233 research outputs found
Towards A Theory Of Quantum Computability
We propose a definition of quantum computable functions as mappings between
superpositions of natural numbers to probability distributions of natural
numbers. Each function is obtained as a limit of an infinite computation of a
quantum Turing machine. The class of quantum computable functions is
recursively enumerable, thus opening the door to a quantum computability theory
which may follow some of the classical developments
Solid-State Effects on the Optical Excitation of Push-Pull Molecular J-Aggregates by First-Principles Simulations
J-aggregates are a class of low-dimensional molecular crystals which display
enhanced interaction with light. These systems show interesting optical
properties as an intense and narrow red-shifted absorption peak (J-band) with
respect to the spectrum of the corresponding monomer. The need to theoretically
investigate optical excitations in J-aggregates is twofold: a thorough
first-principles description is still missing and a renewed interest is rising
recently in understanding the nature of the J-band, in particular regarding the
collective mechanisms involved in its formation. In this work, we investigate
the electronic and optical properties of a J-aggregate molecular crystal made
of ordered arrangements of organic push-pull chromophores. By using a time
dependent density functional theory approach, we assess the role of the
molecular packing in the enhancement and red shift of the J-band along with the
effects of confinement in the optical absorption, when moving from bulk to
low-dimensional crystal structures. We simulate the optical absorption of
different configurations (i.e., monomer, dimers, a polymer chain, and a
monolayer sheet) extracted from the bulk crystal. By analyzing the induced
charge density associated with the J-band, we conclude that it is a
longitudinal excitation, delocalized along parallel linear chains and that its
overall red shift results from competing coupling mechanisms, some giving red
shift and others giving blue shift, which derive from both coupling between
transition densities and renormalization of the single-particle energy levels.Comment: This is the published version of the work, distributed under the
terms of the ACS AuthorChoice licence
https://pubs.acs.org/page/policy/authorchoice_termsofuse.htm
Quantum Turing Machines Computations and Measurements
Contrary to the classical case, the relation between quantum programming
languages and quantum Turing Machines (QTM) has not being fully investigated.
In particular, there are features of QTMs that have not been exploited, a
notable example being the intrinsic infinite nature of any quantum computation.
In this paper we propose a definition of QTM, which extends and unifies the
notions of Deutsch and Bernstein and Vazirani. In particular, we allow both
arbitrary quantum input, and meaningful superpositions of computations, where
some of them are "terminated" with an "output", while others are not. For some
infinite computations an "output" is obtained as a limit of finite portions of
the computation. We propose a natural and robust observation protocol for our
QTMs, that does not modify the probability of the possible outcomes of the
machines. Finally, we use QTMs to define a class of quantum computable
functions---any such function is a mapping from a general quantum state to a
probability distribution of natural numbers. We expect that our class of
functions, when restricted to classical input-output, will be not different
from the set of the recursive functions.Comment: arXiv admin note: substantial text overlap with arXiv:1504.02817 To
appear on MDPI Applied Sciences, 202
A General Theory of Sharing Graphs
Sharing graphs are the structures introduced by Lamping to implement optimal reductions of lambda calculus. Gonthier’s reformulation of Lamping’s technique inside Geometry of Interaction, and Asperti and Laneve’s work on Interaction Systems have shown that sharing graphs can be used to implement a wide class of calculi. Here, we give a general characterization of sharing graphs independent from the calculus to be implemented. Such a characterization rests on an algebraic semantics of sharing graphs exploiting the methods of Geometry of Interaction. By this semantics we can define an unfolding partial order between proper sharing graphs, whose minimal elements are unshared graphs. The least-shared-instance of a sharing graph is the unique unshared graph that the unfolding partial order associates to it. The algebraic semantics allows to prove that we can associate a semantical read-back to each unshared graph and that such a read-back can be computed via suitable read-back reductions. The result is then lifted to sharing graphs proving that any read-back (or unfolding) reduction of them can be simulated on their least-shared- instances. The sharing graphs defined in this way allow to implement in a distributed and local way any calculus with a global reduction rule in the style of the beta rule of lambda calculus. Also in this case the proof technique is to prove that sharing reductions can be simulated on least-shared-instances. The result is proved under the only assumption that the structures of the calculus have a box nesting property, that is, that two beta redexes may not partially overlap. As a result, we get a sharing graph machine that seems to be the most natural low-level computational model for functional languages. The paper concludes showing that optimality is a by-product of this technique: optimal reductions are lazy reductions of the sharing graph machine. We stress the proof strategy followed in the paper: it is based on an amazing interplay between standard rewriting system properties (strong normalization, confluence, and unique normal form) and algebraic properties definable via the techniques of Geometry of Interaction
Quantifying the Plasmonic Character of Optical Excitations in a Molecular J-Aggregate
The definition of plasmon at the microscopic scale is far from being
understood. Yet, it is very important to recognize plasmonic features in
optical excitations, as they can inspire new applications and trigger new
discoveries by analogy with the rich phenomenology of metal nanoparticle
plasmons. Recently, the concepts of plasmonicity index and the generalized
plasmonicity index (GPI) have been devised as computational tools to quantify
the plasmonic nature of optical excitations. The question may arise whether any
strong absorption band, possibly with some sort of collective character in its
microscopic origin, shares the status of plasmon. Here we demonstrate that this
is not always the case, by considering a well-known class of systems
represented by J-aggregates molecular crystals, characterized by the intense J
band of absorption. By means of first-principles simulations, based on a
many-body perturbation theory formalism, we investigate the optical properties
of a J-aggregate made of push-pull organic dyes. We show that the effect of
aggregation is to lower the GPI associated with the J-band with respect to the
isolated dye one, which corresponds to a nonplasmonic character of the
electronic excitations. In order to rationalize our finding, we then propose a
simplified one-dimensional theoretical model of the J-aggregate. A useful
microscopic picture of what discriminates a collective molecular crystal
excitation from a plasmon is eventually obtained.Comment: Published by ACS under ACS AuthorChoice licens
Is the Optimal Implementation Inefficient? Elementarily Not
Sharing graphs are a local and asynchronous implementation of lambda-calculus beta-reduction (or linear logic proof-net cut-elimination) that avoids useless duplications. Empirical benchmarks suggest that they are one of the most efficient machineries, when one wants to fully exploit the higher-order features of lambda-calculus. However, we still lack confirming grounds with theoretical solidity to dispel uncertainties about the adoption of sharing graphs.
Aiming at analysing in detail the worst-case overhead cost of sharing operators, we restrict to the case of elementary and light linear logic, two subsystems with bounded computational complexity of multiplicative exponential linear logic. In these two cases, the bookkeeping component is unnecessary, and sharing graphs are simplified to the so-called "abstract algorithm". By a modular cost comparison over a syntactical simulation, we prove that the overhead of shared reductions is quadratically bounded to cost of the naive implementation, i.e. proof-net reduction. This result generalises and strengthens a previous complexity result, and implies that the price of sharing is negligible, if compared to the obtainable benefits on reductions requiring a large amount of duplication
Interplay between Intra- and Intermolecular Charge Transfer in the Optical Excitations of J-Aggregates
In a first-principles study based on density functional theory and many-body
perturbation theory, we address the interplay between intra- and intermolecular
interactions in a J-aggregate formed by push-pull organic dyes by investigating
its electronic and optical properties. We find that the most intense excitation
dominating the spectral onset of the aggregate, i.e., the J-band, exhibits a
combination of intramolecular charge transfer, coming from the push-pull
character of the constituting dyes, and intermolecular charge transfer, due to
the dense molecular packing. We also show the presence of a pure intermolecular
charge-transfer excitation within the J-band, which is expected to play a
relevant role in the emission properties of the J-aggregate. Our results shed
light on the microscopic character of optical excitations of J-aggregates and
offer new perspectives to further understand the nature of collective
excitations in organic semiconductors.Comment: published under ACS Authorchoice licens
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