34 research outputs found
Area distribution of two-dimensional random walks and non Hermitian Hofstadter quantum mechanics
When random walks on a square lattice are biased horizontally to move solely
to the right, the probability distribution of their algebraic area can be
exactly obtained. We explicitly map this biased classical random system on a
non hermitian Hofstadter-like quantum model where a charged particle on a
square lattice coupled to a perpendicular magnetic field hopps only to the
right. In the commensurate case when the magnetic flux per unit cell is
rational, an exact solution of the quantum model is obtained. Periodicity on
the lattice allows to relate traces of the Nth power of the Hamiltonian to
probability distribution generating functions of biased walks of length N.Comment: 14 pages, 7 figure
Correlation functions in the Calogero-Sutherland model with open boundaries
Calogero-Sutherland models of type are known to be relevant to the
physics of one-dimensional quantum impurity effects. Here we represent certain
correlation functions of these models in terms of generalized hypergeometric
functions. Their asymptotic behaviour supports the predictions of (boundary)
conformal field theory for the orthogonality catastrophy and Friedel
oscillations.Comment: LaTeX, 11 pages, 1 eps-figur
Dimensional reduction on a sphere
The question of the dimensional reduction of two-dimensional (2d) quantum
models on a sphere to one-dimensional (1d) models on a circle is adressed. A
possible application is to look at a relation between the 2d anyon model and
the 1d Calogero-Sutherland model, which would allow for a better understanding
of the connection between 2d anyon exchange statistics and Haldane exclusion
statistics. The latter is realized microscopically in the 2d LLL anyon model
and in the 1d Calogero model. In a harmonic well of strength \omega or on a
circle of radius R - both parameters \omega and R have to be viewed as long
distance regulators - the Calogero spectrum is discrete. It is well known that
by confining the anyon model in a 2d harmonic well and projecting it on a
particular basis of the harmonic well eigenstates, one obtains the
Calogero-Moser model. It is then natural to consider the anyon model on a
sphere of radius R and look for a possible dimensional reduction to the
Calogero-Sutherland model on a circle of the same radius. First, the free
one-body case is considered, where a mapping from the 2d sphere to the 1d
chiral circle is established by projection on a special class of spherical
harmonics. Second, the N-body interacting anyon model is considered : it
happens that the standard anyon model on the sphere is not adequate for
dimensional reduction. One is thus lead to define a new spherical anyon-like
model deduced from the Aharonov-Bohm problem on the sphere where each flux line
pierces the sphere at one point and exits it at its antipode.Comment: 10 pages, 1 figur
Spectra of Dirichlet Laplacian in 3-dimensional polyhedral layers
The structure of the spectrum of the three-dimensional Dirichlet Laplacian in
the 3D polyhedral layer of fixed width is studied. It appears that the
essential spectrum is defined by the smallest dihedral angle that forms the
boundary of the layer while the discrete spectrum is always finite. An example
of a layer with the empty discrete spectrum is constructed. The spectrum is
proved to be nonempty in regular polyhedral layer
Relation between size of mixing zone and intermediate concentration in miscible displacement
We investigate the miscible displacement of a viscous liquid by a less
viscous one in a porous medium, which frequently leads to the formation of a
mixing zone characterized by thin fingers. The mixing zone grows in time due to
the difference in speed between the leading and trailing edges. The transverse
flow equilibrium (TFE) model provides estimates of these speeds. We propose an
enhancement for the TFE estimates. It is based on the assumption that an
intermediate concentration exists near the tip of the finger, which allows to
reduce the integration interval in the speed estimate. Numerical simulations of
the computational fluid dynamics model were conducted to validate the new
estimates. The refined estimates offer greater accuracy than those provided by
the original TFE model.Comment: 16 pages, 11 figure
Genome Sequencing and Comparative Analysis of Saccharomyces cerevisiae Strains of the Peterhof Genetic Collection
The Peterhof genetic collection of Saccharomyces cerevisiae strains (PGC) is a large laboratory stock that has accumulated several thousands of strains for over than half a century. It originated independently of other common laboratory stocks from a distillery lineage (race XII). Several PGC strains have been extensively used in certain fields of yeast research but their genomes have not been thoroughly explored yet. Here we employed whole genome sequencing to characterize five selected PGC strains including one of the closest to the progenitor, 15V-P4, and several strains that have been used to study translation termination and prions in yeast (25-25-2V-P3982, 1B-D1606, 74-D694, and 6P-33G-D373). The genetic distance between the PGC progenitor and S288C is comparable to that between two geographically isolated populations. The PGC seems to be closer to two bakery strains than to S288C-related laboratory stocks or European wine strains. In genomes of the PGC strains, we found several loci which are absent from the S288C genome; 15V-P4 harbors a rare combination of the gene cluster characteristic for wine strains and the RTM1 cluster. We closely examined known and previously uncharacterized gene variants of particular strains and were able to establish the molecular basis for known phenotypes including phenylalanine auxotrophy, clumping behavior and galactose utilization. Finally, we made sequencing data and results of the analysis available for the yeast community. Our data widen the knowledge about genetic variation between Saccharomyces cerevisiae strains and can form the basis for planning future work in PGC-related strains and with PGC-derived alleles.PBD acknowledges the Russian Foundation for Basic Research (www.rfbr.ru) for grant 14-04-31265. OVT and SGIV acknowledge the Russian Foundation for Basic Research for grant 15-29-02526. JVS acknowledges the Russian Science Foundation (www.rscf.ru) for grant 14-50-00069 and the Saint-Petersburg State University for grant 1.38.426.2015. PBD, AGM, EAR, and JVS acknowledge the Saint-Petersburg State University for research grant 1.37.291.2015. PBD and OVT acknowledge the Saint-Petersburg City Committee on Science and High School (knvsh.gov.spb.ru/) for grants 15404 and 15919, respectively. PBD, AGM, JVS, and SGIV acknowledge the Saint-Petersburg State University for research grant 15.61.2218.2013. PBD acknowledges the Saint-Petersburg State University for research grant 1.42.1394.2015
Subgap tunneling through channels of polarons and bipolarons in chain conductors
We suggest a theory of internal coherent tunneling in the pseudogap region where the applied voltage is below the free electron gap. We consider quasi-one-dimensional (1D) systems where the gap is originated by a lattice dimerization (Peierls or SSH effect) as in polyacethylene, as well as low symmetry 1D semiconductors. Results may be applied to several types of conjugated polymers, to semiconducting nanotubes, and to quantum wires of semiconductors. The approach may be generalized to tunneling in strongly correlated systems showing the pseudogap effect, as in the family of high-Tc materials in the undoped limit. We demonstrate the evolution of tunneling current-voltage characteristics from smearing the free electron gap down to threshold for tunneling of polarons and further down to the region of bielectronic tunneling via bipolarons or kink pairs. The interchain tunneling is described in a parallel comparison with the on chain optical absorption, also within the subgap region
Pseudogaps due to sound modes: from incommensurate charge density waves to semiconducting wires
3 figuresWe consider pseudogap effects for electrons interacting with gapless modes. We study both generic 1D semiconductors with acoustic phonons and incommensurate charge density waves. We calculate the subgap absorption as it can be observed by means of the photo electron or tunneling spectroscopy. Within the formalism of functional integration and the adiabatic approximation, the probabilities are described by nonlinear configurations of an instanton type. Particularities of both cases are determined by the topological nature of stationary excited states (acoustic polarons or amplitude solitons) and by presence of gapless phonons which change the usual dynamics to the regime of the quantum dissipation. Below the free particle edge the pseudogap starts with the exponential (stretched exponential for gapful phonons) decrease of transition rates. Deeply within the pseudogap they are dominated by a power law, in contrast with nearly exponential law for gapful modes