Classical orbital paramagnetism in non-equilibrium steady state

We report the results of our numerical simulation of classical-dissipative dynamics of a charged particle subjected to a non-markovian stochastic forcing. We find that the system develops a steady-state orbital magnetic moment in the presence of a static magnetic field. Very significantly, the sign of the orbital magnetic moment turns out to be {\it paramagnetic} for our choice of parameters, varied over a wide range. This is shown specifically for the case of classical dynamics driven by a Kubo-Anderson type non-markovian noise. Natural spatial boundary condition was imposed through (1) a soft (harmonic) confining potential, and (2) a hard potential, approximating a reflecting wall. There was no noticeable qualitative difference. What appears to be crucial to the orbital magnetic effect noticed here is the non-markovian property of the driving noise chosen. Experimental realization of this effect on the laboratory scale, and its possible implications are briefly discussed. We would like to emphasize that the above steady-state classical orbital paramagnetic moment complements, rather than contradicts the Bohr-van Leeuwen (BvL) theorem on the absence of classical orbital diamagnetism in thermodynamic equilibrium.Comment: 6 pages, 4 figures, Has appeared in Journal of Astrophysics and Astronomy special issue on 'Physics of Neutron Stars and Related Objects', celebrating the 75th birth-year of G. Srinivasa

Centre-of-mass separation in quantum mechanics: Implications for the many-body treatment in quantum chemistry and solid state physics

We address the question to what extent the centre-of-mass (COM) separation can change our view of the many-body problem in quantum chemistry and solid state physics. It was shown that the many-body treatment based on the electron-vibrational Hamiltonian is fundamentally inconsistent with the Born-Handy ansatz so that such a treatment can never respect the COM problem. Born-Oppenheimer (B-O) approximation reveals some secret: it is a limit case where the degrees of freedom can be treated in a classical way. Beyond the B-O approximation they are inseparable in principle. The unique covariant description of all equations with respect to individual degrees of freedom leads to new types of interaction: besides the known vibronic (electron-phonon) one the rotonic (electron-roton) and translonic (electron-translon) interactions arise. We have proved that due to the COM problem only the hypervibrations (hyperphonons, i.e. phonons + rotons + translons) have true physical meaning in molecules and crystals; nevertheless, the use of pure vibrations (phonons) is justified only in the adiabatic systems. This fact calls for the total revision of our contemporary knowledge of all non-adiabatic effects, especially the Jahn-Teller effect and superconductivity. The vibronic coupling is responsible only for removing of electron (quasi)degeneracies but for the explanation of symmetry breaking and forming of structure the rotonic and translonic coupling is necessary.Comment: 39 pages, 11 sections, 3 appendice

Direct Evidence for Dominant Bond-directional Interactions in a Honeycomb Lattice Iridate Na2IrO3

Heisenberg interactions are ubiquitous in magnetic materials and have been prevailing in modeling and designing quantum magnets. Bond-directional interactions offer a novel alternative to Heisenberg exchange and provide the building blocks of the Kitaev model, which has a quantum spin liquid (QSL) as its exact ground state. Honeycomb iridates, A2IrO3 (A=Na,Li), offer potential realizations of the Kitaev model, and their reported magnetic behaviors may be interpreted within the Kitaev framework. However, the extent of their relevance to the Kitaev model remains unclear, as evidence for bond-directional interactions remains indirect or conjectural. Here, we present direct evidence for dominant bond-directional interactions in antiferromagnetic Na2IrO3 and show that they lead to strong magnetic frustration. Diffuse magnetic x-ray scattering reveals broken spin-rotational symmetry even above Neel temperature, with the three spin components exhibiting nano-scale correlations along distinct crystallographic directions. This spin-space and real-space entanglement directly manifests the bond-directional interactions, provides the missing link to Kitaev physics in honeycomb iridates, and establishes a new design strategy toward frustrated magnetism.Comment: Nature Physics, accepted (2015

A new twist on the geometry of gravitational plane waves

The geometry of twisted null geodesic congruences in gravitational plane wave spacetimes is explored, with special focus on homogeneous plane waves. The role of twist in the relation of the Rosen coordinates adapted to a null congruence with the fundamental Brinkmann coordinates is explained and a generalised form of the Rosen metric describing a gravitational plane wave is derived. The Killing vectors and isometry algebra of homogeneous plane waves (HPWs) are described in both Brinkmann and twisted Rosen form and used to demonstrate the coset space structure of HPWs. The van Vleck-Morette determinant for twisted congruences is evaluated in both Brinkmann and Rosen descriptions. The twisted null congruences of the Ozsvath-Schucking,`anti-Mach' plane wave are investigated in detail. These developments provide the necessary geometric toolkit for future investigations of the role of twist in loop effects in quantum field theory in curved spacetime, where gravitational plane waves arise generically as Penrose limits; in string theory, where they are important as string backgrounds; and potentially in the detection of gravitational waves in astronomy.Comment: 60 pages, 2 figures. Extended version with new material on Rosen geodesics and isometries. Title change

Quantum nanomagnets and nuclear spins: an overview

This mini-review presents a simple and accessible summary on the fascinating physics of quantum nanomagnets coupled to a nuclear spin bath. These chemically synthesized systems are an ideal test ground for the theories of decoherence in mesoscopic quantum degrees of freedom, when the coupling to the environment is local and not small. We shall focus here on the most striking quantum phenomenon that occurs in such nanomagnets, namely the tunneling of their giant spin through a high anisotropy barrier. It will be shown that perturbative treatments must be discarded, and replaced by a more sophisticated formalism where the dynamics of the nanomagnet and the nuclei that couple to it are treated together from the beginning. After a critical review of the theoretical predictions and their experimental verification, we continue with a set of experimental results that challenge our present understanding, and outline the importance of filling also this last gap in the theory.Comment: 14 pages, 3 figures. Chapter in the Proceedings of the 2006 Les Houches summer school "Quantum Magnetism", ed. B. Barbara & Y. Imry, Springer (2007

Megascopic Quantum Phenomena. A Critical Study of Physical Interpretations

A megascopic revalidation is offered providing responses and resolutions of current inconsistencies and existing contradictions in present-day quantum theory. As the core of this study we present an independent proof of the Goldstone theorem for a quantum field formulation of molecules and solids. Along with phonons two types of new quasiparticles appear: rotons and translons. In full analogy with Lorentz covariance, combining space and time coordinates, a new covariance is necessary, binding together the internal and external degrees of freedom, without explicitly separating the centre-of-mass, which normally applies in both classical and quantum formulations. The generally accepted view regarding the lack of a simple correspondence between the Goldstone modes and broken symmetries, has significant consequences: an ambiguous BCS theory as well as a subsequent Higgs mechanism. The application of the archetype of the classical spontaneous symmetry breaking, i.e. the Mexican hat, as compared to standard quantum relations, i.e. the Jahn-Teller effect, superconductivity or the Higgs mechanism, becomes a disparity. In short, symmetry broken states have a microscopic causal origin, but transitions between them have a teleological component. The different treatments of the problem of the centre of gravity in quantum mechanics and in field theories imply a second type of Bohr complementarity on the many-body level opening the door for megascopic representations of all basic microscopic quantum axioms with further readings for teleonomic megascopic quantum phenomena, which have no microscopic rationale: isomeric transitions, Jahn-Teller effect, chemical reactions, Einstein-de Haas effect, superconductivity-superfluidity, and brittle fracture.Comment: 117 pages, 17 sections, final revised version from 20 May 2019 but uploaded after the DOI was know

The one dimensional Kondo lattice model at partial band filling

The Kondo lattice model introduced in 1977 describes a lattice of localized magnetic moments interacting with a sea of conduction electrons. It is one of the most important canonical models in the study of a class of rare earth compounds, called heavy fermion systems, and as such has been studied intensively by a wide variety of techniques for more than a quarter of a century. This review focuses on the one dimensional case at partial band filling, in which the number of conduction electrons is less than the number of localized moments. The theoretical understanding, based on the bosonized solution, of the conventional Kondo lattice model is presented in great detail. This review divides naturally into two parts, the first relating to the description of the formalism, and the second to its application. After an all-inclusive description of the bosonization technique, the bosonized form of the Kondo lattice hamiltonian is constructed in detail. Next the double-exchange ordering, Kondo singlet formation, the RKKY interaction and spin polaron formation are described comprehensively. An in-depth analysis of the phase diagram follows, with special emphasis on the destruction of the ferromagnetic phase by spin-flip disorder scattering, and of recent numerical results. The results are shown to hold for both antiferromagnetic and ferromagnetic Kondo lattice. The general exposition is pedagogic in tone.Comment: Review, 258 pages, 19 figure