1,232 research outputs found
Effective non-adiabatic Hamiltonians for the quantum nuclear motion over coupled electronic states
The quantum mechanical motion of the atomic nuclei is considered over a
single- or a multi-dimensional subspace of electronic states which is separated
by a gap from the rest of the electronic spectrum over the relevant range of
nuclear configurations. The electron-nucleus Hamiltonian is block-diagonalized
up to through a unitary transformation of the
electronic subspace and the corresponding th-order effective Hamiltonian is
derived for the quantum nuclear motion. Explicit but general formulae are given
for the second- and the third-order corrections. As a special case, the
second-order Hamiltonian corresponding to an isolated electronic state is
recovered which contains the coordinate-dependent mass-correction terms in the
nuclear kinetic energy operator. For a multi-dimensional, explicitly coupled
electronic band, the second-order Hamiltonian contains the usual BO terms and
non-adiabatic corrections but generalized mass-correction terms appear as well.
These, earlier neglected terms, perturbatively account for the outlying
(discrete and continuous) electronic states not included in the explicitly
coupled electronic subspace
A New Approach to Transport Coefficients in the Quantum Spin Hall Effect
We investigate some foundational issues in the quantum theory of spin transport, in the general case when the unperturbed Hamiltonian operator H does not commute with the spin operator in view of Rashba interactions, as in the typical models for the quantum spin Hall effect. A gapped periodic one-particle Hamiltonian H is perturbed by adding a constant electric field of intensity ε≪ 1 in the j-th direction, and the linear response in terms of a S-current in the i-th direction is computed, where S is a generalized spin operator. We derive a general formula for the spin conductivity that covers both the choice of the conventional and of the proper spin current operator. We investigate the independence of the spin conductivity from the choice of the fundamental cell (unit cell consistency), and we isolate a subclass of discrete periodic models where the conventional and the proper S-conductivity agree, thus showing that the controversy about the choice of the spin current operator is immaterial as far as models in this class are concerned. As a consequence of the general theory, we obtain that whenever the spin is (almost) conserved, the spin conductivity is (approximately) equal to the spin-Chern number. The method relies on the characterization of a non-equilibrium almost-stationary state (NEASS), which well approximates the physical state of the system (in the sense of space-adiabatic perturbation theory) and allows moreover to compute the response of the adiabatic S-current as the trace per unit volume of the S-current operator times the NEASS. This technique can be applied in a general framework, which includes both discrete and continuum models
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Annotating argumentative structure in English-as-a-Foreign-Language learner essays
AbstractArgument mining (AM) aims to explain how individual argumentative discourse units (e.g. sentences or clauses) relate to each other and what roles they play in the overall argumentation. The automatic recognition of argumentative structure is attractive as it benefits various downstream tasks, such as text assessment, text generation, text improvement, and summarization. Existing studies focused on analyzing well-written texts provided by proficient authors. However, most English speakers in the world are non-native, and their texts are often poorly structured, particularly if they are still in the learning phase. Yet, there is no specific prior study on argumentative structure in non-native texts. In this article, we present the first corpus containing argumentative structure annotation for English-as-a-foreign-language (EFL) essays, together with a specially designed annotation scheme. The annotated corpus resulting from this work is called “ICNALE-AS” and contains 434 essays written by EFL learners from various Asian countries. The corpus presented here is particularly useful for the education domain. On the basis of the analysis of argumentation-related problems in EFL essays, educators can formulate ways to improve them so that they more closely resemble native-level productions. Our argument annotation scheme is demonstrably stable, achieving good inter-annotator agreement and near-perfect intra-annotator agreement. We also propose a set of novel document-level agreement metrics that are able to quantify structural agreement from various argumentation aspects, thus providing a more holistic analysis of the quality of the argumentative structure annotation. The metrics are evaluated in a crowd-sourced meta-evaluation experiment, achieving moderate to good correlation with human judgments.</jats:p
Variable typing: Assigning meaning to variables in mathematical text
Information about the meaning of mathematical variables in text is useful in NLP/IR tasks such as symbol disambiguation, topic modeling and mathematical information retrieval (MIR). We introduce variable typing, the task of assigning one mathematical type (multi-word technical terms referring to mathematical concepts) to each variable in a sentence of mathematical text. As part of this work, we also introduce a new annotated data set composed of 33,524 data points extracted from scientific documents published on arXiv. Our intrinsic evaluation demonstrates that our data set is sufficient to successfully train and evaluate current classifiers from three different model architectures. The best performing model is evaluated on an extrinsic task: MIR, by producing a typed formula index. Our results show that the best performing MIR models make use of our typed index, compared to a formula index only containing raw symbols, thereby demonstrating the usefulness of variable typing
High Fidelity Adiabatic Quantum Computation via Dynamical Decoupling
We introduce high-order dynamical decoupling strategies for open system
adiabatic quantum computation. Our numerical results demonstrate that a
judicious choice of high-order dynamical decoupling method, in conjunction with
an encoding which allows computation to proceed alongside decoupling, can
dramatically enhance the fidelity of adiabatic quantum computation in spite of
decoherence.Comment: 5 pages, 4 figure
A microscopic derivation of the quantum mechanical formal scattering cross section
We prove that the empirical distribution of crossings of a "detector''
surface by scattered particles converges in appropriate limits to the
scattering cross section computed by stationary scattering theory. Our result,
which is based on Bohmian mechanics and the flux-across-surfaces theorem, is
the first derivation of the cross section starting from first microscopic
principles.Comment: 28 pages, v2: Typos corrected, layout improved, v3: Typos corrected.
Accepted for publication in Comm. Math. Phy
Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality
We present a local-hidden-variable model for positive-operator-valued
measurements (an LHVPOV model) on a class of entangled generalized Werner
states, thus demonstrating that such measurements do not always violate a
Bell-type inequality. We also show that, in general, if the state can
be obtained from with certainty by local quantum operations without
classical communication then an LHVPOV model for the state implies the
existence of such a model for .Comment: 4 pages, no figures. Title changed to accord with Phys. Rev. A
version. Journal reference adde
Effective dynamics for particles coupled to a quantized scalar field
We consider a system of N non-relativistic spinless quantum particles
(``electrons'') interacting with a quantized scalar Bose field (whose
excitations we call ``photons''). We examine the case when the velocity v of
the electrons is small with respect to the one of the photons, denoted by c
(v/c= epsilon << 1). We show that dressed particle states exist (particles
surrounded by ``virtual photons''), which, up to terms of order (v/c)^3, follow
Hamiltonian dynamics. The effective N-particle Hamiltonian contains the kinetic
energies of the particles and Coulomb-like pair potentials at order (v/c)^0 and
the velocity dependent Darwin interaction and a mass renormalization at order
(v/c)^{2}. Beyond that order the effective dynamics are expected to be
dissipative.
The main mathematical tool we use is adiabatic perturbation theory. However,
in the present case there is no eigenvalue which is separated by a gap from the
rest of the spectrum, but its role is taken by the bottom of the absolutely
continuous spectrum, which is not an eigenvalue.
Nevertheless we construct approximate dressed electrons subspaces, which are
adiabatically invariant for the dynamics up to order (v/c)\sqrt{\ln
(v/c)^{-1}}. We also give an explicit expression for the non adiabatic
transitions corresponding to emission of free photons. For the radiated energy
we obtain the quantum analogue of the Larmor formula of classical
electrodynamics.Comment: 67 pages, 2 figures, version accepted for publication in
Communications in Mathematical Physic
Sideband Cooling Micromechanical Motion to the Quantum Ground State
The advent of laser cooling techniques revolutionized the study of many
atomic-scale systems. This has fueled progress towards quantum computers by
preparing trapped ions in their motional ground state, and generating new
states of matter by achieving Bose-Einstein condensation of atomic vapors.
Analogous cooling techniques provide a general and flexible method for
preparing macroscopic objects in their motional ground state, bringing the
powerful technology of micromechanics into the quantum regime. Cavity opto- or
electro-mechanical systems achieve sideband cooling through the strong
interaction between light and motion. However, entering the quantum regime,
less than a single quantum of motion, has been elusive because sideband cooling
has not sufficiently overwhelmed the coupling of mechanical systems to their
hot environments. Here, we demonstrate sideband cooling of the motion of a
micromechanical oscillator to the quantum ground state. Entering the quantum
regime requires a large electromechanical interaction, which is achieved by
embedding a micromechanical membrane into a superconducting microwave resonant
circuit. In order to verify the cooling of the membrane motion into the quantum
regime, we perform a near quantum-limited measurement of the microwave field,
resolving this motion a factor of 5.1 from the Heisenberg limit. Furthermore,
our device exhibits strong-coupling allowing coherent exchange of microwave
photons and mechanical phonons. Simultaneously achieving strong coupling,
ground state preparation and efficient measurement sets the stage for rapid
advances in the control and detection of non-classical states of motion,
possibly even testing quantum theory itself in the unexplored region of larger
size and mass.Comment: 13 pages, 7 figure
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