálmán VargaThe variational method complement … - The spin structure of the nucleon

Author(s): Christine A. Aidala, Steven D. Bass, Delia Hasch, and Gerhard K. MallotThis article reviews our present understanding of QCD spin physics: the proton spin puzzle and new developments aimed … - Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems

Author(s): Ze-Liang Xiang, Sahel Ashhab, J. Q. You, and Franco NoriHybrid quantum circuits combine two or more physical systems, with the goal of harnessing the advantages and strengths of the differe … - Models of wave-function collapse, underlying theories, and experimental tests

Author(s): Angelo Bassi, Kinjalk Lochan, Seema Satin, Tejinder P. Singh, and Hendrik UlbrichtQuantum mechanics is an extremely successful theory that agrees with every experimental test. However, the … - Colloquium: Modeling friction: From nanoscale to mesoscale

Author(s): Andrea Vanossi, Nicola Manini, Michael Urbakh, Stefano Zapperi, and Erio TosattiThe physics of sliding friction is gaining impulse from nanoscale and mesoscale experiments, simulations, and … - Cold atoms in cavity-generated dynamical optical potentials

Author(s): Helmut Ritsch, Peter Domokos, Ferdinand Brennecke, and Tilman EsslingerThis is a review of state-of-the-art theory and experiment of the motion of cold and ultracold atoms coupled to the ra … - Colloquium: Homochirality: Symmetry breaking in systems driven far from equilibrium

Author(s): Yukio Saito and Hiroyuki HyugaSubsequent to the discovery of chirality of organic molecules by Pasteur, living organisms have been found to utilize biomolecules of only one handedness. The … - Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers

Author(s): Miguel C. Soriano, Jordi García-Ojalvo, Claudio R. Mirasso, and Ingo FischerComplex phenomena in photonics, in particular, dynamical properties of semiconductor lasers due to delayed coupli … - Magnetic cluster excitations

Author(s): Albert Furrer and Oliver WaldmannMagnetic clusters, i.e., assemblies of a finite number (between two or three and several hundred) of interacting spin centers which are magnetically decoupl … - Quantum fluids of light

Author(s): Iacopo Carusotto and Cristiano CiutiThis article reviews recent theoretical and experimental advances in the fundamental understanding and active control of quantum fluids of light in nonli … - Colloquium: Perspectives on core-collapse supernova theory

Author(s): Adam BurrowsCore-collapse theory brings together many facets of high-energy and nuclear astrophysics and the numerical arts to present theorists with one of the most important, yet frustrat … - Radiative corrections in precision electroweak physics: A historical perspective

Author(s): Alberto Sirlin and Andrea FerrogliaThe aim of this article is to review the important role played by radiative corrections in precision electroweak physics, in the framework of both the Fer … - Colloquium: Spontaneous magnon decays

Author(s): M. E. Zhitomirsky and A. L. ChernyshevA theoretical overview of the phenomenon of spontaneous magnon decays in quantum antiferromagnets is presented. The intrinsic zero-temperature damping … - Femtosecond x rays from laser-plasma accelerators

Author(s): S. Corde, K. Ta Phuoc, G. Lambert, R. Fitour, V. Malka, A. Rousse, A. Beck, and E. LefebvreRelativistic interaction of short-pulse lasers with underdense plasmas has recently led to the eme … - Stochastic models of intracellular transport

Author(s): Paul C. Bressloff and Jay M. NewbyThe interior of a living cell is a crowded, heterogenuous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to anal … - Colloquium: Three-body forces: From cold atoms to nuclei

Author(s): Hans-Werner Hammer, Andreas Nogga, and Achim SchwenkIt is often assumed that few- and many-body systems can be accurately described by considering only pairwise two-body interactions of the …