21 research outputs found
Time-dependent backgrounds of 2D string theory: Non-perturbative effects
We study the non-perturbative corrections (NPC) to the partition function of
a compactified 2D string theory in a time-dependent background generated by a
tachyon source. The sine-Liouville deformation of the theory is a particular
case of such a background. We calculate the leading as well as the subleading
NPC using the dual description of the string theory as matrix quantum
mechanics. As in the minimal string theories, the NPC are classified by the
double points of a complex curve. We calculate them by two different methods:
by solving Toda equation and by evaluating the quasiclassical fermion wave
functions. We show that the result can be expressed in terms of correlation
functions of the bosonic field associated with the tachyon source and identify
the leading and the subleading corrections as the contributions from the
one-point (disk) and two-point (annulus) correlation functions.Comment: 37 pages, 2 figure
Thermodynamics of 2D string theory
We calculate the free energy, energy and entropy in the matrix quantum
mechanical formulation of 2D string theory in a background strongly perturbed
by tachyons with the imaginary Minkowskian momentum
(``Sine-Liouville'' theory). The system shows a thermodynamical behaviour
corresponding to the temperature . We show that the
microscopically calculated energy of the system satisfies the usual
thermodynamical relations and leads to a non-zero entropy.Comment: 13 pages, lanlmac; typos correcte
2D String Theory as Normal Matrix Model
We show that the bosonic string theory at finite temperature has two
matrix-model realizations related by a kind of duality transformation. The
first realization is the standard one given by the compactified matrix quantum
mechanics in the inverted oscillator potential. The second realization, which
we derive here, is given by the normal matrix model. Both matrix models exhibit
the Toda integrable structure and are associated with two dual cycles (a
compact and a non-compact one) of a complex curve with the topology of a sphere
with two punctures. The equivalence of the two matrix models holds for an
arbitrary tachyon perturbation and in all orders in the string coupling
constant.Comment: lanlmac, 21 page
Hilbert space structure of covariant loop quantum gravity
We investigate the Hilbert space in the Lorentz covariant approach to loop
quantum gravity. We restrict ourselves to the space where all area operators
are simultaneously diagonalizable, assuming that it exists. In this sector
quantum states are realized by a generalization of spin network states based on
Lorentz Wilson lines projected on irreducible representations of an SO(3)
subgroup. The problem of infinite dimensionality of the unitary Lorentz
representations is absent due to this projection. Nevertheless, the projection
preserves the Lorentz covariance of the Wilson lines so that the symmetry is
not broken. Under certain conditions the states can be thought as functions on
a homogeneous space. We define the inner product as an integral over this
space. With respect to this inner product the spin networks form an orthonormal
basis in the investigated sector. We argue that it is the only relevant part of
a larger state space arising in the approach. The problem of the
noncommutativity of the Lorentz connection is solved by restriction to the
simple representations. The resulting structure shows similarities with the
spin foam approach.Comment: 20 pages, RevTE
Time-dependent backgrounds of 2D string theory
We study possible backgrounds of 2D string theory using its equivalence with
a system of fermions in upside-down harmonic potential. Each background
corresponds to a certain profile of the Fermi sea, which can be considered as a
deformation of the hyperbolic profile characterizing the linear dilaton
background. Such a perturbation is generated by a set of commuting flows, which
form a Toda Lattice integrable structure. The flows are associated with all
possible left and right moving tachyon states, which in the compactified theory
have discrete spectrum. The simplest nontrivial background describes the
Sine-Liouville string theory. Our methods can be also applied to the study of
2D droplets of electrons in a strong magnetic field.Comment: 28 pages, 2 figures, lanlma
Non-Perturbative Effects in Matrix Models and D-branes
The large order growth of string perturbation theory in conformal
field theory coupled to world sheet gravity implies the presence of
non-perturbative effects, whose leading behavior can be
calculated in the matrix model approach. Recently it was proposed that the same
effects should be reproduced by studying certain localized D-branes in
Liouville Field Theory, which were constructed by A. and Al. Zamolodchikov. We
discuss this correspondence in a number of different cases: unitary minimal
models coupled to Liouville, where we compare the continuum analysis to the
matrix model results of Eynard and Zinn-Justin, and compact c=1 CFT coupled to
Liouville in the presence of a condensate of winding modes, where we derive the
matrix model prediction and compare it to Liouville theory. In both cases we
find agreement between the two approaches. The c=1 analysis also leads to
predictions about properties of D-branes localized in the vicinity of the tip
of the cigar in SL(2)/U(1) CFT with c=26.Comment: 27 pages, lanlmac; minor change
Phase Fluctuations and Pseudogap Phenomena
This article reviews the current status of precursor superconducting phase
fluctuations as a possible mechanism for pseudogap formation in
high-temperature superconductors. In particular we compare this approach which
relies on the two-dimensional nature of the superconductivity to the often used
-matrix approach. Starting from simple pairing Hamiltonians we present a
broad pedagogical introduction to the BCS-Bose crossover problem. The finite
temperature extension of these models naturally leads to a discussion of the
Berezinskii-Kosterlitz-Thouless superconducting transition and the related
phase diagram including the effects of quantum phase fluctuations and
impurities. We stress the differences between simple Bose-BCS crossover
theories and the current approach where one can have a large pseudogap region
even at high carrier density where the Fermi surface is well-defined. The
Green's function and its associated spectral function, which explicitly show
non-Fermi liquid behaviour, is constructed in the presence of vortices. Finally
different mechanisms including quasi-particle-vortex and vortex-vortex
interactions for the filling of the gap above are considered.Comment: 129 pages, Elsart, 28 EPS figures; Physics Reports, in press. Authors
related information under
"http://nonlin.bitp.kiev.ua/~sharapov/superconductivity.html
Retrospective evaluation of whole exome and genome mutation calls in 746 cancer samples
Funder: NCI U24CA211006Abstract: The Cancer Genome Atlas (TCGA) and International Cancer Genome Consortium (ICGC) curated consensus somatic mutation calls using whole exome sequencing (WES) and whole genome sequencing (WGS), respectively. Here, as part of the ICGC/TCGA Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium, which aggregated whole genome sequencing data from 2,658 cancers across 38 tumour types, we compare WES and WGS side-by-side from 746 TCGA samples, finding that ~80% of mutations overlap in covered exonic regions. We estimate that low variant allele fraction (VAF < 15%) and clonal heterogeneity contribute up to 68% of private WGS mutations and 71% of private WES mutations. We observe that ~30% of private WGS mutations trace to mutations identified by a single variant caller in WES consensus efforts. WGS captures both ~50% more variation in exonic regions and un-observed mutations in loci with variable GC-content. Together, our analysis highlights technological divergences between two reproducible somatic variant detection efforts
In silico study of magnetic nanoparticles transport in channels of various diameters in the presence of a constant magnetic field
In general, this study is concerned with the development of theoretical basis for the use of magnetic nanoparticles (MNPs) for the needs of cardiology. A mathematical model reflecting the fundamental features of MNPs motion and transport in a liquid that flows in a channel modeling a stenotic blood vessel is introduced. The obtained results of computational simulations of MNPs transport revealed the presence of stagnant zones with vortices of the host liquid that appear near the stenosis. The application of a magnetic field to the channel provokes the accumulation of MNPs in these zones. An increased MNPs concentration near the stenosis makes it possible to determine the position and size of the stenosis using an external magnetic sensor