Application Of Quantum Mechanics Research Articles

Classicality versus quantumness in Born's probability

Born's rule, which postulates the probability of a measurement outcome in a quantum state, is pivotal to interpretations and applications of quantum mechanics. By exploiting the departure of the product of two Hermitian operators in Born's rule from Hermiticity, we prescribe an intrinsic and natural scheme to decompose Born's probability into a classical part and a quantum part, which have significant implications in quantum information theory. The classical part constitutes the information compatible with the associated measurement operator, while the quantum part represents the quantum coherence of the state with respect to the measurement operator. Fundamental properties of the decomposition are revealed. As applications, we establish several trade-off relations for the classicality and quantumness in Born's probability, which may be interpreted as alternative realizations of Heisenberg's uncertainty principle. The results shed physical lights on related issues concerning quantification of complementarity, coherence, and uncertainty, as well as the classical-quantum interplay.

Theory and Simulation of the Ultrafast Double-Bond Isomerization of Biological Chromophores.

Ultrafast processes in light-absorbing proteins have been implicated in the primary step in the light-to-energy conversion and the initialization of photoresponsive biological functions. Theory and computations have played an instrumental role in understanding the molecular mechanism of such processes, as they provide a molecular-level insight of structural and electronic changes at ultrafast time scales that often are very difficult or impossible to obtain from experiments alone. Among theoretical strategies, the application of hybrid quantum mechanics and molecular mechanics (QM/MM) models is an important approach that has reached an evident degree of maturity, resulting in several important contributions to the field. This review presents an overview of state-of-the-art computational studies on subnanosecond events in rhodopsins, photoactive yellow proteins, phytochromes, and some other photoresponsive proteins where photoinduced double-bond isomerization occurs. The review also discusses current limitations that need to be solved in future developments.

Computational study of vicarious nucleophilic substitution reactions.

Vicarious nucleophilic substitution reactions are a versatile way of introducing substituents into aromatic and heteroaromatic electron-deficient compounds. In this project, a kinetic study of these reactions by applying quantum mechanics concepts, such as reaction force, force constant, and electronic reaction flow was proposed. Furthermore, absolute theoretical scales of electrophilicity by applying density functional theory electronic indices were established to classify a series of five and six-membered nitroheteroarenes, and nitrobenzenes with substituents in ortho, meta and para positions. The theoretical model was validated by comparison with experimental kinetic results. Calculations using B3LYP/6-311G(d,p) level of theory allowed analysis of the reactivity patterns and the mechanisms of these chemical reactions. The theoretical scale properly accounts for the activating/deactivating effects promoted by the substituents and agrees with the ability of these substituents to accept or donate electrons, electron acceptor substituents are those that increase electrophilicity, and electron donors those that reduce it.

On the almost everywhere convergence of the eigenfunction expansions from Liouville classes

The relevance of waves in quantum mechanics naturally implies that the decomposition of arbitrary wave packets in terms of monochromatic waves plays an important role in applications of the theory. When eigenfunction expansions does not converge, then the expansions of the functions with certain smoothness should be considered. Such functions gained prominence primarily through their application in quantum mechanics. In this work we study the almost everywhere convergence of the eigenfunction expansions from Liouville classes , related to the self-adjoint extension of the Laplace operator in torus TN. The sufficient conditions for summability is obtained using the modified Poisson formula. Isomorphism properties of the elliptic differential operators is applied in order to obtain estimation for the Fourier series of the functions from the classes of Liouville .

(Keynote) Artificial Photosynthesis from First Principles

Someday the world’s liquid fuels needed for ships and airplanes will come from sustainable sources and low-energy processing. We are far from that day. While that fact is unfortunate, it opens up exciting opportunities for researchers from many different fields to work together to realize that vision. I will report on some of my research group’s contributions toward this goal, as we develop and apply quantum mechanics based simulation methods to unravel mechanisms associated with (photo)electrochemical water oxidation and carbon dioxide reduction at semiconductor electrodes. As an example, we believe we have finally identified – after six years of work - the crucial aromatic-amine-derived catalytic intermediate involved in CO2 reduction to methanol at illuminated compound-semiconductor electrodes. Knowledge of this intermediate lends itself to proposed design principles to enhance the efficiency of this promising photoelectroreduction process.

Quantum-Mechanics Methodologies in Drug Discovery: Applications of Docking and Scoring in Lead Optimization.

The development and application of quantum mechanics (QM) methodologies in computer- aided drug design have flourished in the last 10 years. Despite the natural advantage of QM methods to predict binding affinities with a higher level of theory than those methods based on molecular mechanics (MM), there are only a few examples where diverse sets of protein-ligand targets have been evaluated simultaneously. In this work, we review recent advances in QM docking and scoring for those cases in which a systematic analysis has been performed. In addition, we introduce and validate a simplified QM/MM expression to compute protein-ligand binding energies. Overall, QMbased scoring functions are generally better to predict ligand affinities than those based on classical mechanics. However, the agreement between experimental activities and calculated binding energies is highly dependent on the specific chemical series considered. The advantage of more accurate QM methods is evident in cases where charge transfer and polarization effects are important, for example when metals are involved in the binding process or when dispersion forces play a significant role as in the case of hydrophobic or stacking interactions.

Quantum circuit‐based modeling of continuous‐variable quantum key distribution system

SummaryThe second generation Continuous‐Variable Quantum Key Distribution is one of the most promising application of quantum mechanics in communications. This paper investigates a state‐of‐the‐art Continuous‐Variable Quantum Key Distribution solution from circuit modeling point of view in order to build an appropriate simulation framework. This framework allows detailed evaluation of the system's performance and adjusting the system parameters. Copyright © 2017 John Wiley & Sons, Ltd.

A New Concept of the Analytic Operator-Valued Feynman Integral on Wiener Space

ABSTRACTIn this article we introduce a new concept of an analytic operator-valued Feynman integral for functionals on Wiener space, which we then use to explain various physical phenomena. We then establish the existence of some analytic operator-valued Feynman integrals that prove useful in establishing various applications in quantum mechanics.

Beyond computational difficulties: Survey of the two decades from the elaboration to the extensive application of the Hartree-Fock method

The Hartree-Fock method, one of the first applications of the new quantum mechanics in the frame of the many-body problem, had been elaborated by Rayner Douglas Hartree in 1928 and Vladimir Fock in 1930. Promptly, the challenge of tedious computations was being discussed and it is well known that the application of the method benefited greatly from the development of computers from the mid-to-late 1950s. However, the years from 1930 to 1950 were by no means years of stagnation, as the method was the object of several considerations related to its mathematical formulation, possible extension, and conceptual understanding. Thus, with a focus on the respective attitudes of Hartree and Fock, in particular with respect to the concept of quantum exchange, the present work puts forward some mathematical and conceptual clarifications, which played an important role for a better understanding of the many-body problem in quantum mechanics.

Per-Olov Löwdin – father of quantum chemistry

ABSTRACTDuring 2016, we celebrate the 100th anniversary of the birth of Per-Olov Löwdin. He was appointed to the first Lehrstuhl in quantum chemistry at Uppsala University in 1960. Löwdin introduced quantum chemistry as a field in its own right by formulating its goals, establishing fundamental concepts, like the correlation energy, the method of configuration interaction, reduced density matrices, natural spin orbitals, charge and bond order matrices, symmetric orthogonalisation, and generalised self-consistent fields. His exposition of partitioning technique and perturbation theory, wave and reaction operators and associated non-linear summation techniques, introduced mathematical rigour and deductive order in the interpretative organisation of the new field. He brought the first computer to Uppsala University and pioneered the initiation of ‘electronic brains’ and anticipated their significance for quantum chemistry. Perhaps his single most influential contribution to the field was his education of two generations of future faculty in quantum chemistry through Summer Schools in the Scandinavian Mountains, Winter Institutes at Sanibel Island in the Gulf of Mexico. Per-Olov Löwdin founded the book series Advances in Quantum Chemistry and the International Journal of Quantum Chemistry. The evolution of quantum chemistry is appraised, starting from a collection of cross-disciplinary applications of quantum mechanics to the technologically advanced and predominant field of today, virtually used in all branches of chemistry. The scientific work of Per-Olov Löwdin has been crucial for the development of this new important province of science.

Dirac's dream: Understanding metal sorption by geomedia using density functional theory

Density functional theory (DFT) can provide accurate, computationally-manageable, first-principles characterizations of mineral surface speciation at molecular scales. This is accomplished by solving the Kohn-Sham equation, a tractable method of applying quantum mechanics to multi-electron systems that was inspired by some visionary remarks of P. A. M. Dirac, one of the founders of quantum theory. Fifty years of advances in DFT and the development of massively-parallel computing platforms have paved the way for molecular-scale modeling of the mineral surface that is directly relevant to the study of natural nanoparticles. In fact, DFT has matured sufficiently to be applied to metal sorption by geomedia as a “computer experiment,” yielding quantitative molecular-scale information that fully complements insights gained from surface spectroscopy. This powerful approach is illustrated first through a series of structural simulations of chalcophanite group minerals and hetaerolite–hausmannite solid solutions, then through several recent studies by the authors and their collaborators focusing on transition and heavy metal sorption by layer-type Mn(IV) oxide and Fe(II) sulfide nanoparticles. Our results show how DFT simulations reveal the mechanistic basis of metal partitioning trends observed experimentally while creating useful models for resolving experimental surface speciation conundrums.

Quantum Robotics: A Primer on Current Science and Future Perspectives

Quantum robotics is an emerging engineering and scientific research discipline that explores the application of quantum mechanics, quantum computing, quantum algorithms, and related fields to robotics. This work broadly surveys advances in our scientific understanding and engineering of quantum mechanisms and how these developments are expected to impact the technical capability for robots to sense, plan, learn, and act in a dynamic environment. It also discusses the new technological potential that quantum approaches may unlock for sensing and control, especially for exploring and manipulating quantum-scale environments. Finally, the work surveys the state of the art in current implementations, along with their benefits and limitations, and provides a roadmap for the future.

Quantum Inverse Measurement Theory Contributing to the Birth of Interpretation System of Quantum Mechanics of Local-Realism and Determinism

The existing interpretation of quantum mechanics is contrary to common sense. The existing quantum mechanical interpretation schemes are puzzling. The confusing theory is unconvincing, and needs to be amended and completed. The successful interpretation program of quantum mechanics of local-realism and determinism is undoubtedly the most attractive. Preparing the interpretation program deserves to be chosen as a research goal. It is a very good premise to believe that an object particle consists of light-knot of monochromatic waves. According to this premise, the erroneous recognition about “superposition principle, wave-particle duality and uncertainty principle” can be corrected. Under this premise, above research goal is achieved by establishing, applying quantum mechanics inverse measurement theory, adhering to the principle that there must be a complete empirical chain in the derivation process of experimental conclusion, and using the side effect caused by accompanying-light to explain the diffraction experiment of object particles. Electron secondarily diffraction and other experiments directly prove that there is the measurement (observation) which may not destroy quantum coherence. The diffraction experiments of all kinds of particles show that the Keeping and playing of the coherence of moving particles in the vacuum have nothing to do with their previous experience. These are the existing experiments, to be found, that support the theory of quantum inverse measurements. The verification experiment of quantum inverse measurement is designed. The absolute superiorities of quantum inverse measurement and the new view of measurement of quantum mechanics are listed. These superiorities are that: it has the characteristics of local-realism and determinism; it is not contrary to common sense and there is no confusing place; it can predict several phenomena that cannot be predicted by other theories. A solid theoretical foundation has been laid for “correctly understanding the microscopic world” and establishment of local realism quantum mechanics.

Propagating wave correlations in complex systems

We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local mean of these correlation functions in terms of the underlying classical dynamics. By defining appropriate ensemble averages, we show that fluctuations about the mean can be characterised in terms of classical correlations. We give in particular an explicit expression relating fluctuations of diagonal contributions to those of the full wave correlation function. The methods have a wide range of applications both in quantum mechanics and for classical wave problems such as in vibro-acoustics and electromagnetism. We apply the methods here to simple quantum systems, so-called quantum maps, which model the behaviour of generic problems on Poincaré sections. Although low-dimensional, these models exhibit a chaotic classical limit and share common characteristics with wave propagation in complex structures.

The Hartree‐Fock method: from self‐consistency to correct symmetry

The Hartree‐Fock method, one of the first applications of the new quantum mechanics in the frame of the many‐body problem, is a good example of the attempts of many physicists to adapt their work on the old Bohr theory to new discoveries. It also shows the necessity to enlarge the theoretical foundations given by Schrödinger and Heisenberg. The present work illustrates the challenges of the many‐body problem in the new quantum mechanics by evaluating the contributions of both Hartree, who developed a self‐consistent process to calculate the energy of an atom, and Fock, who set out the correct theoretical foundations of the method.

Advances in Computational Prediction of Regioselective and Isoform-Specific Drug Metabolism Catalyzed by CYP450s.

Prediction of drug metabolism is an important step in the early lead optimization phase and preclinical studies. Its main purpose is to avoid late stage (Phase I–III) or post-marketing withdrawals which usually results in a significant financial loss to a pharmaceutical company. Computational methods for identification of soft-spots in the molecules (site of metabolism; SOM) and CYP450 isoforms responsible for drug metabolism have over the past ten years proved an indispensable tool towards achieving this goal. These methods can be broadly classified into i) ligand based, ii) structure based and iii) hybrid methods. In this review we discuss some of the most successful methods of SOM and isoform specificity prediction, their application domain, advantages, and limitations along with recent developments in the last 5 years in this area. Recent applications of molecular dynamics (MD), quantum mechanics (QM) and quantum mechanics/molecular mechanics (QM/MM) methodology for regioselective and isoform specific drug metabolism predictions are also discussed. Finally, a summary of these methods along with expected developments, future challenges and opportunities are discussed.

Evaluating experimental molecular physics studies of radiation damage in DNA*

The field of Atomic and Molecular Physics (AMP) is a mature field exploring the spectroscopy, excitation, ionisation of atoms and molecules in all three phases. Understanding of the spectroscopy and collisional dynamics of AMP has been fundamental to the development and application of quantum mechanics and is applied across a broad range of disparate disciplines including atmospheric sciences, astrochemistry, combustion and environmental science, and in central to core technologies such as semiconductor fabrications, nanotechnology and plasma processing. In recent years the molecular physics also started significantly contributing to the area of the radiation damage at molecular level and thus cancer therapy improvement through both experimental and theoretical advances, developing new damage measurement and analysis techniques. It is therefore worth to summarise and highlight the most prominent findings from the AMP community that contribute towards better understanding of the fundamental processes in biologically-relevant systems as well as to comment on the experimental challenges that were met for more complex investigation targets.

Experimental transmission of quantum digital signatures over 90 km of installed optical fiber using a differential phase shift quantum key distribution system.

Quantum digital signatures (QDSs) apply quantum mechanics to the problem of guaranteeing message integrity and non-repudiation with information-theoretical security, which are complementary to the confidentiality realized by quantum key distribution (QKD). Previous experimental demonstrations have been limited to transmission distances of less than 5 km of optical fiber in a laboratory setting. Here we report, to the best of our knowledge, the first demonstration of QDSs over installed optical fiber, as well as the longest transmission link reported to date. This demonstration used a 90 km long differential phase shift QKD to achieve approximately one signed bit per second, an increase in the signature generation rate of several orders of magnitude over previous optical fiber demonstrations.

Quantum state measurement of any arbitrary entangled field-state via Ramsey interferometry

Multipartite entangled states are the key resource and play a crucial role in latest applications of quantum mechanics. We propose a scheme for the measurement of quantum state of multimode entangled field state trapped in multiple cavities. The scheme is based on the measurement of photon statistics of the displaced entangled field state in Ramsey type set-up. In this set-up, the atoms undergo a dispersive phase shift when they pass through the off-resonant entangled field in cavities. By measuring the internal states of the atoms, the photon statistics and the Wigner function can be reconstructed.

Geometric Algebra as a Unifying Language for Physics and Engineering and Its Use in the Study of Gravity

Geometric Algebra (GA) is a mathematical language that aids a unified approach and understanding in topics across mathematics, physics and engineering. In this contribution, we introduce the Spacetime Algebra (STA), and discuss some of its applications in electromagnetism, quantum mechanics and acoustic physics. Then we examine a gauge theory approach to gravity that employs GA to provide a coordinate free formulation of General Relativity, and discuss what a suitable Lagrangian for gravity might look like in two dimensions. Finally the extension of the gauge theory approach to include scale invariance is briefly introduced, and attention drawn to the interesting properties with respect to the cosmological constant of the type of Lagrangians which are favoured in this approach. The intention throughout is to provide a survey accessible to anyone, equipped only with an introductory knowledge of GA, whether in maths, physics or engineering.