There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

This article reviews the physics of high-temperature superconductors from the point of view of the doping of a Mott insulator. The basic electronic structure of cuprates is reviewed, emphasizing the physics of strong correlation and establishing the model of a doped Mott insulator as a starting point. A variety of experiments are discussed, focusing on the region of the phase diagram close to the Mott insulator (the underdoped region) where the behavior is most anomalous. The normal state in this region exhibits pseudogap phenomenon. In contrast, the quasiparticles in the superconducting state are well defined and behave according to theory. This review introduces Anderson's idea of the resonating valence bond and argues that it gives a qualitative account of the data. The importance of phase fluctuations is discussed, leading to a theory of the transition temperature, which is driven by phase fluctuations and the thermal excitation of quasiparticles. However, an argument is made that phase fluctuations can only explain pseudogap phenomenology over a limited temperature range, and some additional physics is needed to explain the onset of singlet formation at very high temperatures. A description of the numerical method of the projected wave function is presented, which turns out to be a very useful technique for implementing the strong correlation constraint and leads to a number of predictions which are in agreement with experiments. The remainder of the paper deals with an analytic treatment of the $t\text{\ensuremath{-}}J$ model, with the goal of putting the resonating valence bond idea on a more formal footing. The slave boson is introduced to enforce the constraint againt double occupation and it is shown that the implementation of this local constraint leads naturally to gauge theories. This review follows the historical order by first examining the U(1) formulation of the gauge theory. Some inadequacies of this formulation for underdoping are discussed, leading to the SU(2) formulation. Here follows a rather thorough discussion of the role of gauge theory in describing the spin-liquid phase of the undoped Mott insulator. The difference between the high-energy gauge group in the formulation of the problem versus the low-energy gauge group, which is an emergent phenomenon, is emphasized. Several possible routes to deconfinement based on different emergent gauge groups are discussed, which leads to the physics of fractionalization and spin-charge separation. Next the extension of the SU(2) formulation to nonzero doping is described with a focus on a part of the mean-field phase diagram called the staggered flux liquid phase. It will be shown that inclusion of the gauge fluctuation provides a reasonable description of the pseudogap phase. It is emphasized that $d$-wave superconductivity can be considered as evolving from a stable U(1) spin liquid. These ideas are applied to the high-${T}_{c}$ cuprates, and their implications for the vortex structure and the phase diagram are discussed. A possible test of the topological structure of the pseudogap phase is described.

/pdf/doping-a-mott-insulator-physics-of-high-temperature-55r49vtp31.pdf

Doping a Mott insulator: Physics of high-temperature superconductivity

Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

We investigate the evolution of the electronic structure across the metal-to-insulator transition in the isostructural series, BaCo 1−x Ni x S 2 , using electron spectroscopic studies. Our experimental results show a progressive depletion of the spectral intensity at and near the Fermi level across the series, with decreasing x. Analysis of the core-level and valence-band photoemission spectra in conjunction with detailed many-body calculations show that the ground state of the system is highly covalent. We estimate the electronic structure parameters of the system and deduce that the hopping interaction strength t pd decreases in the solid solution with a decrease of the Ni content, while U dd and Δ do not change appreciably. Thus, the metal-to-insulator transition in this system is found to be driven primarily by covalency effects, though the static disorder in the system is expected to play an important role in determining the details of physical properties.

Electronic structure of and covalency driven metal-insulator transition in BaCo 1−x Ni x S 2

Employing first-principles density functional theory based calculations we investigated the change in electronic structure of CaCu3B4O12 compounds as one moves from 3d (Co) to 4d (Rh) to 5d (Ir) element at B site. Our study sheds light on valences of Cu and B ions as one moves from 3d to 4d to 5d based compounds. The valence of Cu in Co and Rh compound turn out to be that of less known 3+ state, while that in Ir compound turn out to be commonly known 2+ state. Our first-principles study provide microscopic understanding of these different valences of Cu, in terms of changes in the mixing of Cu x2 − y2 and B-a1g states, driven by changes in the crystal field and spin splitting. The stronger crystal field splitting for 4d and 5d elements compared to 3d at B site drive the low-spin state at Rh and Ir site as opposed to intermediate spin in case of Co.

First-principles study of CaCu3B4O12 (B=Co, Rh, Ir)

Using first-principles density functional theory based calculations, carried out on the recently measured crystal structure data [K. Oka et al. J. Am. Chem. Soc. 132, 9438 (2010)], we study the changes in the electronic structure of BiCoO${}_{3}$ between the ambient-pressure condition and the high-pressure condition. Our study shows that the application of high pressure drives the high-spin-to-low-spin transition at the Co site. We find that the finite mixing of a Bi lone pair with O $p$ drives the GdFeO${}_{3}$ type of orthorhombic distortion at high pressure, as opposed to previously predicted cubic or tetragonal symmetry of the high-pressure phase. This orthorhombic distortion gives rise to semiconducting behavior in contrast to previously predicted metallic or semimetallic behavior. Our study provides justification for the drop in resistivity on increasing pressure, as observed experimentally.

http://absimage.aps.org/image/MAR12/MWS_MAR12-2011-000167.pdf

Pressure-driven changes in electronic structure of BiCoO$_3$

XY magnetism, Kitaev exchange, and long-range frustration in the Jeff=12 honeycomb cobaltates

The manganese orthophosphate, Mn3(PO4)2, is characterized by the rich variety of polymorphous modifications, α-, β'-, and γ-phases, crystallized in monoclinic P21/c (P21/n) space group type with unit cell volume ratios of 2:6:1. The crystal structures of these phases are constituted by three-dimensional framework of corner- and edge-sharing [MnO5] and [MnO6] polyhedra strengthened by [PO4] tetrahedra. All compounds experience long-range antiferromagnetic order at Neel temperature TN = 21.9 K (α-phase), 12.3 K (β'-phase), and 13.3 K (γ-phase). Additionally, second magnetic phase transition takes place at T* = 10.3 K in β'-phase. The magnetization curves of α- and β'-modifications evidence spin-floplike features at B = 1.9 and 3.7 T, while the γ-Mn3(PO4)2 stands out for an extended one-third magnetization plateau stabilized in the range of magnetic field B = 7.5-23.5 T. The first-principles calculations define the main paths of superexchange interaction between Mn spins in these polymorphs. The spin model for α-phase is found to be characterized by collection of uniform and alternating chains, which are coupled in all three directions. The strongest magnetic exchange interaction in γ-phase emphasizes the trimer units, which make chains that are in turn weakly coupled to each other. The spin model of β'-phase turns out to be more complex compared to α- or γ-phase. It shows complex chain structures involving exchange interactions between Mn2 (Mn2', Mn2″) and Mn3 (Mn3', Mn3″). These chains interact through exchanges involving Mn1 (Mn1', Mn1″) spins.

Tanusri Saha-Dasgupta

Papers

Electronic structure of and covalency driven metal-insulator transition in BaCo 1−x Ni x S 2

First-principles study of CaCu3B4O12 (B=Co, Rh, Ir)

Pressure-driven changes in electronic structure of BiCoO$_3$

XY magnetism, Kitaev exchange, and long-range frustration in the Jeff=12 honeycomb cobaltates

Structure–Property Relationships in α-, β′-, and γ-Modifications of Mn3(PO4)2