A Support Tool for Tagset Mapping

Many different tagsets are used in existing corpora; these tagsets vary according to the objectives of specific projects (which may be as far apart as robust parsing vs. spelling correction). In many situations, however, one would like to have uniform access to the linguistic information encoded in corpus annotations without having to know the classification schemes in detail. This paper describes a tool which maps unstructured morphosyntactic tags to a constraint-based, typed, configurable specification language, a ``standard tagset''. The mapping relies on a manually written set of mapping rules, which is automatically checked for consistency. In certain cases, unsharp mappings are unavoidable, and noise, i.e. groups of word forms {\sl not} conforming to the specification, will appear in the output of the mapping. The system automatically detects such noise and informs the user about it. The tool has been tested with rules for the UPenn tagset \cite{up} and the SUSANNE tagset \cite{garside}, in the framework of the EAGLES\footnote{LRE project EAGLES, cf. \cite{eagles}.} validation phase for standardised tagsets for European languages.Comment: EACL-Sigdat 95, contains 4 ps figures (minor graphic changes

Semiclassical approximations for adiabatic slow-fast systems

In this letter we give a systematic derivation and justification of the semiclassical model for the slow degrees of freedom in adiabatic slow-fast systems first found by Littlejohn and Flynn [5]. The classical Hamiltonian obtains a correction due to the variation of the adiabatic subspaces and the symplectic form is modified by the curvature of the Berry connection. We show that this classical system can be used to approximate quantum mechanical expectations and the time-evolution of operators also in sub-leading order in the combined adiabatic and semiclassical limit. In solid state physics the corresponding semiclassical description of Bloch electrons has led to substantial progress during the recent years, see [1]. Here, as an illustration, we show how to compute the Piezo-current arising from a slow deformation of a crystal in the presence of a constant magnetic field

Adiabatic Decoupling and Time-Dependent Born-Oppenheimer Theory

We reconsider the time-dependent Born-Oppenheimer theory with the goal to carefully separate between the adiabatic decoupling of a given group of energy bands from their orthogonal subspace and the semiclassics within the energy bands. Band crossings are allowed and our results are local in the sense that they hold up to the first time when a band crossing is encountered. The adiabatic decoupling leads to an effective Schroedinger equation for the nuclei, including contributions from the Berry connection.Comment: Revised version. 19 pages, 2 figure

Hamiltonians Without Ultraviolet Divergence for Quantum Field Theories

We propose a way of defining Hamiltonians for quantum field theories without any renormalization procedure. The resulting Hamiltonians, called IBC Hamiltonians, are mathematically well-defined (and in particular, ultraviolet finite) without an ultraviolet cut-off such as smearing out the particles over a nonzero radius; rather, the particles are assigned radius zero. These Hamiltonians agree with those obtained through renormalization whenever both are known to exist. We describe explicit examples of IBC Hamiltonians. Their definition, which is best expressed in the particle-position representation of the wave function, involves a kind of boundary condition on the wave function, which we call an interior-boundary condition (IBC). The relevant configuration space is one of a variable number of particles, and the relevant boundary consists of the configurations with two or more particles at the same location. The IBC relates the value (or derivative) of the wave function at a boundary point to the value of the wave function at an interior point (here, in a sector of configuration space corresponding to a lesser number of particles).Comment: 27 pages LaTeX, 1 figure. The old version v1 has been (revised and) split into two papers, the first of which is v2 of this post, and the second of which is available as arXiv:1808.06262. v3, v4, v5: minor improvements, updated references, corrected prefactor in Eq. (58

Adiabatic currents for interacting electrons on a lattice

We prove an adiabatic theorem for general densities of observables that are sums of local terms in finite systems of interacting fermions, without periodicity assumptions on the Hamiltonian and with error estimates that are uniform in the size of the system. Our result provides an adiabatic expansion to all orders, in particular, also for initial data that lie in eigenspaces of degenerate eigenvalues. Our proof is based on ideas from a recent work of Bachmann et al. who proved an adiabatic theorem for interacting spin systems. As one important application of this adiabatic theorem, we provide the first rigorous derivation of the so-called linear response formula for the current density induced by an adiabatic change of the Hamiltonian of a system of interacting fermions in a ground state, with error estimates uniform in the system size. We also discuss the application to quantum Hall systems.Comment: 46 pages; v1->v2: typos corrected, references added, Remark 4 after Thm 2 slightly reworded, v2->v3: major revision of the presentation of the result, 3 figures adde

Precise coupling terms in adiabatic quantum evolution

It is known that for multi-level time-dependent quantum systems one can construct superadiabatic representations in which the coupling between separated levels is exponentially small in the adiabatic limit. For a family of two-state systems with real-symmetric Hamiltonian we construct such a superadiabatic representation and explicitly determine the asymptotic behavior of the exponentially small coupling term. First order perturbation theory in the superadiabatic representation then allows us to describe the time-development of exponentially small adiabatic transitions. The latter result rigorously confirms the predictions of Sir Michael Berry for our family of Hamiltonians and slightly generalizes a recent mathematical result of George Hagedorn and Alain Joye.Comment: 24 page

Peierls substitution for magnetic Bloch bands

We consider the Schr\"odinger operator in two dimensions with a periodic potential and a strong constant magnetic field perturbed by slowly varying non-periodic scalar and vector potentials, $\phi(\epsilon x)$ and $A(\epsilon x)$, for $\epsilon\ll 1$. For each isolated family of magnetic Bloch bands we derive an effective Hamiltonian that is unitarily equivalent to the restriction of the Schr\"odinger operator to a corresponding almost invariant subspace. At leading order, our effective Hamiltonian can be interpreted as the Peierls substitution Hamiltonian widely used in physics for non-magnetic Bloch bands. However, while for non-magnetic Bloch bands the corresponding result is well understood, for magnetic Bloch bands it is not clear how to even define a Peierls substitution Hamiltonian beyond a formal expression. The source of the difficulty is a topological obstruction: magnetic Bloch bundles are generically not trivializable. As a consequence, Peierls substitution Hamiltonians for magnetic Bloch bands turn out to be pseudodifferential operators acting on sections of non-trivial vector bundles over a two-torus, the reduced Brillouin zone. Part of our contribution is the construction of a suitable Weyl calculus for such pseudos. As an application of our results we construct a new family of canonical one-band Hamiltonians $H^B_{\theta,q}$ for magnetic Bloch bands with Chern number $\theta\in \mathbb{Z}$ that generalizes the Hofstadter model $H^B_{\rm Hof} = H^B_{0,1}$ for a single non-magnetic Bloch band. It turns out that $H^B_{\theta,q}$ is isospectral to $H^{q^2B}_{\rm Hof}$ for any $\theta$ and all spectra agree with the Hofstadter spectrum depicted in his famous black and white butterfly. However, the resulting Chern numbers of subbands, corresponding to Hall conductivities, depend on $\theta$ and $q$, and thus the models lead to different colored butterflies.Comment: 39 pages, 4 figures. Final version to appear in Analysis & PD

Non-equilibrium almost-stationary states and linear response for gapped quantum systems

We prove the validity of linear response theory at zero temperature for perturbations of gapped Hamiltonians describing interacting fermions on a lattice. As an essential innovation, our result requires the spectral gap assumption only for the unperturbed Hamiltonian and applies to a large class of perturbations that close the spectral gap. Moreover, we prove formulas also for higher order response coefficients. Our justification of linear response theory is based on a novel extension of the adiabatic theorem to situations where a time-dependent perturbation closes the gap. According to the standard version of the adiabatic theorem, when the perturbation is switched on adiabatically and as long as the gap does not close, the initial ground state evolves into the ground state of the perturbed operator. The new adiabatic theorem states that for perturbations that are either slowly varying potentials or small quasi-local operators, once the perturbation closes the gap, the adiabatic evolution follows non-equilibrium almost-stationary states (NEASS) that we construct explicitly.Comment: v1->v2 section 4 on linear response added, presentation partly reworked. v2->v3 slightly stronger statements for "fast" switching. Final version as to appear in CM