Quantum Formalism Research Articles

Nanostructured titanium dioxide coatings prepared by Aerosol Assisted Chemical Vapour Deposition (AACVD)

Titanium dioxide is a compound of great interest, due to its functional properties; one of its most important uses is as a photocatalyst. TiO2 coatings can be deposited using different techniques. Aerosol Assisted Chemical Vapour Deposition (AACVD) is particularly interesting, as high temperature or pressure are not necessary to generate the gaseous precursors. Furthermore, by carefully choosing the deposition conditions (i.e. deposition temperature, solvent), it is possible to obtain deposits with different morphology and, consequently, different functional properties. In this paper we present the synthesis of titanium dioxide coatings with AACVD using complexes between titanium isopropoxide (TIPP) and acetyl acetone (acac) as precursors. Deposition experiments were performed using different ratios of TIPP to acac, to assess the effect on the composition of the coatings, their morphology and photocatalytic activity. Results showed that the use of acac led to nanostructured titanium dioxide (nanoparticles of about 10−25 nm diameter). Raman analysis showed the presence of both anatase and rutile phases. XPS analysis indicated the presence of residual carbonaceous species in the coatings; despite this, they displayed photocatalytic properties similar or superior to AACVD films without carbon. Photocatalytic tests, performed measuring the Formal Quantum Efficiency (FQE) and the Formal Quantum Yield (FQY) in the degradation of resazurin, showed that a acac:TIPP ratio equal to 1 led to the material with the highest performance, as the FQE value was about three times higher than that for the coating prepared with TIPP alone. Overall the complexes between TIPP and acac are promising precursors for the AACVD technique, leading to nanostructured coatings with enhanced performance.

ELECTRONIC, STRUCTURAL AND PHARMACOCINETIC CHARACTERIZATION OF TRICYCLIC ALKALOID ALTERNAMIDE A: A SEMI-EMPIRICAL QUANTUM STUDY AND ADMET

Chagas disease is one of the biggest socioeconomic problems in Latin America. Caused by the protozoan parasite Trypanosoma cruzi, affecting 7 million people, causing approximately 14,000 deaths per year. Alternamide, a tricyclic alkaloid present in Alternanthera littoralis, an herbaceous plant found on beaches of the Brazilian its extracts are used in traditional medicine for treatment of infectious and inflammatory diseases, which showed anti Trypanocida activity. In this context, in the present work we present the results of the electronic, structural and pharmacokinetic characterization study of the promising phytopharmaceutical Alternamide A. Using the semi-empirical quantum formalism it was possible to identify the most stable conformation, boundary orbitals, calculate to identify nucleophilic sites and reactivity descriptors. Through in silico absorption, distribution, metabolism, excretion and toxicity (ADMET) simulations, including solubility, blood-brain barrier (BHE), plasma protein binding, CYP2D6 binding, gastrointestinal absorption and hepatotoxicity, it was observed that good oral bioavailability and high-water solubility high gastrointestinal absorption. The synthetic accessibility score was 2.75, which means that it would be easy to synthesize the molecule under study. Highlighting what this study represents is a key step for future molecular docking and drug design studies for the development of inhibitors of the evolutionary forms of the molecule T-crossed.

Symmetric Quantum Sets and L-Algebras

Abstract Quantum analogues of sets are defined by two simple assumptions, allowing enumeration, reminiscent of the Gram–Schmidt orthogonalization process. It is shown that any symmetric quantum set is a classical set of irreducible components, and that each irreducible component of size $>3$ is representable by an orthomodular space over a skew field with involution. For finite or sufficiently large irreducible components, invariance of quantum cardinality is proved. Topological quantum sets are introduced as quantum analogues of topological spaces; irreducible ones of size $>3$ are shown to be representable by Hilbert spaces over ${\mathbb{R}}$, ${\mathbb{C}}$, or ${\mathbb{H}}$. Symmetric quantum sets are characterized as a class of $L$-algebras with an intrinsic geometry, and they are shown to be equivalent to Piron’s quantum formalism. Equivalences between symmetric quantum sets and several other structures are established. To any symmetric quantum set, a group with a right invariant lattice structure is associated as a complete invariant. A simple and self-contained proof of Solèr’s theorem is included, which is used to prove that sufficiently large irreducible symmetric quantum sets come from a classical Hilbert space.

EPLETION DENSITY OF IDEAL GAS BOSE-EINSTEIN CONDENSATE BY TWO PARALLEL PLATES

By means of the second quantization formalism, the condensate density of an infinite Bose gas and finite Bose gas is studied in the broken phase. Our results show that the compactification in one-direction makes the remarkable changes in the condensate density.

On the Testability of the Equivalence Principle as a Gauge Principle Detecting the Gravitational t3 Phase

There have been various claims that the Equivalence Principle, as originally formulated by Einstein, presents several difficulties when extended to the quantum domain, even in the regime of weak gravity. Here we point out that by following the same approach as used for other classical principles, e.g. the principle of conservation of energy, one can, for weak fields, obtain a straightforward quantum formulation of the principle. We draw attention to a recently performed test that confirms the equivalence principle in this form and discuss its implications.

Atomic test of higher-order interference

Canonical quantum formalism predicts that the interference pattern registered in multi-slit experiments should be a simple combination of patterns observed in two-slit experiments. This has been linked to the validity of Born's rule and verified in precise experiments with photons as well as molecules via nuclear magnetic resonance. Due to the expected universal validity of Born rule, it is instructive to conduct similar tests with yet other physical systems. Here we discuss analogs of triple-slit experiment using atoms allowing tripod energy level configuration, as realisable e.g. with alkaline-earth-like atoms. We cover all the stages of the setup including various ways of implementing analogs of slit blockers. The precision of the final setup is estimated and offers improvement over the previous experiments.

The Bell Theorem Revisited: Geometric Phases in Gauge Theories

The Bell theorem stands as an insuperable roadblock in the path to a very desired intuitive solution of the EPR paradox and, hence, it lies at the core of the current lack of a clear interpretation of the quantum formalism. The theorem states through an experimentally testable inequality that the predictions of quantum mechanics for the Bell polarization states of two entangled particles cannot be reproduced by any statistical model of hidden variables that shares certain intuitive features. In this paper, we show, however, that the proof of the Bell theorem involves a subtle, though crucial, assumption that is not required by fundamental physical principles and, hence, it is not necessarily fulfilled in the experimental setup that tests the inequality. Indeed, this assumption can neither be properly implemented within the standard framework of quantum mechanics. Namely, the proof of the theorem assumes that there exists a preferred absolute frame of reference, supposedly provided by the lab, which enables to compare the orientation of the polarization measurement devices for successive realizations of the experiment and, hence, to define jointly their response functions over the space of hypothetical hidden configurations for all their possible alternative settings. We notice, however, that only the relative orientation between the two measurement devices in every single realization of the experiment is a properly defined physical degree of freedom, while their global rigid orientation is a spurious gauge degree of freedom. Hence, the preferred frame of reference required by the proof of the Bell theorem does not necessarily exist. Following this observation, we build an explicitly local model of hidden variables that reproduces the predictions of quantum mechanics for the Bell states.

Effect of time-dependent inhomogeneous magnetic fields on the particle momentum spectrum in electron-positron pair production

Electron-positron pair production in spatially and temporally inhomogeneous electric and magnetic fields is studied within the Dirac-Heisenberg-Wigner formalism (quantum kinetic theory) through computing the corresponding Wigner functions. The focus is on discussing the particle momentum spectrum regarding signatures of Schwinger and multiphoton pair production. Special emphasis is put on studying the impact of a strong dynamical magnetic field on the particle distribution functions. As the equal-time Wigner approach is formulated in terms of partial integro-differential equations an entire section of the manuscript is dedicated to present numerical solution techniques applicable to Wigner function approaches in general.

Operational foundations for complementarity and uncertainty relations

The so-called preparation uncertainty can be understood in purely operational terms. Namely, it occurs when for some pair of observables, there is no preparation, for which they both exhibit deterministic statistics. However, the right-hand side of uncertainty relation is generally not operational as it depends on the quantum formalism. Also, while joint non-measurability of observables is an operational notion, the complementarity in Bohr sense (i.e. excess of information needed to describe the system) has not yet been expressed in purely operational terms. In this paper we propose a solution to these problems, by introducing an operational definition for complementarity, and further postulating uncertainty as a necessary price for complementarity in physical theories. In other words, we propose to put the (operational) complementarity as the right-hand side of uncertainty relation. Concretely, we first identify two different notions of uncertainty and complementarity for which the above principle holds in quantum mechanics. We also introduce postulates for the general measures of uncertainty and complementarity. In order to define quantifiers of complementarity we first turn to the simpler notion of independence that is defined solely in terms of statistics two observables. We also use our framework to define new complementarity indicators based on (i) performance of random access codes, (ii) geometrical properties of the body of observed statistics, and (iii) variation of information. We then show that they can be used to state uncertainty relations. Moreover, we show that non-signaling and uncertainty relation expressed by complementarity of type (ii) leads to the Tsirelson bound for CHSH inequality. Lastly, we show that a variant of Information Causality called Information Content Principle, can be interpreted as uncertainty relation in the above sense.

Electromagnetically induced grating with second field quantization in spherical semiconductor quantum dots

A new approach for diffracting the weak probe beam into higher-order directions is proposed via electromagnetically induced grating in second field quantization formalism, offering a new way for implementations of quantum information with semiconductor quantum dots. The formalism of second field quantization allows describing atoms and photons as a many-body system. An induced diffraction grating is formed based on the electromagnetic induced transparency when a standing-wave coupling field is applied to a spherical quantum dot as a three-level system. Due to phase modulation, the zeroth-order light intensity becomes weak, and the first-order diffraction is improved affectedly. On the contrary, the probe beam is barely diffracted via absorption modulation. The simulation results verify that photon numbers of probe and control fields, as well as other parameters in the QD, can lead to the diffraction efficiency of phase grating to be improved. Phase diffraction grating accompanied with a high transmissivity is demonstrated, and the first-order diffraction efficiency reaches $$30\%$$. Also, the impact of QD dimensions on its optical response is investigated. This model may find potential applications in designing the semiconductor quantum dot-based photonic devices in optical communications and quantum information networks.

Strict deformation quantization of the state space of Mk(ℂ) with applications to the Curie–Weiss model

Increasing tensor powers of the [Formula: see text] matrices [Formula: see text] are known to give rise to a continuous bundle of [Formula: see text]-algebras over [Formula: see text] with fibers [Formula: see text] and [Formula: see text], where [Formula: see text], the state space of [Formula: see text], which is canonically a compact Poisson manifold (with stratified boundary). Our first result is the existence of a strict deformation quantization of [Formula: see text] à la Rieffel, defined by perfectly natural quantization maps [Formula: see text] (where [Formula: see text] is an equally natural dense Poisson subalgebra of [Formula: see text]). We apply this quantization formalism to the Curie–Weiss model (an exemplary quantum spin with long-range forces) in the parameter domain where its [Formula: see text] symmetry is spontaneously broken in the thermodynamic limit [Formula: see text]. If this limit is taken with respect to the macroscopic observables of the model (as opposed to the quasi-local observables), it yields a classical theory with phase space [Formula: see text] (i.e. the unit three-ball in [Formula: see text]). Our quantization map then enables us to take the classical limit of the sequence of (unique) algebraic vector states induced by the ground state eigenvectors [Formula: see text] of this model as [Formula: see text], in which the sequence converges to a probability measure [Formula: see text] on the associated classical phase space [Formula: see text]. This measure is a symmetric convex sum of two Dirac measures related by the underlying [Formula: see text]-symmetry of the model, and as such the classical limit exhibits spontaneous symmetry breaking, too. Our proof of convergence is heavily based on Perelomov-style coherent spin states and at some stage it relies on (quite strong) numerical evidence. Hence the proof is not completely analytic, but somewhat hybrid.

Ultrarelativistic quark-nucleus scattering in a light-front Hamiltonian approach

We investigate the scattering of a quark on a heavy nucleus at high energies using the time-dependent basis light-front quantization (tBLFQ) formalism, which is the first application of the tBLFQ formalism in QCD. We present the real-time evolution of the quark wave function in a strong classical color field of the relativistic nucleus, described as the Color Glass Condensate. The quark and the nucleus color field are simulated in the QCD SU(3) color space. We calculate the total and the differential cross sections, and the quark distribution in coordinate and color spaces using the tBLFQ approach. We recover the eikonal cross sections in the eikonal limit. We find that the differential cross section from the tBLFQ simulation is in agreement with a perturbative calculation at large $p_\perp$, and it deviates from the perturbative calculation at small $p_\perp$ due to higher-order contributions. In particular, we relax the eikonal limit by letting the quark carry realistic finite longitudinal momenta. We study the sub-eikonal effect on the quark through the transverse coordinate distribution of the quark with different longitudinal momentum, and we find the sub-eikonal effect to be sizable. Our results can significantly reduce the theoretical uncertainties in small $p_\perp$ region which has important implications to the phenomenology of the hadron-nucleus and deep inelastic scattering at high energies.

Introducing the γ function in quantum theory

AbstractThrough a series of postulates, we define a function γ(x) whose square acts as Dirac's δ(x) and exhibits several unusual properties. Though the square root of δ cannot be defined among distributions, it appears in quantum theory if one wants to associate a wave function to a (quasi)classical particle having charge distribution δ(x). The newly defined function γ(x) serves to describe quasi‐classical particles using part of the quantum formalism (eg, wave functions, operators, expectation values) but exhibiting classical properties. The function γ(x) appears to be useful to define model wave functions for simple (quasi)quantum systems. In a spherical coordinate system, γ(r − r0) leads to a quasi‐classical “bubble” model of the hydrogen atom, where the electron is distributed on the surface of a sphere with radius r0, and it provides exact quantum mechanical energies of its total symmetric levels. For other simple quantum systems, it provides approximate but meaningful energies. In particular, exact energy differences for harmonic oscillator levels are obtained, with the zero‐point energy missing.

Born's Rule from the Principle of Unitary Equivalence

Complex phase factors are viewed not only as redundancies of the quantum formalism but instead as remnants of unitary transformations under which the probabilistic properties of observables are invariant. It is postulated that a quantum observable corresponds to a unitary representation of an abelian Lie group, the irreducible subrepresentations of which correspond to the observable's outcomes. It is shown that this identification agrees with the conventional identification as self-adjoint operators. The upshot of this formalism is that one may 'second quantize' the representation to which an observable corresponds, thus obtaining the corresponding Fock space representation. This Fock space representation is then also identifiable as an observable in the same sense, the outcomes of which are naturally interpretable as ensembles of outcomes of the corresponding non-second quantized observable. The frequency interpretation of probability is adopted, i.e. probability as the average occurrence, from which Born's rule is deduced by enforcing the notion of 'average' to such that are invariant under the second quantized unitary representation which defines the quantum observable to which the initial state is an outcome. The enforcement of this invariance is an application the principle referred to as the 'principle of unitary equivalence'.

Quantum Computing-Inspired Network Optimization for IoT Applications

Internet of Things (IoT) is defined as the interconnection of millions of wireless devices to acquire data in a ubiquitous manner. With multiple devices targeting to perceive data over a common platform, it becomes indispensable to analyze accuracy for realizing an optimal IoT environment. Inspired from these aspects, this article presents a novel quantum computing-inspired (IoT-QCiO) optimization technique to maximize data accuracy (DA) in a real-time environment of IoT application. Specifically, the presented model incorporates quantum formalization of sensor-specific parameters to quantify IoT devices in terms of sensors in vicinity (SIV) and optimal sensor space (OSS). The optimality of the presented algorithm is estimated in terms of three key performance indicators of data cost (DC), DA, and data temporal efficiency (DTE). For validation purposes, the proposed algorithm is implemented for monitoring geographical traffic to address vehicular routing problems using 90 WiSense nodes, Raspberry Pi v3, and quantum simulators. Results obtained were compared with several state-of-the-art optimization algorithms. Based on the results, significant improvement was registered for the proposed model in terms of statistical parameters of precision, sensitivity, specificity, and ${F}$ -measure. Moreover, enhanced values of reliability depict the optimal performance of the proposed approach.

Quantum GestART: identifying and applying correlations between mathematics, art, and perceptual organization

Mathematics can help analyze the arts and inspire new artwork. Mathematics can also help make transformations from one artistic medium to another, considering exceptions and choices, as well as artists' individual and unique contributions. We propose a method based on diagrammatic thinking and quantum formalism. We exploit decompositions of complex forms into a set of simple shapes, discretization of complex images, and Dirac notation, imagining a world of “prototypes” that can be connected to obtain a fine or coarse-graining approximation of a given visual image. Visual prototypes are exchanged with auditory ones, and the information (position, size) characterizing visual prototypes is connected with the information (onset, duration, loudness, pitch range) characterizing auditory prototypes. The topic is contextualized within a philosophical debate (discreteness and comparison of apparently unrelated objects), it develops through mathematical formalism, and it leads to programming, to spark interdisciplinary thinking and ignite creativity within STEAM.

Two Faced Janus of Quantum Nonlocality.

This paper is a new step towards understanding why “quantum nonlocality” is a misleading concept. Metaphorically speaking, “quantum nonlocality” is Janus faced. One face is an apparent nonlocality of the Lüders projection and another face is Bell nonlocality (a wrong conclusion that the violation of Bell type inequalities implies the existence of mysterious instantaneous influences between distant physical systems). According to the Lüders projection postulate, a quantum measurement performed on one of the two distant entangled physical systems modifies their compound quantum state instantaneously. Therefore, if the quantum state is considered to be an attribute of the individual physical system and if one assumes that experimental outcomes are produced in a perfectly random way, one quickly arrives at the contradiction. It is a primary source of speculations about a spooky action at a distance. Bell nonlocality as defined above was explained and rejected by several authors; thus, we concentrate in this paper on the apparent nonlocality of the Lüders projection. As already pointed out by Einstein, the quantum paradoxes disappear if one adopts the purely statistical interpretation of quantum mechanics (QM). In the statistical interpretation of QM, if probabilities are considered to be objective properties of random experiments we show that the Lüders projection corresponds to the passage from joint probabilities describing all set of data to some marginal conditional probabilities describing some particular subsets of data. If one adopts a subjective interpretation of probabilities, such as QBism, then the Lüders projection corresponds to standard Bayesian updating of the probabilities. The latter represents degrees of beliefs of local agents about outcomes of individual measurements which are placed or which will be placed at distant locations. In both approaches, probability-transformation does not happen in the physical space, but only in the information space. Thus, all speculations about spooky interactions or spooky predictions at a distance are simply misleading. Coming back to Bell nonlocality, we recall that in a recent paper we demonstrated, using exclusively the quantum formalism, that CHSH inequalities may be violated for some quantum states only because of the incompatibility of quantum observables and Bohr’s complementarity. Finally, we explain that our criticism of quantum nonlocality is in the spirit of Hertz-Boltzmann methodology of scientific theories.

Coherence and interactions between geodesics

Following our previous paper, where it was shown that classical internal forces are the outcome of entangled states that collapsed into labeled states, we show that reformulating the GR geodesic equation of motion in a formalism of second quantization causes distant geodesics to interact.

Quantum Enhancement of a S/D Tunneling Model in a 2D MS-EMC Nanodevice Simulator: NEGF Comparison and Impact of Effective Mass Variation.

As complementary metal-oxide-semiconductor (CMOS) transistors approach the nanometer scale, it has become mandatory to incorporate suitable quantum formalism into electron transport simulators. In this work, we present the quantum enhancement of a 2D Multi-Subband Ensemble Monte Carlo (MS-EMC) simulator, which includes a novel module for the direct Source-to-Drain tunneling (S/D tunneling), and its verification in the simulation of Double-Gate Silicon-On-Insulator (DGSOI) transistors and FinFETs. Compared to ballistic Non-Equilibrium Green’s Function (NEGF) simulations, our results show accurate I vs. V and subthreshold characteristics for both devices. Besides, we investigate the impact of the effective masses extracted Density Functional Theory (DFT) simulations, showing that they are the key of not only the general thermionic emission behavior of simulated devices, but also the electron probability of experiencing tunneling phenomena.

Deformation quantization of constrained systems: a group averaging approach

Motivated by certain concepts introduced by the refined algebraic quantization formalism for constrained systems which has been successfully applied within the context of loop quantum gravity, in this paper we propose a phase space implementation of the Dirac quantization formalism to appropriately include systems with constraints. In particular, we propose a physically prescribed Wigner distribution which allows for the definition of a well-defined inner product by judiciously introducing a star version of the group averaging of the constraints. This star group averaging procedure is obtained by considering the star-exponential of the constraints and then integrating with respect to a suitable measure. In this manner, the proposed physical Wigner distribution explicitly solves the constraints by including generalized functions on phase space. Finally, in order to illustrate our approach, our proposal is tested in a couple of simple examples which recover standard results found in the literature.