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The optoelectronic characteristics of AlGaN-based deep ultraviolet light-emitting diodes (DUV LEDs) with quaternary last quantum barrier (QLQB) and step-graded electron blocking layer (EBL) are investigated numerically. The results show that the internal quantum efficiency (IQE) and radiative recombination rate are remarkably improved with AlInGaN step-graded EBL and QLQB as compared to conventional or ternary AlGaN EBL and last quantum barrier (LQB). This significant improvement is assigned to the optimal recombination of electron–hole pairs in the multiple quantum wells (MQWs). It is due to the decrease in strain and lattice mismatch between the epi-layers which alleviates the effective potential barrier height of the conduction band and suppressed the electron leakage without affecting the holes transportation to the active region. Moreover, to figure out quantitatively, the electron and hole quantity increased by ~ 25% and ~ 15%, respectively. Additionally, the IQE and radiative recombination rate are enhanced by 48% and 55%, respectively, as compared to conventional LED. So, we believe that our proposed structure is not only a feasible approach for achieving highly efficient DUV LEDs, but the device physics presented in this study establishes a fruitful understanding of III nitride-based optoelectronic devices.

We study quantum corrections to hypersurfaces of dimension d + 1 > 2 embedded in generic higher-dimensional spacetimes. Manifest covariance is maintained throughout the analysis and our methods are valid for arbitrary co-dimension and arbitrary bulk metric. A variety of theories which are prominent in the modern amplitude literature arise as special limits: the scalar sector of Dirac-Born-Infeld theories and their multi-field variants, as well as generic non-linear sigma models and extensions thereof. Our explicit one-loop results unite the leading corrections of all such models under a single umbrella. In contrast to naive computations which generate effective actions that appear to violate the non-linear symmetries of their classical counterparts, our efficient methods maintain manifest covariance at all stages and make the symmetry properties of the quantum action clear. We provide an explicit comparison between our compact construction and other approaches and demonstrate the ultimate physical equivalence between the superficially different results., Journal of High Energy Physics, 2021 (1), ISSN:1126-6708, ISSN:1029-8479

In this final chapter, we continue investigating the theory of deformed scalar field uncovering its simplest quantum aspects.

Despite the scientific and engineering challenges facing the development of quantum computers, considerable progress is being made toward applying the technology to commercial applications. In this article, we discuss the solutions that some companies are already building using quantum hardware. Framing these as examples of combinatorics problems, we illustrate their application in four industry verticals: cybersecurity, materials and pharmaceuticals, banking and finance, and advanced manufacturing. While quantum computers are not yet available at the scale needed to solve all of these combinatorics problems, we identify three types of near-term opportunities resulting from advances in quantum computing: quantum-safe encryption, material and drug discovery, and quantum-inspired algorithms.

The mechanism of SSB does not only provide a general strategy for unifying the description of apparently different systems, but it also provides information on the energy spectrum of an infinite dimensional system, by means of the so-called Goldstone theorem,40 according to which to each broken generator T of a continuous symmetry there corresponds a massless mode, i.e. a free wave. The quantum version of such a statement has been turned into a theorem,41 whereas, as far as we know, no analogous theorem has been proved for classical (infinite dimensional) systems and the standard accounts seem to rely on heuristic arguments.

In this work, we introduce the first practical post-quantum verifiable random function (VRF) that relies on well-known (module) lattice problems, namely Module-SIS and Module-LWE. Our construction, named LB-VRF, results in a VRF value of only 84 bytes and a proof of around only 5 KB (in comparison to several MBs in earlier works), and runs in about 3 ms for evaluation and about 1 ms for verification.

From the discussion of the previous Chapter, it appears that the description of infinite systems looks much more difficult than in the finite dimensional case, above all because of the existence of (too) many possible representations of the algebra of canonical variables. A big step in the direction of controlling the problem has been taken by Haag et al., who emphasized the need of exploiting crucial physical properties of the algebra of observables in order to restrict their possible representations to the physically relevant ones. The crucial ingredient is the localization property of observable operations.

We study conditions under which the lattice \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathrm{\mathbf {Id}}}}\mathbf R$$\end{document}IdR of ideals of a given a commutative semiring \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {R}}$$\end{document}R is complemented. At first we check when the annihilator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I^*$$\end{document}I∗ of a given ideal I of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {R}}$$\end{document}R is a complement of I. Further, we study complements of annihilator ideals. Next we investigate so-called Łukasiewicz semirings. These form a counterpart to MV-algebras which are used in quantum structures as they form an algebraic semantic of many-valued logics as well as of the logic of quantum mechanics. We describe ideals and congruence kernels of these semirings with involution. Finally, using finite unitary Boolean rings, a construction of commutative semirings with complemented lattice of ideals is presented.

In this paper we study various forms of RG, applying them to the BFSS model of $N$ coincident D0-branes. Firstly, as a warm-up, we perform standard Wilsonian RG, investigating the conditions under which supersymmetry is preserved along the flow. Next, we develop a local RG scheme such that the cutoff is spacetime dependent, which could have further applications to studying QFT in curved spacetime. Finally, we test the conjecture put forward in arXiv:1305.3908 that the method of quantum RG could be the mechanism responsible for the gauge/gravity duality by applying it to the BFSS model, which has a known gravitational dual. Although not entirely conclusive some questions are raised about the applicability of quantum RG as a description of the AdS/CFT correspondence., Comment: 34 pages, 1 figure, minor corrections, version to appear in JHEP

We revisit the question of frame equivalence in Quantum Field Theory in the presence of gravity, a situation of relevance for theories aiming to describe the early Universe dynamics and Inflation in particular. We show that in those cases, the path integral measure must be carefully defined and that the requirement of diffeomorphism invariance forces it to depend non-trivially on the fields. As a consequence, the measure will transform also non-trivially between different frames and it will induce a new finite contribution to the Quantum Effective Action that we name frame discriminant. This new contribution must be taken into account in order to asses the dynamics and physical consequences of a given theory. We apply our result to scalar-tensor theories described in the Einstein and Jordan frame, where we find that the frame discriminant can be thought as inducing a scale-invariant regularization scheme in the Jordan frame., 33 pages, minor corrections

The role of non-trivial quantum mechanical effects in biology has been the subject of intense scrutiny over the past decade. Much of the focus on potential “quantum biology” has been on energy transfer processes in photosynthetic light harvesting systems. Ultrafast laser spectroscopy of several light harvesting proteins has uncovered coherent oscillations dubbed “quantum beats” that persist for hundreds of femtoseconds and are putative signatures for quantum transport phenomena. This review describes the language and basic quantum mechanical phenomena that underpin quantum transport in open systems such as light harvesting and photosynthetic proteins, including the photosystem reaction centre. Coherent effects are discussed in detail, separating various meanings of the term, from delocalized excitations, or excitons, to entangled states and coherent transport. In particular, we focus on the time, energy and length scales of energy transport processes, as these are critical in understanding whether or not coherent processes are important. The role played by the protein in maintaining chromophore systems is analysed. Finally, the spectroscopic techniques that are used to probe energy transfer dynamics and that have uncovered the quantum beats are described with reference to coherent phenomena in light harvesting.

The chapter introduces the main principles and several algorithms of both evolutionary computation (EC) and its further development as quantum inspired evolutionary computation (QiEC).

We study the extent of quantum gravitational effects in the internal region of non-singular, Hayward-like solutions of Einstein's field equations according to the formalism known as Horizon Quantum Mechanics. We grant a microscopic description to the horizon by considering a huge number of soft, off-shell gravitons, which superimpose in the same quantum state, as suggested by Dvali and Gomez. In addition to that, the constituents of such a configuration are understood as loosely confined in a binding harmonic potential. A simple analysis shows that the resolution of a central singularity through quantum physics does not tarnish the classical description, which is bestowed upon this extended self-gravitating system by General Relativity. Finally, we estimate the appearance of an internal horizon as being negligible, because of the suppression of the related probability caused by the large number of virtual gravitons., Comment: 17 pages, no figures

The phenomenological models and the quantum theoretical methods which are currently used to calculate the dispersion curves of surface phonons are reviewed for the various classes of solids.

In this chapter we present some methods that are employed in performing electronic structure calculations. We start by presenting a general quantum mechanical framework to describe a molecule or a solid. We then introduce the Born–Oppenheimer approximation (also called the adiabatic approximation), which allows us to reduce the problem to its corresponding electronic part.

Perhaps the first thing to understand about quantum mechanics is that it has as much to do with mechanics as with, say, electrodynamics, optics, condensed-matter, or high-energy physics. Rather than describing a particular class of physical phenomena, quantum mechanics provides a universal theoretical framework that can be used in all fields of physics — akin to a computer’s operating system that provides a foundation upon which other applications can run. The term “quantum mechanics” emerged historically, because the first successful applications of the quantum framework were in studies of the mechanical motion of electrons in an atom. A better term would be “quantum physics” or “quantum theory”.

Despite recent major developments in algorithms and computer hardware, the simulation of large systems of particles by ab initio methods is still limited to about a few hundred particles. For treating larger systems by molecular dynamics, one can use either tight-binding (TB) or classical molecular-dynamics methods. The TB method has the advantage of being quantum mechanical; therefore one has, in addition to its higher accuracy, information about the electronic structure of the system. In the field of quantum chemistry, other semi-empirical methods, such as MNDO (modified neglect of differential overlap), also exist. These are, in their nature, very similar to Hartree—Fock methods, but the computations of the Hamiltonian and overlap matrix elements are based on semi-empirical formulae.

Transport phenomena in low dimensional systems such as in quantum wells (2D), quantum wires (1D), and quantum dots (0D) are dominated by quantum effects not included in the classical treatments based on the Boltzmann equation and discussed in Chaps. 7– 10.

pH is a critical parameter for biological and technological systems directly related with electrical charges. It can give rise to peculiar electrostatic phenomena, which also makes them more challenging. Due to the quantum nature of the process, involving the forming and breaking of chemical bonds, quantum methods should ideally by employed. Nevertheless, due to the very large number of ionizable sites, different macromolecular conformations, salt conditions, and all other charged species, the CPU time cost simply becomes prohibitive for computer simulations, making this a quite complex problem. Simplified methods based on Monte Carlo sampling have been devised and will be reviewed here, highlighting the updated state-of-the-art of this field, advantages, and limitations of different theoretical protocols for biomolecular systems (proteins and nucleic acids). Following a historical perspective, the discussion will be associated with the applications to protein interactions with other proteins, polyelectrolytes, and nanoparticles.

The models of quantum gases were already developed in the 1920s: the Fermi gas model for degenerate Fermi systems and the model of Bose condensates for degenerate bosonic systems.

We propose an epistemic strategy logic with future and past time operators, called \(\text {SLKP}\), for Strategy Logic with Knowledge of the Past. With \(\text {SLKP}\) we can model mutually observed moves/actions in strategic contexts. In a semantic game, agents may completely or partially observe other agents’ moves, their moves may depend on their knowledge of other players’ strategies, and their knowledge may depend on the history of their own or other’s moves. The logic \(\text {SLKP}\) also allows us to describe temporal properties involving past, future, and composed tenses such as future perfect or counterfactual assertions. We illustrate SLKP by formalising the quantum cryptography protocol BB84, with the purpose to initiate an integrated epistemic and strategic treatment of agent interactions in quantum systems.

Casimir has shown that quantum fluctuations of the electromagnetic field produce an attractive force between macroscopic bodies. It has recently been shown that two non-contacting bodies moving relative to each other experience a friction due to the same quantum fluctuations of the electromagnetic field. However, until recent time there was no experimental evidence for or against this effect, because the predicted friction forces are very small, and precise measurements of quantum forces are incredibly difficult with present technology. The existence of quantum friction is still debated even among theoreticians. However, the situation drastically changed with the discovery of a new material—graphene. We recently proposed that quantum friction can be detected in frictional drag experiments between graphene sheets, and in the transport properties of nonsuspended graphene on an SiO\(_2\) substrate in a high electric field.

On the atomistic and microscopic scale, the possible conformations (the spatial arrangements) of particles – besides their energy – begins to play a fundamental role. This is why after an introduction in Sect. 6.1 we discuss statistical physics and thermodynamics in Sect. 6.2. Classical interaction potentials (that may or may not be derived from quantum mechanical ab initio methods) are treated in Sect. 6.3, which brings us to the important MD method, the nuts and bolts of which are discussed in detail in Sect. 6.4. Here, we provide many tricks of the trade of this method. A discussion of liquids, soft matter and polymers in Sect. 6.5 is then followed by a short discussion of the Monte Carlo method in Sect. 6.6. A couple of problems are provided at the end of this chapter.

The meso- and macroscopic scales, due to their complexity and the difficulties to prepare systems in reproducible initial conditions is usually treated with phenomenological approaches from engineering. Yet, more and more scientists increasingly deal with model building and simulation on these scales due to the progress in computing power during the past 10 years, which for example allow routinely simulating multi-billion atom systems of the size of microns. In this chapter, we begin our discussion with a short introduction before we look at concrete examples for modeling and simulation on these scales in Sects. 6.2 and 7.2. In Sect. 7.3 we introduce the important dissipate particle dynamics method and in Sect.Ginzburg we discuss Ginzburg–Landau type modeling approaches. In Sect. 7.5 we introduce a scale-bridging example from the field of shock wave physics that shows how to perform computer simulations coupling the mesoscale with the macroscale. Section 7.6 provides further examples for scale bridging applications between MD and FEM and in Sects. 7.7–7.9 we discuss the continuum theory and elasticity theory which form the underlying mathematical basis for many computational approaches on the macroscale. In engineering, the world is usually treated as if it was a continuum, completely neglecting the discrete quantum mechanical structure and in these sections we will see by using the linear chain model of a solid state, how the transition from a description based on discrete particles to a continuum description can be done. This chapter ends with another application example from the area of crack propagation.

In quantum mechanics, the state reduction due to a measurement is called the collapse of a wavefunction. Its study is often perceived as a somewhat mystical phenomenon because of the lack of proper understanding. As a result, the formalism for the state reduction is often somewhat inadequately presented. However, as will be explained in Sect. 7.1, the state reduction due to a measurement follows automatically from the formulation of quantum mechanics, as described in Sect. 1.2. Starting with the formulation of quantum mechanics given in Sects. 1.2 and 1.4, we give a detailed formulation of the state reduction due to a measurement. In Sect. 7.2, we discuss the relation with the uncertainty relation using these concepts. Finally, in Sect. 7.4, we propose a measurement with negligible state reduction.

The problems of transmitting a classical message via a quantum channel (Chap. 4) and estimating a quantum state (Chaps. 3 and 6) have a classical analog. These are not intrinsically quantum-specific problems but quantum extensions of classical problems. The difficulties of these quantum extensions are mainly caused by the non-commutativity of quantum mechanics. However, quantum information processing is not merely a non-commuting version of classical information processing. There exist many quantum protocols without any classical analog. In this context, quantum information theory covers a greater field than a noncommutative analog of classical information theory. The key to these additional effects is the advantage of using entanglement treated in Chap. 8, where we examined mainly the quantification of entanglement. In this chapter, we will introduce several quantum communication protocols that are possible only by using entanglement and are therefore classically impossible. (Some of protocols introduced in this section have classical analogs.) We also examine the transmission of quantum states (quantum error correction), communication in the presence of eavesdroppers, and several other types of communication that we could not handle in Chap. 4. As seen in this chapter, the transmission of a quantum state is closely related to communication with no information leakage to eavesdroppers. The noise in the transmission of a quantum state clearly corresponds to the eavesdropper in a quantum communication.

Quantum mechanics violates daily intuition not only because the measured outcome can only be predicted probabilistically but also because of a quantum-specific correlation called entanglement. It is believed that this type of correlation does not exist in macroscopic objects. Entanglement can be used to produce nonlocal phenomena. States possessing such correlations are called entangled states (or states that possess entanglement). A state on a bipartite system is called called a maximally entangled state or an EPR state when it has the highest degree of entanglement among these states. Historically, the idea of a nonlocal effect due to entanglement was pointed out by Einstein, Podolsky, and Rosen; hence, the name EPR state. In order to transport a quantum state over a long distance, we have to retain its coherence during its transmission. However, it is often very difficult because the transmitted system can be easily correlated with the environment system. If the sender and receiver share an entangled state, the sender can transport his/her quantum state to the receiver without transmitting it, as explained in Chap. 9. This protocol is called quantum teleportation and clearly explains the effect of entanglement in quantum systems. Many other effects of entanglement have also been examined, some of which are given in Chap. 9. However, it is difficult to take advantage of entanglement if the shared state is insufficiently entangled. Therefore, we investigate how much of a maximally entangled state can be extracted from a state with a partially entangled state. Of course, if we allow quantum operations between two systems, we can always produce maximally entangled states. Therefore, we examine cases where locality conditions are imposed to our possible operations.

Until now, we have considered only quantum states and quantum measurement as quantum concepts. In order to prefer information processing with quantum systems, we should manipulate a wider class of state operations. This chapter examines what kinds of operations are allowed on quantum systems. The properties of these operations will also be examined.

Various types of information processing occur in quantum systems. The most fundamental processes are state discrimination and hypothesis testing. These problems often form the basis for an analysis of other types of quantum information processes. The difficulties associated with the noncommutativity of quantum mechanics appear in the most evident way among these problems. Therefore, we examine state discrimination and hypothesis testing before examining other types of information processing in quantum systems in this text. In two-state discrimination, we discriminate between two unknown candidate states by performing a measurement and examining the measurement data. Note that in this case, the two hypotheses for the unknown state are treated symmetrically. In contrast, if the two hypotheses are treated asymmetrically, the process is called hypothesis testing rather than state discrimination. Hypothesis testing is not only interesting in itself but is also relevant to other topics in quantum information theory. In particular, the quantum version of Stein’s lemma, which is the central topic of this chapter, is closely related to quantum channel coding discussed in Chap. 4. Moreover, Stein’s lemma is also connected to the distillation of maximally entangled states, as discussed in Sect. 8.5, in addition to other topics discussed in Chap. 9. The importance of Stein’s lemma may not be apparent at first sight since it considers the tensor product states of identical states, which rarely appear in real communications. However, the asymptotic analysis for these tensor product states provides the key to the analysis of asymptotic problems in quantum communications. For these reasons, this topic is discussed in an earlier chapter in this text.

In this chapter, we cover the fundamentals of linear algebra and provide a mathematical formulation of quantum mechanics for use in later chapters. It is necessary to understand these topics since they form the foundation of quantum information processing discussed later. In the first section, we cover the fundamentals of linear algebra and introduce some notation. The next section describes the formulation of quantum mechanics. Further, we examine a quantum two-level system, which is the simplest example of a quantum-mechanical system. Finally, we discuss the tensor product and matrix inequalities. More advanced discussions on linear algebra are available in Appendix.

High Harmonic generation can be used as a probe of the emitting medium with attosecond and Angstrom resolutions. We show that polarization-resolved pump-probe spectroscopy with high harmonics improves the detection sensitivity of rotationally excited molecules.

One of the outstanding contemporary challenges in condensed matter physics is to understand the dynamics of interacting quantum systems exposed to an external perturbation. We theoretically examine nonequilibrium photo dynamics and its interplay of charge, spin, and lattice degrees of freedom on a Hubbard-Holstein chain in one dimension and a t-J-Holstein square lattice in two dimensions. In the chain, performing dynamical density-matrix renormalization group calculations, we find that many phonons generated dynamically after photo irradiation in Mott insulators cause initial relaxation process. On the other hand, in the square lattice with model parameters as relevant for cuprates, a Lanczos-type exact diagonalization calculation shows that the majority of absorbed energy flows into spin subsystem rather than phonon subsystem.

A handful of recent cryptographic proposals rely on the conjectured hardness of the following problem in the ring of integers of a cyclotomic number field: given a basis of a principal ideal that is guaranteed to have a ``rather short'' generator, find such a generator. Recently, Bernstein and Campbell-Groves-Shepherd sketched potential attacks against this problem; most notably, the latter authors claimed a \emph{polynomial-time quantum} algorithm. (Alternatively, replacing the quantum component with an algorithm of Biasse and Fieker would yield a \emph{classical subexponential-time} algorithm.) A key claim of Campbell \etal\ is that one step of their algorithm---namely, decoding the \emph{log-unit} lattice of the ring to recover a short generator from an arbitrary one---is classically efficient (whereas the standard approach on general lattices takes exponential time). However, very few convincing details were provided to substantiate this claim. In this work, we clarify the situation by giving a rigorous proof that the log-unit lattice is indeed efficiently decodable, for any cyclotomic of prime-power index. Combining this with the quantum algorithm from a recent work of Biasse and Song confirms the main claim of Campbell \etal\xspace Our proof consists of two main technical contributions: the first is a geometrical analysis, using tools from analytic number theory, of the standard generators of the group of cyclotomic units. The second shows that for a wide class of typical distributions of the short generator, a standard lattice-decoding algorithm can recover it, given any generator. By extending our geometrical analysis, as a second main contribution we obtain an efficient algorithm that, given any generator of a principal ideal (in a prime-power cyclotomic), finds a 2^O~(n^1/2) -approximate shortest vector in the ideal. Combining this with the result of Biasse and Song yields a quantum polynomial-time algorithm for the 2^O~(n^1/2)-approximate Shortest Vector Problem on principal ideal lattices.

Grover's algorithm is a quantum query algorithm solving the unstructured search problem of size N using $$O\sqrt{N}$$ queries. It provides a significant speed-up over any classical algorithm [2]. The running time of the algorithm, however, is very sensitive to errors in queries. Multiple authors have analysed the algorithm using different models of query errors and showed the loss of quantum speed-up [1, 4]. We study the behavior of Grover's algorithm in the model where the search space contains both faulty and non-faulty marked elements. We show that in this setting it is indeed possible to find one of marked elements in $$O\sqrt{N}$$ queries.

We present a new definition of computationally binding commitment schemes in the quantum setting, which we call "collapse-binding". The definition applies to string commitments, composes in parallel, and works well with rewinding-based proofs. We give simple constructions of collapse-binding commitments in the random oracle model, giving evidence that they can be realized from hash functions like SHA-3. We evidence the usefulness of our definition by constructing three-round statistical zero-knowledge quantum arguments of knowledge for all NP languages.