Canonical representation for electrons and its application to the Hubbard model

A new representation for electrons is introduced, in which the electron operators are written in terms of a spinless fermion and the Pauli operators. This representation is canonical, invertible and constraint-free. Importantly, it simplifies the Hubbard interaction. On a bipartite lattice, the Hubbard model is reduced to a form in which the exchange interaction emerges simply by decoupling the Pauli subsystem from the spinless fermion bath. This exchange correctly reproduces the large $U$ superexchange. Also derived, for $U=\pm\infty$, is the Hamiltonian to study Nagaoka ferromagnetism. In this representation, the infinite-$U$ Hubbard problem becomes elegant and easier to handle. Interestingly, the ferromagnetism in Hubbard model is found to be related to the gauge invariance of the spinless fermions. Generalization of this representation for the multicomponent fermions, a new representation for bosons, the notion of a `soft-core' fermion, and some interesting unitary transformations are introduced and discussed in the appendices.Comment: 10+ pages, 3 Figure

Conformational analysis of cyclolinopeptide A, a cyclic nonapeptide: nuclear overhauser effect and energy minimization studies

The conformation of cyclolinopeptide A [cyclo(Pro-Pro-Phe-Phe-Leu-Ile-Ile-Leu-Val)], a naturally occurring cyclic nonapeptide has been investigated in dimethylsulfoxide solution by 270 MHz 1H-nmr. A complete assignment of all CαH and NH resonances has been accomplished using two-dimensional correlated spectroscopy and nuclear Overhauser effects (NOEs). Analysis of interresidue NOEs and JHNCαH values permit construction of a molecular model for the cyclic peptide backbone. The crude model derived from nmr has been used as a starting point for energy minimization, which yields a refined structure largely compatible with nmr observations. The major features of the conformation of cyclolinopeptide A are a Type VI β-turn centered at Pro(1)-Pro(2), with a cis peptide bond between these residues and a γ-turn (C7) structure centered at Ile(6). Two intramolecular hydrogen bonds Val(9) CO - Phe(3)NH (4 →1) and Leu(5) CO - Ile(7)NH (3 → 1) are observed in the low-energy conformation. The limited solvent accessibility observed for the Val(9) and Leu(5) NH groups in the nmr studies are rationalized in terms of steric shielding

Pairing Fluctuations Determine Low Energy Electronic Spectra in Cuprate Superconductors

We describe here a minimal theory of tight binding electrons moving on the square planar Cu lattice of the hole-doped cuprates and mixed quantum mechanically with pairs of them (Cooper pairs). Superconductivity occurring at the transition temperature T_c is the long-range, d-wave symmetry phase coherence of these Cooper pairs. Fluctuations necessarily associated with incipient long-range superconducting order have a generic large distance behaviour near T_c. We calculate the spectral density of electrons coupled to such Cooper pair fluctuations and show that features observed in Angle Resolved Photo Emission Spectroscopy (ARPES) experiments on different cuprates above T_c as a function of doping and temperature emerge naturally in this description. These include `Fermi arcs' with temperature-dependent length and an antinodal pseudogap which fills up linearly as the temperature increases towards the pseudogap temperature. Our results agree quantitatively with experiment. Below T_c, the effects of nonzero superfluid density and thermal fluctuations are calculated and compared successfully with some recent ARPES experiments, especially the observed `bending' or deviation of the superconducting gap from the canonical d-wave form.Comment: 14 pages, 8 figures (to appear in Phys. Rev. B

Flux jumps, Second Magnetization Peak anomaly and the Peak Effect phenomenon in single crystals of YNi2B2CYNi_2B_2C and LuNi2B2CLuNi_2B_2C

We present magnetization measurements in single crystals of the tetragonal $YNi_2B_2C$ compound, which exhibit the phenomenon of peak effect as well as the second magnetization peak anomaly for H $>$ 0.5T (H $||$ c). At the lower field (50mT $<$ H $<$ 200mT), we have observed the presence of flux jumps, which seem to relate to a structural change in the local symmetry of the flux line lattice (a first order re-orientation transition across a local field in some parts of the sample, in the range of 100mT to 150mT). These flux jumps are also observed in a single crystal of $LuNi_2B_2C$ for H $||$ c in the field region from 2 mT to 25 mT, which are compatible with the occurrence of a re-orientation transition at a lower field in a cleaner crystal of this compound, as compared to those of $YNi_2B_2C$. Vortex phase diagrams drawn for H $||$ c in $LuNi_2B_2C$ and $YNi_2B_2C$ show that the ordered elastic glass phase spans a larger part of (H, T) space in the former as compared to latter, thereby, reaffirming the difference in the relative purity of the two samples.Comment: 11 pages, 14 figure

Personalisation and recommender systems in digital libraries

Widespread use of the Internet has resulted in digital libraries that are increasingly used by diverse communities of users for diverse purposes and in which sharing and collaboration have become important social elements. As such libraries become commonplace, as their contents and services become more varied, and as their patrons become more experienced with computer technology, users will expect more sophisticated services from these libraries. A simple search function, normally an integral part of any digital library, increasingly leads to user frustration as user needs become more complex and as the volume of managed information increases. Proactive digital libraries, where the library evolves from being passive and untailored, are seen as offering great potential for addressing and overcoming these issues and include techniques such as personalisation and recommender systems. In this paper, following on from the DELOS/NSF Working Group on Personalisation and Recommender Systems for Digital Libraries, which met and reported during 2003, we present some background material on the scope of personalisation and recommender systems in digital libraries. We then outline the working group’s vision for the evolution of digital libraries and the role that personalisation and recommender systems will play, and we present a series of research challenges and specific recommendations and research priorities for the field

A Pathwise Ergodic Theorem for Quantum Trajectories

If the time evolution of an open quantum system approaches equilibrium in the time mean, then on any single trajectory of any of its unravelings the time averaged state approaches the same equilibrium state with probability 1. In the case of multiple equilibrium states the quantum trajectory converges in the mean to a random choice from these states.Comment: 8 page

Magnetization hysteresis and time decay measurements in FeSe0.50_{0.50}Te0.50_{0.50} : Evidence for fluctuation in mean free path induced pinning

We present results of magnetic measurements relating to vortex phase diagram in a single crystal of FeSe$_{0.5}$Te$_{0.5}$ which displays second magnetization peak anomaly for $H \parallel c$. The possible role of the crystalline anisotropy on vortex pinning is explored via magnetic torque magnetometry. We present evidence in favor of pinning related to spatial variations of the charge carrier mean free path leading to small bundle vortex pinning by randomly distributed (weak) pinning centers for both $H \parallel c$ and $H \perp c$. This is further corroborated using magnetization data for $H \parallel c$ in a single crystal of FeSe$_{0.35}$Te$_{0.65}$. Dynamical response across second magnetization peak (SMP) anomaly in FeSe$_{0.5}$Te$_{0.5}$ has been compared with that across the well researched phenomenon of peak effect (PE) in a single crystal of CeRu$_2$.Comment: 11 figures, provided additional data in another sample, added Fig.