16,343 research outputs found
Nonperturbative Quantum Physics from Low-Order Perturbation Theory
The Stark effect in hydrogen and the cubic anharmonic oscillator furnish
examples of quantum systems where the perturbation results in a certain
ionization probability by tunneling processes. Accordingly, the perturbed
ground-state energy is shifted and broadened, thus acquiring an imaginary part
which is considered to be a paradigm of nonperturbative behavior. Here we
demonstrate how the low order coefficients of a divergent perturbation series
can be used to obtain excellent approximations to both real and imaginary parts
of the perturbed ground state eigenenergy. The key is to use analytic
continuation functions with a built in analytic structure within the complex
plane of the coupling constant, which is tailored by means of Bender-Wu
dispersion relations. In the examples discussed the analytic continuation
functions are Gauss hypergeometric functions, which take as input fourth order
perturbation theory and return excellent approximations to the complex
perturbed eigenvalue. These functions are Borel-consistent and dramatically
outperform widely used Pad\'e and Borel-Pad\'e approaches, even for rather
large values of the coupling constant.Comment: 5 pages, 3 figures, PDFLaTe
Optical second harmonic generation from Wannier excitons
Excitonic effects in the linear optical response of semiconductors are
well-known and the subject of countless experimental and theoretical studies.
For the technologically important second order nonlinear response, however,
description of excitonic effects has proved to be difficult. In this work, a
simplified three-band Wannier exciton model of cubic semiconductors is applied
and a closed form expression for the complex second harmonic response function
including broadening is derived. Our calculated spectra are found to be in
excellent agreement with the measured response near the band edge. In addition,
a very substantial enhancement of the nonlinear response is predicted for the
transparency region
A library of ab initio Raman spectra for automated identification of 2D materials
Raman spectroscopy is frequently used to identify composition, structure and
layer thickness of 2D materials. Here, we describe an efficient
first-principles workflow for calculating resonant first-order Raman spectra of
solids within third-order perturbation theory employing a localized atomic
orbital basis set. The method is used to obtain the Raman spectra of 733
different monolayers selected from the computational 2D materials database
(C2DB). We benchmark the computational scheme against available experimental
data for 15 known monolayers. Furthermore, we propose an automatic procedure
for identifying a material based on an input experimental Raman spectrum and
illustrate it for the cases of MoS (H-phase) and WTe
(T-phase). The Raman spectra of all materials at different excitation
frequencies and polarization configurations are freely available from the C2DB.
Our comprehensive and easily accessible library of \textit{ab initio} Raman
spectra should be valuable for both theoreticians and experimentalists in the
field of 2D materialsComment: 17 pages, 7 figure
Conditional expectations associated with quantum states
An extension of the conditional expectations (those under a given subalgebra
of events and not the simple ones under a single event) from the classical to
the quantum case is presented. In the classical case, the conditional
expectations always exist; in the quantum case, however, they exist only if a
certain weak compatibility criterion is satisfied. This compatibility criterion
was introduced among others in a recent paper by the author. Then,
state-independent conditional expectations and quantum Markov processes are
studied. A classical Markov process is a probability measure, together with a
system of random variables, satisfying the Markov property and can equivalently
be described by a system of Markovian kernels (often forming a semigroup). This
equivalence is partly extended to quantum probabilities. It is shown that a
dynamical (semi)group can be derived from a given system of quantum observables
satisfying the Markov property, and the group generators are studied. The
results are presented in the framework of Jordan operator algebras, and a very
general type of observables (including the usual real-valued observables or
self-adjoint operators) is considered.Comment: 10 pages, the original publication is available at http://www.aip.or
Inducing spin-dependent tunneling to probe magnetic correlations in optical lattices
We suggest a simple experimental method for probing antiferromagnetic spin
correlations of two-component Fermi gases in optical lattices. The method
relies on a spin selective Raman transition to excite atoms of one spin species
to their first excited vibrational mode where the tunneling is large. The
resulting difference in the tunneling dynamics of the two spin species can then
be exploited, to reveal the spin correlations by measuring the number of doubly
occupied lattice sites at a later time. We perform quantum Monte Carlo
simulations of the spin system and solve the optical lattice dynamics
numerically to show how the timed probe can be used to identify
antiferromagnetic spin correlations in optical lattices.Comment: 5 pages, 5 figure
DFT study of graphene antidot lattices: The roles of geometry relaxation and spin
Graphene sheets with regular perforations, dubbed as antidot lattices, have
theoretically been predicted to have a number of interesting properties. Their
recent experimental realization with lattice constants below 100 nanometers
stresses the urgency of a thorough understanding of their electronic
properties. In this work we perform calculations of the band structure for
various hydrogen-passivated hole geometries using both spin-polarized density
functional theory (DFT) and DFT based tight-binding (DFTB) and address the
importance of relaxation of the structures using either method or a combination
thereof. We find from DFT that all structures investigated have band gaps
ranging from 0.2 eV to 1.5 eV. Band gap sizes and general trends are well
captured by DFTB with band gaps agreeing within about 0.2 eV even for very
small structures. A combination of the two methods is found to offer a good
trade-off between computational cost and accuracy. Both methods predict
non-degenerate midgap states for certain antidot hole symmetries. The inclusion
of spin results in a spin-splitting of these states as well as magnetic moments
obeying the Lieb theorem. The local spin texture of both magnetic and
non-magnetic symmetries is addressed
Bose Einstein condensation on inhomogeneous amenable graphs
We investigate the Bose-Einstein Condensation on nonhomogeneous amenable
networks for the model describing arrays of Josephson junctions. The resulting
topological model, whose Hamiltonian is the pure hopping one given by the
opposite of the adjacency operator, has also a mathematical interest in itself.
We show that for the nonhomogeneous networks like the comb graphs, particles
condensate in momentum and configuration space as well. In this case different
properties of the network, of geometric and probabilistic nature, such as the
volume growth, the shape of the ground state, and the transience, all play a
role in the condensation phenomena. The situation is quite different for
homogeneous networks where just one of these parameters, e.g. the volume
growth, is enough to determine the appearance of the condensation.Comment: 43 pages, 12 figures, final versio
A Mesolithic settlement site at Howick, Northumberland: a preliminary report
Excavations at a coastal site at Howick during 2000 and 2002 have revealed evidence for a substantial Mesolithic settlement and a Bronze Age cist cemetery. Twenty one radiocarbon determinations of the earlier eighth millennium BP (Cal.) indicate that the Mesolithic site is one of the earliest known in northern Britain. An 8m core of sediment was recovered from stream deposits adjacent to the archaeological site which provides information on local environmental conditions. Howick offers a unique opportunity to understand aspects of hunter-gatherer colonisation and settlement during a period of rapid palaeogeographical change around the margins of the North Sea basin, at a time when it was being progressively inundated by the final stages of the postglacial marine transgression. The cist cemetery will add to the picture of Bronze Age occupation of the coastal strip and again reveals a correlation between the location of Bronze Age and Mesolithic sites which has been observed elsewhere in the region
- …