Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model

We propose 1D and 2D lattice wave functions constructed from the SU(n)_1 Wess-Zumino-Witten (WZW) model and derive their parent Hamiltonians. When all spins in the lattice transform under SU(n) fundamental representations, we obtain a two-body Hamiltonian in 1D, including the SU(n) Haldane-Shastry model as a special case. In 2D, we show that the wave function converges to a class of Halperin's multilayer fractional quantum Hall states and belongs to chiral spin liquids. Our result reveals a hidden SU(n) symmetry for this class of Halperin states. When the spins sit on bipartite lattices with alternating fundamental and conjugate representations, we provide numerical evidence that the state in 1D exhibits quantum criticality deviating from the expected behaviors of the SU(n)_1 WZW model, while in 2D they are chiral spin liquids being consistent with the prediction of the SU(n)_1 WZW model.Comment: 28 pages, 9 figures, published versio

Front Stability in Mean Field Models of Diffusion Limited Growth

We present calculations of the stability of planar fronts in two mean field models of diffusion limited growth. The steady state solution for the front can exist for a continuous family of velocities, we show that the selected velocity is given by marginal stability theory. We find that naive mean field theory has no instability to transverse perturbations, while a threshold mean field theory has such a Mullins-Sekerka instability. These results place on firm theoretical ground the observed lack of the dendritic morphology in naive mean field theory and its presence in threshold models. The existence of a Mullins-Sekerka instability is related to the behavior of the mean field theories in the zero-undercooling limit.Comment: 26 pp. revtex, 7 uuencoded ps figures. submitted to PR

Conformal Covariantization of Moyal-Lax Operators

A covariant approach to the conformal property associated with Moyal-Lax operators is given. By identifying the conformal covariance with the second Gelfand-Dickey flow, we covariantize Moyal-Lax operators to construct the primary fields of one-parameter deformation of classical $W$-algebras.Comment: 13 pages, Revtex, no figures, v.2: typos corrected, references added and conclusion modifie

Molecular Motor of Double-Walled Carbon Nanotube Driven by Temperature Variation

An elegant formula for coordinates of carbon atoms in a unit cell of a single-walled nanotube (SWNT) is presented and a new molecular motor of double-walled carbon nanotube whose inner tube is a long (8,4) SWNT and outer tube a short (14,8) SWNT is constructed. The interaction between inner an outer tubes is analytically derived by summing the Lennard-Jones potentials between atoms in inner and outer tubes. It is proved that the molecular motor in a thermal bath exhibits a directional motion with the temperature variation of the bath.Comment: 9 pages, 4 figures, revtex

Are Bosonic Replicas Faulty?

Motivated by the ongoing discussion about a seeming asymmetry in the performance of fermionic and bosonic replicas, we present an exact, nonperturbative approach to zero-dimensional replica field theories belonging to the broadly interpreted "beta=2" Dyson symmetry class. We then utilise the formalism developed to demonstrate that the bosonic replicas do correctly reproduce the microscopic spectral density in the QCD inspired chiral Gaussian unitary ensemble. This disproves the myth that the bosonic replica field theories are intrinsically faulty.Comment: 4.3 pages; final version to appear in PR

Partially Chloritized Smectites: Analogues of Smectites at Gale Crater, Mars

Characterizing the structure and composition of phyllosilicates is important for interpreting the aqueous history of Mars and identifying potential habitable environments. Smectites and chlorites are the most dominant clay types on Mars, and there is evidence of the presence of smectite/chlorite intergrades. Smectite has been detected at Gale Crater, Mars, via orbital observations and in-situ measurements, in abundances up to approximately 25 weight percentage of bulk rock. John Klein (JK) and Cumberland (CB) were analyzed by the Chemistry and Mineralogy (CheMin) and Samples Analysis at Mars (SAM) evolved gas analysis experiment (EGA) instruments, onboard Mars Science Laboratory (MSL), Curiosity, to distinguish clay mineralogy. John Klein has a collapsed 2:1 smectite with a d-spacing of 10 Angstroms, whereas Cumberland smectite did not fully collapse and has a d-spacing of approximately 13.2 Angstroms. It has been suggested that partial chloritization or pillaring could be responsible for the expanded Cumberland smectite because pillaring inhibits the collapse of smectites down to 10 Angstrom, even under the desiccating conditions on the martian surface. Clay minerals have been detected in ancient fluvio-lacustrine rocks throughout Curiositys traverse and catalog the changes of the lake water chemistry and diagenetic conditions at Gale Crater, Mars. Investigating clay minerals is important for identifying them on the Martian surface, in particular as Curiosity proceeds into the upcoming Clay-bearing Unit

Loop groups and noncommutative geometry

We describe the representation theory of loop groups in terms of K-theory and noncommutative geometry. This is done by constructing suitable spectral triples associated with the level l projective unitary positive-energy representations of any given loop group $LG$. The construction is based on certain supersymmetric conformal field theory models associated with LG in the setting of conformal nets. We then generalize the construction to many other rational chiral conformal field theory models including coset models and the moonshine conformal net.Comment: Revised versio

Classical Poisson structures and r-matrices from constrained flows

We construct the classical Poisson structure and $r$-matrix for some finite dimensional integrable Hamiltonian systems obtained by constraining the flows of soliton equations in a certain way. This approach allows one to produce new kinds of classical, dynamical Yang-Baxter structures. To illustrate the method we present the $r$-matrices associated with the constrained flows of the Kaup-Newell, KdV, AKNS, WKI and TG hierarchies, all generated by a 2-dimensional eigenvalue problem. Some of the obtained $r$-matrices depend only on the spectral parameters, but others depend also on the dynamical variables. For consistency they have to obey a classical Yang-Baxter-type equation, possibly with dynamical extra terms.Comment: 16 pages in LaTe