325 research outputs found
Density-Matrix Algorithm for Phonon Hilbert Space Reduction in the Numerical Diagonalization of Quantum Many-Body Systems
Combining density-matrix and Lanczos algorithms we propose a new optimized
phonon approach for finite-cluster diagonalizations of interacting
electron-phonon systems. To illustrate the efficiency and reliability of our
method, we investigate the problem of bipolaron band formation in the extended
Holstein Hubbard model.Comment: 14 pages, 6 figures, Workshop on High Performance Computing in
Science and Engineering, Stuttgart 200
Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
In the case of SU(2), associated by the AGT relation to the 2d Liouville
theory, the Seiberg-Witten prepotential is constructed from the Bohr-Sommerfeld
periods of 1d sine-Gordon model. If the same construction is literally applied
to monodromies of exact wave functions, the prepotential turns into the
one-parametric Nekrasov prepotential F(a,\epsilon_1) with the other epsilon
parameter vanishing, \epsilon_2=0, and \epsilon_1 playing the role of the
Planck constant in the sine-Gordon Shroedinger equation, \hbar=\epsilon_1. This
seems to be in accordance with the recent claim in arXiv:0908.4052 and poses a
problem of describing the full Nekrasov function as a seemingly straightforward
double-parametric quantization of sine-Gordon model. This also provides a new
link between the Liouville and sine-Gordon theories.Comment: 10 page
Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
The AGT relation identifies the Nekrasov functions for various N=2 SUSY gauge
theories with the 2d conformal blocks, which possess explicit Dotsenko-Fateev
matrix model (beta-ensemble) representations the latter being polylinear
combinations of Selberg integrals. The "pure gauge" limit of these matrix
models is, however, a non-trivial multiscaling large-N limit, which requires a
separate investigation. We show that in this pure gauge limit the Selberg
integrals turn into averages in a Brezin-Gross-Witten (BGW) model. Thus, the
Nekrasov function for pure SU(2) theory acquires a form very much reminiscent
of the AMM decomposition formula for some model X into a pair of the BGW
models. At the same time, X, which still has to be found, is the pure gauge
limit of the elliptic Selberg integral. Presumably, it is again a BGW model,
only in the Dijkgraaf-Vafa double cut phase.Comment: 21 page
The matrix model version of AGT conjecture and CIV-DV prepotential
Recently exact formulas were provided for partition function of conformal
(multi-Penner) beta-ensemble in the Dijkgraaf-Vafa phase, which, if interpreted
as Dotsenko-Fateev correlator of screenings and analytically continued in the
number of screening insertions, represents generic Virasoro conformal blocks.
Actually these formulas describe the lowest terms of the q_a-expansion, where
q_a parameterize the shape of the Penner potential, and are exact in the
filling numbers N_a. At the same time, the older theory of CIV-DV prepotential,
straightforwardly extended to arbitrary beta and to non-polynomial potentials,
provides an alternative expansion: in powers of N_a and exact in q_a. We check
that the two expansions coincide in the overlapping region, i.e. for the lowest
terms of expansions in both q_a and N_a. This coincidence is somewhat
non-trivial, since the two methods use different integration contours:
integrals in one case are of the B-function (Euler-Selberg) type, while in the
other case they are Gaussian integrals.Comment: 27 pages, 1 figur
AKSZ construction from reduction data
We discuss a general procedure to encode the reduction of the target space
geometry into AKSZ sigma models. This is done by considering the AKSZ
construction with target the BFV model for constrained graded symplectic
manifolds. We investigate the relation between this sigma model and the one
with the reduced structure. We also discuss several examples in dimension two
and three when the symmetries come from Lie group actions and systematically
recover models already proposed in the literature.Comment: 42 page
The Poisson sigma model on closed surfaces
Using methods of formal geometry, the Poisson sigma model on a closed surface
is studied in perturbation theory. The effective action, as a function on
vacua, is shown to have no quantum corrections if the surface is a torus or if
the Poisson structure is regular and unimodular (e.g., symplectic). In the case
of a Kahler structure or of a trivial Poisson structure, the partition function
on the torus is shown to be the Euler characteristic of the target; some
evidence is given for this to happen more generally. The methods of formal
geometry introduced in this paper might be applicable to other sigma models, at
least of the AKSZ type.Comment: 32 pages; references adde
Gap modification of atomically thin boron nitride by phonon mediated interactions
A theory is presented for the modification of bandgaps in atomically thin
boron nitride (BN) by attractive interactions mediated through phonons in a
polarizable substrate, or in the BN plane. Gap equations are solved, and gap
enhancements are found to range up to 70% for dimensionless electron-phonon
coupling \lambda=1, indicating that a proportion of the measured BN bandgap may
have a phonon origin
Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
We give a concise summary of the impressive recent development unifying a
number of different fundamental subjects. The quiver Nekrasov functions
(generalized hypergeometric series) form a full basis for all conformal blocks
of the Virasoro algebra and are sufficient to provide the same for some
(special) conformal blocks of W-algebras. They can be described in terms of
Seiberg-Witten theory, with the SW differential given by the 1-point resolvent
in the DV phase of the quiver (discrete or conformal) matrix model
(\beta-ensemble), dS = ydz + O(\epsilon^2) = \sum_p \epsilon^{2p}
\rho_\beta^{(p|1)}(z), where \epsilon and \beta are related to the LNS
parameters \epsilon_1 and \epsilon_2. This provides explicit formulas for
conformal blocks in terms of analytically continued contour integrals and
resolves the old puzzle of the free-field description of generic conformal
blocks through the Dotsenko-Fateev integrals. Most important, this completes
the GKMMM description of SW theory in terms of integrability theory with the
help of exact BS integrals, and provides an extended manifestation of the basic
principle which states that the effective actions are the tau-functions of
integrable hierarchies.Comment: 14 page
Carbon stock growth in a forest stand: the power of age
BACKGROUND: Understanding the relationship between the age of a forest stand and its biomass is essential for managing the forest component of the global carbon cycle. Since biomass increases with stand age, postponing harvesting to the age of biological maturity may result in the formation of a large carbon sink. This article quantifies the carbon sequestration capacity of forests by suggesting a default rule to link carbon stock and stand age. RESULTS: The age dependence of forest biomass is shown to be a power-law monomial where the power of age is theoretically estimated to be 4/5. This theoretical estimate is close to the known empirical estimate; therefore, it provides a scientific basis for a quick and transparent assessment of the benefits of postponing the harvest, suggesting that the annual magnitude of the sink induced by delayed harvest lies in the range of 1–2% of the baseline carbon stock. CONCLUSION: The results of this study imply that forest age could be used as an easily understood and scientifically sound measure of the progress in complying with national targets on the protection and enhancement of forest carbon sinks
From Matrices to Strings and Back
We discuss an explicit construction of a string dual for the Gaussian matrix
model. Starting from the matrix model and employing Strebel differential
techniques we deduce hints about the structure of the dual string. Next,
following these hints a worldheet theory is constructed. The correlators in
this string theory are assumed to localize on a finite set of points in the
moduli space of Riemann surfaces. To each such point one associates a Feynman
diagram contributing to the correlator in the dual matrix model, and thus
recasts the worldsheet expression as a sum over Feynman diagrams.Comment: 27 pages, 3 figure
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