Matrix Models and Lorentz Invariance

The question of Lorentz invariance in the membrane matrix model is addresse

Structural analysis of the GH43 enzyme Xsa43E from Butyrivibrio proteoclasticus

The rumen of dairy cattle can be thought of as a large, stable fermentation vat and as such it houses a large and diverse community of microorganisms. The bacterium Butyrivibrio proteoclasticus is a representative of a significant component of this microbial community. It is a xylan-degrading organism whose genome encodes a large number of open reading frames annotated as fibre-degrading enzymes. This suite of enzymes is essential for the organism to utilize the plant material within the rumen as a fuel source, facilitating its survival in this competitive environment. Xsa43E, a GH43 enzyme from B. proteoclasticus, has been structurally and functionally characterized. Here, the structure of selenomethionine-derived Xsa43E determined to 1.3 Å resolution using single-wavelength anomalous diffraction is reported. Xsa43E possesses the characteristic five-bladed β-propeller domain seen in all GH43 enzymes. GH43 enzymes can have a range of functions, and the functional characterization of Xsa43E shows it to be an arabinofuranosidase capable of cleaving arabinose side chains from short segments of xylan. Full functional and structural characterization of xylan-degrading enzymes will aid in creating an enzyme cocktail that can be used to completely degrade plant material into simple sugars. These molecules have a range of applications as starting materials for many industrial processes, including renewable alternatives to fossil fuels

A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem

A quantum system will stay near its instantaneous ground state if the Hamiltonian that governs its evolution varies slowly enough. This quantum adiabatic behavior is the basis of a new class of algorithms for quantum computing. We test one such algorithm by applying it to randomly generated, hard, instances of an NP-complete problem. For the small examples that we can simulate, the quantum adiabatic algorithm works well, and provides evidence that quantum computers (if large ones can be built) may be able to outperform ordinary computers on hard sets of instances of NP-complete problems.Comment: 15 pages, 6 figures, email correspondence to [email protected] ; a shorter version of this article appeared in the April 20, 2001 issue of Science; see http://www.sciencemag.org/cgi/content/full/292/5516/47

Exact solutions of classical scalar field equations

We give a class of exact solutions of quartic scalar field theories. These solutions prove to be interesting as are characterized by the production of mass contributions arising from the nonlinear terms while maintaining a wave-like behavior. So, a quartic massless equation has a nonlinear wave solution with a dispersion relation of a massive wave and a quartic scalar theory gets its mass term renormalized in the dispersion relation through a term depending on the coupling and an integration constant. When spontaneous breaking of symmetry is considered, such wave-like solutions show how a mass term with the wrong sign and the nonlinearity give rise to a proper dispersion relation. These latter solutions do not change the sign maintaining the property of the selected value of the equilibrium state. Then, we use these solutions to obtain a quantum field theory for the case of a quartic massless field. We get the propagator from a first order correction showing that is consistent in the limit of a very large coupling. The spectrum of a massless quartic scalar field theory is then provided. From this we can conclude that, for an infinite countable number of exact classical solutions, there exist an infinite number of equivalent quantum field theories that are trivial in the limit of the coupling going to infinity.Comment: 7 pages, no figures. Added proof of existence of a zero mode and two more references. Accepted for publication in Journal of Nonlinear Mathematical Physic

Quantum orders in an exact soluble model

We find all the exact eigenstates and eigenvalues of a spin-1/2 model on square lattice: $H=16g \sum_i S^y_i S^x_{i+x} S^y_{i+x+y} S^x_{i+y}$. We show that the ground states for $g0$ have different quantum orders described by Z2A and Z2B projective symmetry groups. The phase transition at $g=0$ represents a new kind of phase transitions that changes quantum orders but not symmetry. Both the Z2A and Z2B states are described by $Z_2$ lattice gauge theories at low energies. They have robust topologically degenerate ground states and gapless edge excitations.Comment: 4 pages, RevTeX4, More materials on topological/quantum orders and quantum computing can be found in http://dao.mit.edu/~we

Redox regulation of the mitogen-activated protein kinase pathway during lymphocyte activation

AbstractWe have previously demonstrated an obligatory requirement for intracellular reactive oxygen species generation during T lymphocyte activation, and have proposed that intracellular reactive oxygen species may act as signalling agents in the regulation of certain cellular processes, for example, during cell cycle entry. To test this hypothesis, we have been interested to determine which, if any, cell cycle entry events are affected by oxidative signalling. In earlier studies, we have identified the transcription factors NF-κB and AP-1 as molecular targets for oxidative signalling processes during cell cycle entry, and have shown that oxidative signalling is involved in the regulation of early changes in gene expression during the G0 to G1 phase transition. To extend these initial observations, we have examined the effect of antioxidant treatment on the activity of the mitogen-activated protein kinases erk1 and erk2, as members of a signal transduction pathway known to directly regulate transcription factor function. Using as a probe cysteamine, an aminothiol compound with both antioxidant and antiproliferative activity, we have identified erk2, a key element of the MAP kinase pathway, as being responsive to oxidative signalling during lymphocyte activation. These observations provide further evidence to suggest a role for intracellular oxidant generation as a regulatory mechanism during cell cycle entry, and establish a link between oxidative signalling and other aspects of the intracellular signalling network that is activated in response to mitogenic stimulation

Spatial search and the Dirac equation

We consider the problem of searching a d-dimensional lattice of N sites for a single marked location. We present a Hamiltonian that solves this problem in time of order sqrt(N) for d>2 and of order sqrt(N) log(N) in the critical dimension d=2. This improves upon the performance of our previous quantum walk search algorithm (which has a critical dimension of d=4), and matches the performance of a corresponding discrete-time quantum walk algorithm. The improvement uses a lattice version of the Dirac Hamiltonian, and thus requires the introduction of spin (or coin) degrees of freedom.Comment: 5 pages, 1 figur

Improved Error-Scaling for Adiabatic Quantum State Transfer

We present a technique that dramatically improves the accuracy of adiabatic state transfer for a broad class of realistic Hamiltonians. For some systems, the total error scaling can be quadratically reduced at a fixed maximum transfer rate. These improvements rely only on the judicious choice of the total evolution time. Our technique is error-robust, and hence applicable to existing experiments utilizing adiabatic passage. We give two examples as proofs-of-principle, showing quadratic error reductions for an adiabatic search algorithm and a tunable two-qubit quantum logic gate.Comment: 10 Pages, 4 figures. Comments are welcome. Version substantially revised to generalize results to cases where several derivatives of the Hamiltonian are zero on the boundar

Quantum States of String-Inspired Lineal Gravity

We construct quantum states for a (1+1) dimensional gravity-matter model that is also a gauge theory based on the centrally extended Poincar\'e group. Explicit formulas are found, which exhibit interesting structures. For example wave functionals are gauge invariant except for a gauge non-invariant phase factor that is the Kirillov-Kostant 1-form on the (co-) adjoint orbit of the group. However no evidence for gravity-matter forces is found.Comment: 23 pages in REVTEX, MIT-CTP-227

Spontaneously Broken Spacetime Symmetries and Goldstone's Theorem

Goldstone's theorem states that there is a massless mode for each broken symmetry generator. It has been known for a long time that the naive generalization of this counting fails to give the correct number of massless modes for spontaneously broken spacetime symmetries. We explain how to get the right count of massless modes in the general case, and discuss examples involving spontaneously broken Poincare and conformal invariance.Comment: 4 pages; 1 figure; v2: minor corrections. version to appear on PR