Numerical simulation of lattice-regulated QCD has become an important source of information about strong interactions. In the last few years there has been an explosion of techniques for performing ...ever more accurate studies on the properties of strongly interacting particles. Lattice predictions directly impact many areas of particle and nuclear physics theory and phenomenology. This book provides a thorough introduction to the specialized techniques needed to carry out numerical simulations of QCD: a description of lattice discretizations of fermions and gauge fields, methods for actually doing a simulation, descriptions of common strategies to connect simulation results to predictions of physical quantities, and a discussion of uncertainties in lattice simulations. More importantly, while lattice QCD is a well-defined field in its own right, it has many connections to continuum field theory and elementary particle physics phenomenology, which are carefully elucidated in this book.
Hansen and Sharpe Phys. Rev. D 92, 114509 (2015) derived a relation between the scattering amplitude of three identical bosons, M3, and a real function referred to as the divergence-free K matrix and ...denoted Kdf,3. The result arose in the context of a relation between finite-volume energies and Kdf,3, derived to all orders in the perturbative expansion of a generic low-energy effective field theory. In this work we set aside the role of the finite volume and focus on the infinite-volume relation between Kdf,3 and M3. We show that, for any real choice of Kdf,3, M3 satisfies the three-particle unitarity constraint to all orders. Given that Kdf,3 is also free of a class of kinematic divergences, the function may provide a useful tool for parametrizing three-body scattering data. Applications include the phenomenological analysis of experimental data (where the connection to the finite volume is irrelevant) as well as calculations in lattice quantum chromodynamics (where the volume plays a key role).
Materials based on cubic tetrahedrites (Cu12Sb4S13) are useful thermoelectrics with unusual thermal and electrical transport properties, such as very low and nearly temperature-independent lattice ...thermal conductivity (κL). We explain the microscopic origin of the glasslike κL in Cu12Sb4S13 by explicitly treating anharmonicity up to quartic terms for both phonon energies and phonon scattering rates. We show that the strongly unstable phonon modes associated with trigonally coordinated Cu atoms are anharmonically stabilized above approximately 100 K and continue hardening with increasing temperature in accord with experimental data. This temperature-induced hardening effect reduces scattering of heat carrying acoustic modes by reducing the available phase space for three-phonon processes, thereby balancing the conventional ∝ T increase in scattering due to phonon population and yielding nearly temperature-independent κL. Furthermore, we find that very strong phonon broadening leads to a qualitative breakdown of the conventional phonon-gas model and modify the dominant heat transport mechanism from the particlelike phonon wave packet propagation to incoherent contributions described by the off-diagonal terms in the heat-flux operator, which are typically prevailing in glasses and disordered crystals. Our work paves the way to a deeper understanding of glasslike thermal conductivity in complex crystals with strong anharmonicity.
Ultraviolet photodetectors (UV PDs) with “5S” (high sensitivity, high signal‐to‐noise ratio, excellent spectrum selectivity, fast speed, and great stability) have been proposed as promising ...optoelectronics in recent years. To realize high‐performance UV PDs, heterojunctions are created to form a built‐in electrical field for suppressing recombination of photogenerated carriers and promoting collection efficiency. In this progress report, the fundamental components of heterojunctions including UV response semiconductors and other materials functionalized with unique effects are discussed. Then, strategies of building PDs with lattice‐matched heterojunctions, van der Waals heterostructures, and other heterojunctions are summarized. Finally, several applications based on heterojunction/heterostructure UV PDs are discussed, compromising flexible photodetectors, logic gates, and image sensors. This work draws an outline of diverse materials as well as basic assembly methods applied in heterojunction/heterostructure UV PDs, which will help to bring about new possibilities and call for more efforts to unleash the potential of heterojunctions.
Heterojunction UV photodetectors with high responsivity and fast speed are an essential part of optoelectronics. This article summarizes recently developed sensitive materials applied in heterojunction UV photodetectors and different integration methods including lattice matching and van der Waals integration, as well as other heterojunctions. Several representative applications are also reviewed to provide a comprehensive insight.
A
bstract
The nature of the QCD chiral phase transition in the limit of vanishing quark masses has remained elusive for a long time, since it cannot be simulated directly on the lattice and is ...strongly cutoff-dependent. We report on a comprehensive ongoing study using unimproved staggered fermions with
N
f
∈ 2, 8 mass-degenerate flavours on
N
τ
∈ {4
,
6
,
8} lattices, in which we locate the chiral critical surface separating regions with first-order transitions from crossover regions in the bare parameter space of the lattice theory. Employing the fact that it terminates in a tricritical line, this surface can be extrapolated to the chiral limit using tricritical scaling with known exponents. Knowing the order of the transitions in the lattice parameter space, conclusions for approaching the continuum chiral limit in the proper order can be drawn. While a narrow first-order region cannot be ruled out, we find initial evidence consistent with a second-order chiral transition in all massless theories with
N
f
≤ 6, and possibly up to the onset of the conformal window at 9 ≲
N
f
∗
≲ 12. A reanalysis of already published
O
(
a
)-improved
N
f
= 3 Wilson data on
N
τ
∈ 4
,
12 is also consistent with tricritical scaling, and the associated change from first to second-order on the way to the continuum chiral limit. We discuss a modified Columbia plot and a phase diagram for many-flavour QCD that reflect these possible features.
Three-dimensional lattices have applications across a range of fields including structural lightweighting, impact absorption and biomedicine. In this work, lattices based on triply periodic minimal ...surfaces were produced by polymer additive manufacturing and examined with a combination of experimental and computational methods. This investigation elucidates their deformation mechanisms and provides numerical parameters crucial in establishing relationships between their geometries and mechanical performance. Three types of lattice were examined, with one, known as the primitive lattice, being found to have a relative elastic modulus over twice as large as those of the other two. The deformation process of the primitive lattice was also considerably different from those of the other two, exhibiting strut stretching and buckling, while the gyroid and diamond lattices deformed in a bending dominated manner. Finite element predictions of the stress distributions in the lattices under compressive loading agreed with experimental observations. These results can be used to create better informed lattice designs for a range of mechanical and biomedical applications.
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•Manufactured and tested lattice structures based on triply periodic minimal surfaces.•Lattices with equivalent masses deform differently depending on their cell geometry.•High stiffness seen for the structure which showed buckling and low failure strain.•Determined Gibson-Ashby factors enabling the design of optimised latticed components.
The lattice strain has been increasing with increasing Ca concentration in the barium hexaferrite and the variation of coercive field and saturation magnetization with increasing Ca concentration due ...to lattice strain.
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•Increase of lattice strain due to Ca substitution in the barium hexaferrite.•The saturation magnetism increases with Ca concentration in the barium hexaferrite.•Increase in Ms and magnetocrystalline anisotropy up to 5% Ca in Ba1-xCaxFe12O19.•Correlation between lattice strain and magnetic parameters (Ms.K1,Hc).
The calcium (Ca2+) substituted M-type barium hexaferrite (Ba1-xCaxFe12O19) for Ca2+ (x = 0.00, 0.025, 0.050, 0.075, 0.100, 0.150, and 0.200) have been synthesized by the citrate sol-gel method. The X-ray diffraction (XRD) patterns with Rietveld refinement reveal the formation of hexagonal crystal structure with P63/mmc space group. The lattice parameters a = b and c decrease, whereas lattice strain found to increase with the increase in Ca concentration in the samples. The analysis of Raman spectra well supports the XRD patterns analysis. The average particle size is obtained from the FE-SEM (Field Emission Scanning Electron Microscopy) micrographs and these are similar to that of crystallite size obtained from the XRD pattern analysis. The saturation magnetization and magnetocrystalline anisotropy have been obtained by employing the “Law of Approach (LA) to Saturation magnetization” technique at room temperature. The saturation magnetization and magnetocrystalline anisotropy constant are maximum for 5% Ca substitution in barium hexaferrite. It could be due to lattice strain mediated magnetism. However, these magnetic properties decrease for more than the 5% Ca substitution in barium hexaferrite. It could be due to decrease of magnetic exchange interaction (Fe-O-Fe) in the sample. A correlation between magnetic interaction and lattice strain has been observed in Ca2+ substituted M-type barium hexaferrite.
Statistical modeling is a key component in the extraction of physical results from lattice field theory calculations. Although the general models used are often strongly motivated by physics, many ...model variations can frequently be considered for the same lattice data. Model averaging, which amounts to a probability-weighted average over all model variations, can incorporate systematic errors associated with model choice without being overly conservative. We discuss the framework of model averaging from the perspective of Bayesian statistics, and give useful formulas and approximations for the particular case of least-squares fitting, commonly used in modeling lattice results. In addition, we frame the common problem of data subset selection (e.g., choice of minimum and maximum time separation for fitting a two-point correlation function), as a model selection problem and study model averaging as a straightforward alternative to manual selection of fit ranges. Numerical examples involving both mock and real lattice data are given.
Group communication enables Internet of Things (IoT) devices to communicate in an efficient and fast manner. In most instances, a group message needs to be encrypted using a cryptographic key that ...only devices in the group know. In this paper, we address the problem of establishing such a key using a lattice-based one-way function, which can easily be inverted using a suitably designed lattice trapdoor. Using the notion of a bad/good basis, we present a new method of coupling multiple private keys into a single public key, which is then used for encrypting a group message. The protocol has the apparent advantage of having a conjectured resistance against potential quantum-computer-based attacks. All functions-key establishment, session key update, node addition, encryption, and decryption-are effected in constant time, using simple linear-algebra operations, making the protocol suitable for resource-constrained IoT networks. We show how a cryptographic session group key can be constructed on the fly by a user with legitimate credentials, making node-capture-type attacks impractical. The protocol also incorporates a mechanism for node addition and session-key generation in a forward- and backward-secrecy-preserving manner.
We extend the bijective correspondence between finite semimodular lattices and Faigle geometries to an analogous correspondence between semimodular lattices of finite lengths and a larger class of ...geometries. As the main application, we prove that if
e
is a join-irreducible element of a semimodular lattice
L
of finite length and
h
<
e
in
L
such that
e
does not cover
h
, then
e
can be “lowered” to a covering of
h
by taking a length-preserving semimodular extension
K
of
L
but not changing the rest of join-irreducible elements. With the help of our “lowering construction”, we prove a general theorem on length-preserving semimodular extensions of semimodular lattices. This theorem implies earlier results proved by Grätzer and Kiss (Order
2
351–365,
1986
), Wild (Discrete Math.
112
, 207–244,
1993
), and Czédli and Schmidt (Adv. Math.
225
, 2455–2463,
2010
) on extensions to geometric lattices, and an unpublished result of E. T. Schmidt. Our approach offers shorter proofs of these results than the original ones.
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