9,616 research outputs found
On Chow Stability for algebraic curves
In the last decades there have been introduced different concepts of
stability for projective varieties. In this paper we give a natural and
intrinsic criterion of the Chow, and Hilbert, stability for complex irreducible
smooth projective curves .
Namely, if the restriction of the tangent bundle of
to is stable then is Chow stable,
and hence Hilbert stable. We apply this criterion to describe a smooth open set
of the irreducible component of the Hilbert scheme of
containing the generic smooth Chow-stable curve of genus
and degree Moreover, we
describe the quotient stack of such curves. Similar results are obtained for
the locus of Hilbert stable curves.Comment: Minor corrections and improvements to presentation. We add Theorem
4.
Total correlations as fully additive entanglement monotones
We generalize the strategy presented in Refs. [1, 2], and propose general
conditions for a measure of total correlations to be an entanglement monotone
using its pure (and mixed) convex-roof extension. In so doing, we derive
crucial theorems and propose a concrete candidate for a total correlations
measure which is a fully additive entanglement monotone.Comment: 8 pages, 3 figures. Title changed, new result
Quantum work and the thermodynamic cost of quantum measurements
Quantum work is usually determined from two projective measurements of the
energy at the beginning and at the end of a thermodynamic process. However,
this paradigm cannot be considered thermodynamically consistent as it does not
account for the thermodynamic cost of these measurements. To remedy this
conceptual inconsistency we introduce a novel paradigm that relies only on the
expected change of the average energy given the initial energy eigenbasis. In
particular, we completely omit quantum measurements in the definition of
quantum work, and hence quantum work is identified as a thermodynamic quantity
of only the system. As main results we derive a modified quantum Jarzynski
equality and a sharpened maximum work theorem in terms of the information free
energy. Comparison of our results with the standard approach allows to quantify
the informational cost of projective measurements.Comment: 5 pages, 2 figure; published versio
Gaussian Decoherence and Gaussian Echo from Spin Environments
We examine an exactly solvable model of decoherence -- a spin-system
interacting with a collection of environment spins. We show that in this simple
model (introduced some time ago to illustrate environment--induced
superselection) generic assumptions about the coupling strengths lead to a
universal (Gaussian) suppression of coherence between pointer states. We
explore the regime of validity of this result and discuss its relation to
spectral features of the environment. We also consider its relevance to the
experiments on the so-called Loschmidt echo (which measures, in effect, the
fidelity between the initial and time-reversed or "echo" signal). In
particular, we show that for partial reversals (e.g., when of only a part of
the total Hamiltonian changes sign) fidelity will exhibit a Gaussian dependence
on the time of reversal. In such cases echo may become independent of the
details of the reversal procedure or the specifics of the coupling to the
environment. This puzzling behavior was observed in several NMR experiments.
Natural candidates for such two environments (one of which is easily reversed,
while the other is ``irreversible'') are suggested for the experiment involving
ferrocene.Comment: Improved text and figures, to appear in the special issue of Acta
Physica Polonica B celebrating the 100th anniversary of Smoluchowski's
equation and his paper explaining Brownian motion (in
http://th-www.if.uj.edu.pl/acta/vol38/pdf/v38p1685.pdf
Decoherence and the Loschmidt echo
Environment--induced decoherence causes entropy increase. It can be
quantified using, e.g., the purity . When the
Hamiltonian of a quantum system is perturbed, its sensitivity to such
perturbation can be measured by the Loschmidt echo . It is given by
the average squared overlap between the perturbed and unperturbed state. We
describe the relation between the temporal behavior of and . In this way we show that the decay of the Loschmidt echo can be analyzed
using tools developed in the study of decoherence. In particular, for systems
with a classically chaotic Hamiltonian the decay of and
has a regime where it is dominated by the classical Lyapunov exponent
Quantum finite automata and linear context-free languages: a decidable problem
We consider the so-called measure once finite quantum automata model introduced by Moore and Crutchfield in 2000. We show that given a language recognized by such a device and a linear context-free language, it is recursively decidable whether or not they have a nonempty intersection. This extends a result of Blondel et al. which can be interpreted as solving the problem with the free monoid in place of the family of linear context-free languages. © 2013 Springer-Verlag
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