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Fermi surface nesting and the origin of Charge Density Waves in metals
M. D. Johannes,I. I. Mazin
Physics , 2007, DOI: 10.1103/PhysRevB.77.165135
Abstract: The concept of a CDW induced by Fermi-surface nesting originated from the Peierls idea of electronic instabilities in purely 1D metals and is now often applied to charge ordering in real low-dimensional materials. The idea is that if Fermi surface contours coincide when shifted along the observed CDW wave vector, then the CDW is considered to be nesting-derived. We show that in most cases this procedure has no predictive power, since Fermi surfaces either do not nest at the right wave vector, or nest more strongly at the wrong vector. We argue that only a tiny fraction, if any, of the observed charge ordering phase transitions are true analogues of the Peierls instability because electronic instabilities are easily destroyed by even small deviations from perfect nesting conditions. Using prototypical CDW materials NbSe$_2$, TaSe$_2$, and CeTe$_3$, we show that such conditions are hardly ever fulfilled, and that the CDW phases are actually structural phase transitions, driven by the concerted action of electronic and ionic subsystems, \textit{i.e.,} \textbf{q}-dependent electron-phonon coupling plays an indispensable part. We also show mathematically that the original Peierls construction is so fragile as to be unlikely to apply to real materials. We argue that no meaningful distinction between a CDW and an incommensurate lattice transition exists.
A key role for unusual spin dynamics in ferropnictides
I. I. Mazin,M. D. Johannes
Physics , 2008, DOI: 10.1038/nphys1160
Abstract: The 2008 discovery of superconducting ferropnictides with Tc~26K-56K introduced a new family of materials into the category of high Tc superconductors. The ongoing project of understanding the superconducting mechanism and pairing symmetry has already revealed a complicated and often contradictory underlying picture of the structural and magnetic properties. There is an almost unprecedented sensitivity of the calculated magnetism and Fermi surface to structural details that prohibits correspondence with experiment. Furthermore, experimental probes of the order parameter symmetry are in surprisingly strong disagreement, even considering the relative immaturity of the field. Here we outline all of the various and seemingly contradictory evidences, both theoretical and experimental, and show that they can be rectified if the system is assumed to be highly magnetic with a spin density wave that is well-defined but with magnetic twin and anti-phase boundaries that are dynamic on the time-scale of experiments. Under this assumption, we find that our calculations can accurately reproduce even very fine details of the structure, and a natural explanation for the temperature separation of structural and magnetic transitions is provided. Thus, our theory restores agreement between experiment and theory in crucial areas, making further cooperative progress possible on both fronts. We believe that fluctuating magnetic domains will be an essential component of unravelling the interplay between magnetic interactions and superconductivity in these newest high Tc superconductors.
A critical assessment of the pairing symmetry in NaxCoO2.yH2O
I. I. Mazin,M. D. Johannes
Physics , 2005, DOI: 10.1038/nphys126
Abstract: We examine each of the symmetry-allowed pairing states of NaxCoO2.yH2O and compare their properties to what is experimentally and theoretically established about the compound. In this way, we can eliminate the vast majority of states that are technically allowed and narrow the field to two, both of f-wave type states. We discuss the expected features of these states and suggest experiments that can distinguish between them. We also discuss odd-frequency gap pairing and how it relates to available experimental evidence.
Mellin Representation for the Heavy Flavor Contributions to Deep Inelastic Structure Functions
Sergey I. Alekhin,Johannes Blümlein
Physics , 2004, DOI: 10.1016/j.physletb.2004.05.042
Abstract: We derive semi--analytic expressions for the analytic continuation of the Mellin transforms of the heavy flavor QCD coefficient functions for neutral current deep inelastic scattering in leading and next-to-leading order to complex values of the Mellin variable $N$. These representations are used in Mellin--space QCD evolution programs to provide fast evaluations of the heavy flavor contributions to the structure functions $F_2(x,Q^2), F_L(x,Q^2)$ and $g_1(x,Q^2)$.
A curvature theory for discrete surfaces based on mesh parallelity
Alexander I. Bobenko,Helmut Pottmann,Johannes Wallner
Mathematics , 2009,
Abstract: We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces' areas and mixed areas. Remarkably these notions are capable of unifying notable previously defined classes of surfaces, such as discrete isothermic minimal surfaces and surfaces of constant mean curvature. We discuss various types of natural Gauss images, the existence of principal curvatures, constant curvature surfaces, Christoffel duality, Koenigs nets, contact element nets, s-isothermic nets, and interesting special cases such as discrete Delaunay surfaces derived from elliptic billiards.
On a degenerate non-local parabolic problem describing infinite dimensional replicator dynamics
Nikos I. Kavallaris,Johannes Lankeit,Michael Winkler
Mathematics , 2015,
Abstract: We establish the existence of locally positive weak solutions to the homogeneous Dirichlet problem for \[ u_t = u \Delta u + u \int_\Omega |\nabla u|^2 \] in bounded domains $\Omega\subset\mathbb{R}^n$ and prove that solutions converge to $0$ if the initial mass is small, whereas they undergo blow-up in finite time if the initial mass is large. We show that in this case the blow-up set coincides with $\overline{\Omega}$, i.e. the finite-time blow-up is global. Key words: Degenerate diffusion, non-local nonlinearity, blow-up, evolutionary games, infinite dimensional replicator dynamics
Deterministic Sparse Suffix Sorting on Rewritable Texts
Johannes Fischer,Tomohiro I,Dominik K？ppl
Computer Science , 2015,
Abstract: Given a rewriteable text $T$ of length $n$ on an alphabet of size $\sigma$, we propose an online algorithm that computes the sparse suffix array and the sparse longest common prefix array of $T$ in $\Oh{\abs{\Comlcp} \sqrt{\lg n} + m \lg m \lg n \lg^* n}$ time by using the text space and $\Oh{m}$ additional working space, where $m$ is the number of some positions $\Pos$ on $[1..n]$, provided online and arbitrarily, and $\Comlcp = \bigcup_{p,p' \in \Pos, p \neq p'} [p..p+\lcp(T[p..], T[p'..])]$.
Lempel Ziv Computation In Small Space (LZ-CISS)
Johannes Fischer,Tomohiro I,Dominik K？ppl
Computer Science , 2015,
Abstract: For both the Lempel Ziv 77- and 78-factorization we propose algorithms generating the respective factorization using $(1+\epsilon) n \lg n + O(n)$ bits (for any positive constant $\epsilon \le 1$) working space (including the space for the output) for any text of size \$n\$ over an integer alphabet in $O(n / \epsilon^{2})$ time.
Buchbesprechungen
Br？i？, Marita,Reikerstorfer, Johann,Thomas, Johannes
- , 2008,
Abstract: Hr？ak ID: 3722
Book Reviews
Br？i？, Marita,Reikerstorfer, Johann,Thomas, Johannes
- , 2008,
Abstract: Hr？ak ID: 3722
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