31,673 research outputs found

### Gamow Vectors in a Periodically Perturbed Quantum System

We analyze the behavior of the wave function $\psi(x,t)$ for one dimensional
time-dependent Hamiltonian $H=-\partial_x^2\pm2\delta(x)(1+2r\cos\omega t)$
where $\psi(x,0)$ is compactly supported. We show that $\psi(x,t)$ has a Borel
summable expansion containing finitely many terms of the form
\sum_{n=-\infty}^{\infty} e^{i^{3/2}\sqrt{-\lambda_{k}+n\omegai}|x|} A_{k,n}
e^{-\lambda_{k}t+n\omega it}, where $\lambda_k$ represents the associated
resonance. This expression defines Gamow vectors and resonances in a rigorous
and physically relevant way for all frequencies and amplitudes in a
time-dependent model. For small amplitude ($|r|\ll 1$) there is one resonance
for generic initial conditions. We calculate the position of the resonance and
discuss its physical meaning as related to multiphoton ionization. We give
qualitative theoretical results as well as numerical calculations in the
general case.Comment: 21 pages, 6 figure

### Positivity for quantum cluster algebras from unpunctured orbifolds

We give the quantum Laurent expansion formula for the quantum cluster
algebras from unpunctured orbifolds with arbitrary coefficients and
quantization. As an application, positivity for such class of quantum cluster
algebras is given. For technical reasons, it will always be assumed that the
weights of the orbifold points are 2.Comment: 43 pages. arXiv admin note: substantial text overlap with
arXiv:1807.0691

### Modular Anomaly from Holomorphic Anomaly in Mass Deformed N=2 Superconformal Field Theories

We study the instanton partition functions of two well-known superconformal
field theories with mass deformations. Two types of anomaly equations, namely,
the modular anomaly and holomorphic anomaly, have been discovered in the
literature. We provide a clean solution to the long standing puzzle about their
precise relation, and obtain some universal formulas. We show that the
partition function is invariant under the SL(2,Z) duality which exchanges
theories at strong coupling with those of weak coupling.Comment: 5 pages. v2: journal versio

### Great enhancement of strong-field ionization in femtosecond-laser subwavelength-structured fused silica

A wavelength-degenerate pump-probe spectroscopy is used to study the
ultrafast dynamics of strong-field ionization in femtosecond-laser
subwavelength-structured fused silica. The comparative spectra demonstrate that
femtosecond-laser subwavelength structuring always give rise to great
enhancement for strong-field ionization as well as third-order nonlinear
optical effects, which is the direct evidence of great local field enhancement
in subwavelength apertures of fs-laser highly-excited surface. In short, the
study shows the prominent subwavelength spatial effect of strong-field
ionization in femtosecond-laser ablation of dielectrics, which greatly
contributes to the well-known "incubation effect".Comment: 4 pages, 4 figure

### Gamow vectors and Borel summability

We analyze the detailed time dependence of the wave function $\psi(x,t)$ for
one dimensional Hamiltonians $H=-\partial_x^2+V(x)$ where $V$ (for example
modeling barriers or wells) and $\psi(x,0)$ are {\em compactly supported}. We
show that the dispersive part of $\psi(x,t)$, its asymptotic series in powers
of $t^{-1/2}$, is Borel summable. The remainder, the difference between $\psi$
and the Borel sum, is a convergent expansion of the form
$\sum_{k=0}^{\infty}g_k \Gamma_k(x)e^{-\gamma_k t}$, where $\Gamma_k$ are the
Gamow vectors of $H$, and $\gamma_k$ are the associated resonances;
generically, all $g_k$ are nonzero. For large $k$, $\gamma_{k}\sim const\cdot
k\log k +k^2\pi^{2}i/4$. The effect of the Gamow vectors is visible when time
is not very large, and the decomposition defines rigorously resonances and
Gamow vectors in a nonperturbative regime, in a physically relevant way. The
decomposition allows for calculating $\psi$ for moderate and large $t$, to any
prescribed exponential accuracy, using optimal truncation of power series plus
finitely many Gamow vectors contributions. The analytic structure of $\psi$ is
perhaps surprising: in general (even in simple examples such as square wells),
$\psi(x,t)$ turns out to be $C^\infty$ in $t$ but nowhere analytic on \RR^+.
In fact, $\psi$ is $t-$analytic in a sector in the lower half plane and has the
whole of \RR^+ a natural boundary

### Projected Euler method for stochastic delay differential equation under a global monotonicity condition

This paper investigates projected Euler-Maruyama method for stochastic delay
differential equations under a global monotonicity condition. This condition
admits some equations with highly nonlinear drift and diffusion coefficients.
We appropriately generalized the idea of C-stability and B-consistency given by
Beyn et al. [J. Sci. Comput. 67 (2016), no. 3, 955-987] to the case with delay.
Moreover, the method is proved to be convergent with order $\frac{1}{2}$ in a
succinct way. Finally, some numerical examples are included to illustrate the
obtained theoretical results

### #Cyberbullying in the Digital Age: Exploring People's Opinions with Text Mining

This study used text mining to investigate people's insights about
cyberbullying. English-language tweets were collected and analyzed by R
software. Our analysis demonstrated three major themes: (a) the major actions
that needed to be taken into consideration (e.g. guiding parents and teachers
to cyberbullying prevention, funding schools to fight cyberbullying), (b)
certain events that were important to people (e.g. the Michigan cyberbullying
law), and (c) people's major concerns in this regard (e.g. mental health issues
among students). Parents and teachers have an important role in educating,
informing, warning, preventing, and protecting against cyberbullying behaviors.
The frequency of negative sentiments was almost 2.45 times more than positive
sentiments

### On the Distribution of Plasmoids In High-Lundquist-Number Magnetic Reconnection

The distribution function $f(\psi)$ of magnetic flux $\psi$ in plasmoids
formed in high-Lundquist-number current sheets is studied by means of an
analytic phenomenological model and direct numerical simulations. The
distribution function is shown to follow a power law $f(\psi)\sim\psi^{-1}$,
which differs from other recent theoretical predictions. Physical explanations
are given for the discrepant predictions of other theoretical models.Comment: Accepted for publication in Phys. Rev. Let

### Andreev bound states in iron pnictide superconductors

Recently, Andreev bound states in iron pnictide have been proposed as an
experimental probe to detect the relative minus sign in the $s_\pm$-wave
pairing. While previous theoretical investigations demonstrated the feasibility
of the approach, the local density of states in the midgap regime is small,
making the detection hard in experiments. We revisit this important problem
from the Bogoliubov-de Gennes Hamiltonian on the square lattice with
appropriate boundary conditions. Significant spectral weights in the midgap
regime are spotted, leading to easy detection of the Andreev bound states in
experiments. Peaks in the momentum-resolved local density of states appear and
lead to enhanced quasiparticle interferences at specific momenta. We analyze
the locations of these magic spots and propose they can be verified in
experiments by the Fourier-transformed scanning tunneling spectroscopy.Comment: 5 pages, 3 figure

### Categorification of sign-skew-symmetric cluster algebras and some conjectures on g-vectors

Using the unfolding method given in \cite{HL}, we prove the conjectures on
sign-coherence and a recurrence formula respectively of ${\bf g}$-vectors for
acyclic sign-skew-symmetric cluster algebras. As a following consequence, the
conjecture is affirmed in the same case which states that the ${\bf g}$-vectors
of any cluster form a basis of $\mathbb Z^n$. Also, the additive
categorification of an acyclic sign-skew-symmetric cluster algebra $\mathcal
A(\Sigma)$ is given, which is realized as $(\mathcal C^{\widetilde Q},\Gamma)$
for a Frobenius $2$-Calabi-Yau category $\mathcal C^{\widetilde Q}$ constructed
from an unfolding $(Q,\Gamma)$ of the acyclic exchange matrix $B$ of $\mathcal
A(\Sigma)$.Comment: 12 page

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