3,765 research outputs found
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
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 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
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
Constrained Quantum Systems as an Adiabatic Problem
We derive the effective Hamiltonian for a quantum system constrained to a
submanifold (the constraint manifold) of configuration space (the ambient
space) in the asymptotic limit where the restoring forces tend to infinity. In
contrast to earlier works we consider at the same time the effects of
variations in the constraining potential and the effects of interior and
exterior geometry which appear at different energy scales and thus provide, for
the first time, a complete picture ranging over all interesting energy scales.
We show that the leading order contribution to the effective Hamiltonian is the
adiabatic potential given by an eigenvalue of the confining potential
well-known in the context of adiabatic quantum wave guides. At next to leading
order we see effects from the variation of the normal eigenfunctions in form of
a Berry connection. We apply our results to quantum wave guides and provide an
example for the occurrence of a topological phase due to the geometry of a
quantum wave circuit, i.e. a closed quantum wave guide.Comment: 19 pages, 4 figure
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
- …