Hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices

We investigate the hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices. We construct a suitable scaling limit by using a discrete harmonic map. As we shall observe, the quasi-linear parabolic equation in the limit is defined on a flat torus and depends on both the local structure of the crystal lattice and the discrete harmonic map. We formulate the local ergodic theorem on the crystal lattice by introducing the notion of local function bundle, which is a family of local functions on the configuration space. The ideas and methods are taken from the discrete geometric analysis to these problems. Results we obtain are extensions of ones by Kipnis, Olla and Varadhan to crystal lattices.Comment: 41 pages, 7 figure

Quantum Graphs II: Some spectral properties of quantum and combinatorial graphs

The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and other areas. A Schnol type theorem is proven that allows one to detect that a point belongs to the spectrum when a generalized eigenfunction with an subexponential growth integral estimate is available. A theorem on spectral gap opening for ``decorated'' quantum graphs is established (its analog is known for the combinatorial case). It is also shown that if a periodic combinatorial or quantum graph has a point spectrum, it is generated by compactly supported eigenfunctions (``scars'').Comment: 4 eps figures, LATEX file, 21 pages Revised form: a cut-and-paste blooper fixe

Mixed Weyl Symbol Calculus and Spectral Line Shape Theory

A new and computationally viable full quantum version of line shape theory is obtained in terms of a mixed Weyl symbol calculus. The basic ingredient in the collision--broadened line shape theory is the time dependent dipole autocorrelation function of the radiator-perturber system. The observed spectral intensity is the Fourier transform of this correlation function. A modified form of the Wigner--Weyl isomorphism between quantum operators and phase space functions (Weyl symbols) is introduced in order to describe the quantum structure of this system. This modification uses a partial Wigner transform in which the radiator-perturber relative motion degrees of freedom are transformed into a phase space dependence, while operators associated with the internal molecular degrees of freedom are kept in their original Hilbert space form. The result of this partial Wigner transform is called a mixed Weyl symbol. The star product, Moyal bracket and asymptotic expansions native to the mixed Weyl symbol calculus are determined. The correlation function is represented as the phase space integral of the product of two mixed symbols: one corresponding to the initial configuration of the system, the other being its time evolving dynamical value. There are, in this approach, two semiclassical expansions -- one associated with the perturber scattering process, the other with the mixed symbol star product. These approximations are used in combination to obtain representations of the autocorrelation that are sufficiently simple to allow numerical calculation. The leading O(\hbar^0) approximation recovers the standard classical path approximation for line shapes. The higher order O(\hbar^1) corrections arise from the noncommutative nature of the star product.Comment: 26 pages, LaTeX 2.09, 1 eps figure, submitted to 'J. Phys. B.

On the derivation of the t-J model: electron spectrum and exchange interactions in narrow energy bands

A derivation of the t-J model of a highly-correlated solid is given starting from the general many-electron Hamiltonian with account of the non-orthogonality of atomic wave functions. Asymmetry of the Hubbard subbands (i.e. of ``electron'' and ``hole''cases) for a nearly half-filled bare band is demonstrated. The non-orthogonality corrections are shown to lead to occurrence of indirect antiferromagnetic exchange interaction even in the limit of the infinite on-site Coulomb repulsion. Consequences of this treatment for the magnetism formation in narrow energy bands are discussed. Peculiarities of the case of ``frustrated'' lattices, which contain triangles of nearest neighbors, are considered.Comment: 4 pages, RevTe

Two-body quantum mechanical problem on spheres

The quantum mechanical two-body problem with a central interaction on the sphere ${\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.Comment: 41 pages, no figures, typos corrected; appendix D was adde

Mixing Quantum and Classical Mechanics

Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket is antisymmetric and satisfies the Jacobi identity, and, therefore, leads to a natural description of interaction between quantum and classical degrees of freedom. We apply the formalism to coupled quantum and classical oscillators and show how various approximations, such as the mean-field and the multiconfiguration mean-field approaches, can be obtained from the quantum-classical equation of motion.Comment: 31 pages, LaTeX2

An orphan gene is necessary for preaxial digit formation during salamander limb development

Limb development in salamanders differs from other tetrapods in that the first digits to form are the two most anterior (preaxial dominance). This has been proposed as a salamander novelty and its mechanistic basis is unknown. Salamanders are the only adult tetrapods able to regenerate the limb, and the contribution of preaxial dominance to limb regeneration is unclear. Here we show that during early outgrowth of the limb bud, a small cohort of cells express the orphan gene Prod1 together with Bmp2, a critical player in digit condensation in amniotes. Disruption of Prod1 with a gene-editing nuclease abrogates these cells, and blocks formation of the radius and ulna, and outgrowth of the anterior digits. Preaxial dominance is a notable feature of limb regeneration in the larval newt, but this changes abruptly after metamorphosis so that the formation of anterior and posterior digits occurs together within the autopodium resembling an amniote-like pattern

The Cyprinodon variegatus genome reveals gene expression changes underlying differences in skull morphology among closely related species

Genes in durophage intersection set at 15 dpf. This is a comma separated table of the genes in the 15 dpf durophage intersection set. Given are edgeR results for each pairwise comparison. Columns indicating whether a gene is included in the intersection set at a threshold of 1.5 or 2 fold are provided. (CSV 13 kb

Two-hole problem in the t-J model: A canonical transformation approach

The t-J model in the spinless-fermion representation is studied. An effective Hamiltonian for the quasiparticles is derived using canonical transformation approach. It is shown that the rather simple form of the transformation generator allows to take into account effect of hole interaction with the short-range spin waves and to describe the single-hole groundstate. Obtained results are very close to ones of the self-consistent Born approximation. Further accounting for the long-range spin-wave interaction is possible on the perturbative basis. Both spin-wave exchange and an effective interaction due to minimization of the number of broken antiferromagnetic bonds are included in the effective quasiparticle interaction. Two-hole bound state problem is solved using Bethe-Salpeter equation. The only d-wave bound state is found to exist in the region of 1< (t/J) <5. Combined effect of the pairing interactions of both types is important to its formation. Discussion of the possible relation of the obtained results to the problem of superconductivity in real systems is presented.Comment: 19 pages, RevTeX, 12 postscript figure