Quantum Theory Research Articles

Supramolecular Assemblies in Mn (II) and Zn (II) Metal–Organic Compounds Involving Phenanthroline and Benzoate: Experimental and Theoretical Studies

Two new Mn(II) and Zn(II) metal–organic compounds of 1,10-phenanthroline and methyl benzoates viz. [Mn(phen)2Cl2]2-ClBzH (1) and [Zn(4-MeBz)2(2-AmPy)2] (2) (where 4-MeBz = 4-methylbenzoate, 2-AmPy = 2-aminopyridine, phen = 1,10-phenanthroline, 2-ClBzH = 2-chlorobenzoic acid) were synthesized and characterized using elemental analysis, TGA, spectroscopic (FTIR, electronic) and single crystal X-ray diffraction techniques. The crystal structure analysis of the compounds revealed the presence of various non-covalent interactions, which provides stability to the crystal structures. The crystal structure analysis of compound 1 revealed the formation of a supramolecular dimer of 2-ClBzH enclathrate within the hexameric host cavity formed by the neighboring monomeric units. Compound 2 is a mononuclear compound of Zn(II) where flexible binding topologies of 4-CH3Bz are observed with the metal center. Moreover, various non-covalent interactions, such as lp(O)-π, lp(Cl)-π, C–H∙∙∙Cl, π-stacking interactions as well as N–H∙∙∙O, C–H∙∙∙O and C–H∙∙∙π hydrogen bonding interactions, are found to be involved in plateauing the molecular self-association of the compounds. The remarkable enclathration of the H-bonded 2-ClBzH dimer into a supramolecular cavity formed by two [Mn(phen)2Cl2] complexes were further studied theoretically using density functional theory (DFT) calculations, the non-covalent interaction (NCI) plot index and quantum theory of atoms in molecules (QTAIM) computational tools. Synergistic effects were also analyzed using molecular electrostatic potential (MEP) surface analysis.

Weak-valued correlation functions: Insights and precise readout strategies

The correlation function in quantum systems plays a vital role in decoding their properties and gaining insights into physical phenomena. Its interpretation corresponds to the propagation of particle excitations between space-time, similar in spirit to the idea of quantum weak measurement in terms of recording the system information by interaction. By defining weak-valued correlation function, we propose the basic insights and the universal methods for recording them on the apparatus through weak measurement. To demonstrate the feasibility of our approach, we perform numerical experiments of perturbed quantum harmonic oscillators, addressing the intricate interplay between the coupling strength and the number of ensemble copies. Additionally, we extend our protocol to the domain of quantum field theory, where joint weak values encode crucial information about the correlation function. Hopefully, this comprehensive investigation can advance our understanding of the fundamental nature of the correlation function and weak measurement in quantum theories. Published by the American Physical Society 2024

An algebraic formulation of nonassociative quantum mechanics

Abstract We develop a version of quantum mechanics that can handle nonassociative algebras of observables and which reduces to standard quantum theory in the traditional associative setting. Our algebraic approach is naturally probabilistic and is based on using the universal enveloping algebra of a general nonassociative algebra to introduce a generalized notion of associative composition product. We formulate properties of states together with notions of trace, and use them to develop GNS constructions. We describe Heisenberg and Schrödinger pictures of completely positive dynamics, and we illustrate our formalism on the explicit examples of finite-dimensional matrix Jordan algebras as well as the octonion algebra.

Efficient wastewater decontamination using magnetic bentonite-alginate beads: A comprehensive study of adsorption dynamics, regeneration, and molecular interactions

This study enhances wastewater treatment methodologies by developing magnetic bentonite-alginate beads (MBent-A beads) for adsorbing methylene blue (MB) from aqueous solutions. Experimental and computational analyses were employed to evaluate the beads' adsorption efficiency, utilizing characterization techniques including Fourier-transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), point of zero charge (pHpzc), Brunauer-Emmett-Teller method (BET), scanning electron microscopy (SEM), and energy-dispersive X-ray spectroscopy (EDS) to examine the composite’s morphology and chemistry. Findings reveal a significant adsorption capacity with the beads' specific surface area at 3.94 m2/g and a maximum adsorption capacity of 774.32 mg/g. Adsorption kinetics adhered closely to the pseudo-second-order model, indicating a rapid adsorption process, while Langmuir isotherm analysis confirmed a uniform monolayer adsorption and temperature-dependent capacities. Thermodynamic analysis showed the adsorption process to be spontaneous and exothermic, reflecting a strong affinity between MB molecules and the bead surface. The beads demonstrated durability with more than 90% removal efficiency after five regeneration cycles, highlighting a minimal decrease from 98.54% to 90.60%. In-depth theoretical investigations using density functional theory (DFT), frontier molecular orbital (FMO), reduced density gradient (RDG), and quantum theory of atoms in molecules (QTAIM) analyses identified van der Waals forces and hydrogen bonding as primary interactions driving the adsorption. The synthesis of MBent-A beads and their confirmed efficacy in dye adsorption integrates experimental research with theoretical modeling, offering a robust solution for treating dye-contaminated wastewater and underlining the potential of MBent-A beads in environmental remediation.

Do qubits dream of entangled sheep? Quantum measurement without classical output

Abstract Quantum mechanics is usually formulated with an implicit assumption that agents who can observe and interact with the world are external to it and have a classical memory. However, there is no accepted way to define the quantum-classical cut and no a priori reason to rule out fully quantum agents with coherent quantum memories. In this work, we introduce an entirely quantum notion of measurement, called a sensation, to account for quantum agents that experience the world through quantum sensors. Sensations eschew probabilities and instead describe a deterministic flow of quantum information. We quantify the information gain and disturbance of a sensation using concepts from quantum information theory and find that sensations always disturb at least as much as they inform. Viewing measurements as sensations could lead to a new understanding of quantum theory in general and to new results in the context of quantum networks.

N-Lüders channels: A novel class of rebit channels, their properties and applications

Abstract In a very recent paper, the complete classification of rebit channels has been achieved. Here, we exploit that result to show how the classification can be used to perform an exhaustive analyze a novel class of rebit channels induced by effects called n-Lüders channels. In the final part of the paper we propose a concrete application of these channels within the mathematical framework of a quantum theory of color perception that originated the interest about a rebit channels classification.

Quantum time dilation in a gravitational field

According to relativity, the reading of an ideal clock is interpreted as the elapsed proper time along its classical trajectory through spacetime. In contrast, quantum theory allows the association of many simultaneous trajectories with a single quantum clock, each weighted appropriately. Here, we investigate how the superposition principle affects the gravitational time dilation observed by a simple clock – a decaying two-level atom. Placing such an atom in a superposition of positions enables us to analyze a quantum contribution to a classical time dilation manifest in spontaneous emission. In particular, we show that the emission rate of an atom prepared in a coherent superposition of separated wave packets in a gravitational field is different from the emission rate of an atom in a classical mixture of these packets, which gives rise to a quantum gravitational time dilation effect. We demonstrate that this nonclassical effect also manifests in a fractional frequency shift of the internal energy of the atom that is within the resolution of current atomic clocks. In addition, we show the effect of spatial coherence on the atom's emission spectrum.

DFT-D3 and TD-DFT Studies of the Adsorption and Sensing Behavior of Mn-Phthalocyanine toward NH3, PH3, and AsH3 Molecules

This study employs density functional theory (DFT) calculations at the B3LYP/6-311+g(d,p) level to investigate the interaction of XH3 gases (X = N, P, As) with the Mn-phthalocyanine molecule (MnPc). Grimme’s D3 dispersion correction is applied to consider long-range interactions. The adsorption behavior is explored under the influence of an external static electric field (EF) ranging from −0.514 to 0.514 V/Å. Chemical adsorption of XH3 molecules onto the MnPc molecule is confirmed. The adsorption results in a significant decrease in the energy gap (Eg) of MnPc, indicating the potential alteration of its optical properties. Quantum theory of atoms in molecules (QTAIM) analysis reveals partially covalent bonds between XH3 and MnPc, and the charge density differenc (Δρ) calculations suggest a charge donation-back donation mechanism. The UV-vis spectrum of MnPc experiences a blue shift upon XH3 adsorption, highlighting MnPc’s potential as a naked-eye sensor for XH3 molecules. Thermodynamic calculations indicate exothermic interactions, with NH3/MnPc being the most stable complex. The stability of NH3/MnPc decreases with increasing temperature. The direction and magnitude of the applied electric field (EF) play a crucial role in determining the adsorption energy (Eads) for XH3/MnPc complexes. The Eg values decrease with an increasing negative EF, which suggests that the electrical conductivity (σ) and the electrical sensitivity (ΔEg) of the XH3/MnPc complexes are influenced by the magnitude and direction of the applied EF. Overall, this study provides valuable insights into the suggested promising prospects for the utilization of MnPc in sensing applications of XH3 gases.

Algebraic Structures Formalizing the Logic of Quantum Mechanics Incorporating Time Dimension

AbstractAs Classical Propositional Logic finds its algebraic counterpart in Boolean algebras, the logic of Quantum Mechanics, as outlined within G. Birkhoff and J. von Neumann’s approach to Quantum Theory (Birkhoff and von Neumann in Ann Math 37:823–843, 1936) [see also (Husimi in I Proc Phys-Math Soc Japan 19:766–789, 1937)] finds its algebraic alter ego in orthomodular lattices. However, this logic does not incorporate time dimension although it is apparent that the propositions occurring in the logic of Quantum Mechanics are depending on time. The aim of the present paper is to show that tense operators can be introduced in every logic based on a complete lattice, in particular in the logic of quantum mechanics based on a complete orthomodular lattice. If the time set is given together with a preference relation, we introduce tense operators in a purely algebraic way. We derive several important properties of such operators, in particular we show that they form dynamic pairs and, altogether, a dynamic algebra. We investigate connections of these operators with logical connectives conjunction and implication derived from Sasaki projections in an orthomodular lattice. Then we solve the converse problem, namely to find for given time set and given tense operators a time preference relation in order that the resulting time frame induces the given operators. We show that the given operators can be obtained as restrictions of operators induced by a suitable extended time frame.

Multimode Emission in GaN Microdisk Lasers

AbstractQuantum well nanolasers usually show single‐mode lasing, as gain saturation suppresses emissions in other modes. In contrast, for whispering gallery mode microdisk lasers with GaN quantum wells as active material, above threshold multimode laser emission is observed. This intriguing emission feature is manifested in the fact that several modes simultaneously show the characteristic kink in the input–output curve at the onset of lasing. A quantum theory for nanolasers is used to support the experimental finding and to analyze this behavior in the presence of gain saturation. Coupling effects between neighboring modes are identified as the origin of multimode lasing, which initiate photon exchange between modes via population pulsations similar to classical wave‐mixing effects. A reduction of this type of mode coupling with increasing mode spacing is demonstrated. The results can pave the way for multimode application of nanolasers in integrated photonic circuits.

Quantum theory of spin transfer and spin pumping in collinear antiferromagnets and ferrimagnets

Quantum theory of spin transfer and spin pumping in collinear antiferromagnets and ferrimagnets

Complexity in tame quantum theories

Inspired by the notion that physical systems can contain only a finite amount of information or complexity, we introduce a framework that allows for quantifying the amount of logical information needed to specify a function or set. We then apply this methodology to a variety of physical systems and derive the complexity of parameter-dependent physical observables and coupling functions appearing in effective Lagrangians. In order to implement these ideas, it is essential to consider physical theories that can be defined in an o-minimal structure. O-minimality, a concept from mathematical logic, encapsulates a tameness principle. It was recently argued that this property is inherent to many known quantum field theories and is linked to the UV completion of the theory. To assign a complexity to each statement in these theories one has to further constrain the allowed o-minimal structures. To exemplify this, we show that many physical systems can be formulated using Pfaffian o-minimal structures, which have a well-established notion of complexity. More generally, we propose adopting sharply o-minimal structures, recently introduced by Binyamini and Novikov, as an overarching framework to measure complexity in quantum theories.

Quantum Gravity Effective Action Provides Entropy of the Universe

The effective action in the renormalizable quantum theory of gravity provides entropy because the total Hamiltonian vanishes. Since it is a renormalization group invariant that is constant in the process of cosmic evolution, we can show conservation of entropy, which is an ansatz in the standard cosmology. Here, we study renormalizable quantum gravity that exhibits conformal dominance at high energy beyond the Planck scale. The current entropy of the universe is derived by calculating the effective action under the scenario of quantum gravity inflation caused by its dynamics. We then argue that ghost modes must be unphysical but are necessary for the Hamiltonian to vanish and for entropy to exist in gravitational systems.

The Born rule: Axiom or result?

The Born rule is part of the collapse axioms in the standard version of quantum theory, as presented by most textbooks on the subject. We show here that its signature quadratic dependence on the initial wavefunction's projection onto the measured outcome state follows from a single additional assumption beyond the other axioms. We give two examples of such an assumption, with a separate derivation for each, and we discuss their relationship with existing derivations. Our presentation is suitable for advanced undergraduates or graduate students who have taken a standard course in quantum theory. It does not depend on any particular interpretation of the theory.

Determination of GaN nanosensor for scavenging of toxic heavy metal ions (Mn2+, Zn2+, Ag+, Au3+, Al3+, Sn2+) from water: Application of green sustainable materials by molecular modeling approach

Gallium nitride nanocage (GaN_NC) can select toxic heavy metals from water. Therefore, it has been found a selective competition for metal cations in the GaN_NC. The electromagnetic and thermodynamic attributes of heavy metals cations-trapped gallium nitride nanocage (GaN_NC) was depicted by material modeling. The data display that heavy metals cations-trapped in the GaN_NC system are resistant materials, with the firm adsorption zone in the center of the cage. Furthermore, charge transfer from GaN_NC to the heavy metals cations demonstrates clear n-type adsorbing manner. The encapsulation of heavy metals cations occurs via chemisorption. In this article, the behavior of trapping of heavy metal ions of Mn2+, Zn2+, Ag+, Au3+, Al3+ and Sn2+ by gallium nitride nanocone for sensing the water metal cations was observed. The nature of covalent features for these complexes has represented the analogous energy amount and vision of the PDOS for the p states of N and d states of heavy metal cations of Mn2+, Zn2+, Ag+, Au3+, Al3+ and Sn2+ through water treatment. The partial density of states (PDOS) can also evaluate an appointed charge group between Mn2+, Zn2+, Ag+, Au3+, Al3+, Sn2+ and GaN_NC which indicate the most stable complex of metallic visage and a certain degree of covalent specifications between heavy metals cations and gallium nitride nanocage. Furthermore, the NMR analysis indicated the notable peaks surrounding metal elements of Mn2+, Zn2+, Ag+, Au3+, Al3+ and Sn2+ through the trapping in the GaN_NC during ion detection and removal from water; however, it can be seen some fluctuations in the chemical shielding treatment of isotropic and anisotropy tensors. Based on the results in this research, the selectivity of metal ion adsorption by gallium nitride nanocage (ion sensor) has been approved as: Ag+ ˃ Au3+ ˃ Mn2+ ≫ Zn2+ ˃ Sn2+ ˃ Al3+. Using quantum theory of atoms in molecules (QTAIMs) method, intermolecular interactions and corresponding parameters at critical bonding points were also investigated.

Investigation of drug delivery capability of single-walled carbon and boron-nitride nanotubes, boron-nitride (B16N16), and C32 fullerenes as nanocarriers of captopril drug; DFT study

Density functional theory (DFT) calculations were performed on M062X/6-31G (d) and M062X/6-311G (d, p) surfaces to investigate the interaction of captopril molecules with single-walled carbon nanotubes (SWCNT) and C32 nanoclusters. In order to enhance adsorption, a doping method was employed, and structures of single-walled boron nitride nanotubes (SWBNNT) and boron nitride nanoclusters (B16N16) were selected for improved drug delivery purposes in this study. The adsorption energy of captopril on the nanostructures was calculated in both phases. In both phases, captopril adsorption energy on nanostructures was calculated. The negative values of adsorption energy showed that the interaction between captopril and nanostructures is exothermic. The adsorption energy values were higher in the gas phase compared to the aqueous phase, indicating a stronger interaction in the gas phase. The density of states (DOS) study was employed to evaluate the effect of molecular adsorption on the electronic properties of nanostructures. The results revealed that the B16N16 nanocluster approached the Fermi level more closely after drug adsorption compared to other nanostructures. Quantum Theory of Atoms in Molecules (QTAIM) calculations showed that there is a weak interaction between captopril and both nanostructures. Based on the adsorption energy values obtained from both methods, the interaction between captopril and SWCNT was found to be stronger than that between captopril and SWBNNT, whereas the interaction in the B16N16 nanocluster was found to be equal to that in C32-fullerene. Significant changes in ΔEg values were observed for Captopril@SWCNT and Captopril@B16N16-fullerene in each method, indicating the conductivity of these two structures increased more after captopril adsorption compared to other nanostructures. Therefore, SWBNNT and B16N16-fullerene can serve as captopril nanosensors.

Exploring Trans Effect Concept in Pt(II) Complexes through the Quantum Theory of Atoms in Molecules and Chemical Bond Overlap Model Perspectives (Adv. Theory Simul. 5/2024)

Exploring <i>Trans</i> Effect Concept in Pt(II) Complexes through the Quantum Theory of Atoms in Molecules and Chemical Bond Overlap Model Perspectives (Adv. Theory Simul. 5/2024)

Circuit Theory Based on New Concepts and Its Application to Quantum Theory

Circuit Theory Based on New Concepts and Its Application to Quantum Theory

Reconstructions of quantum theory: methodology and the role of axiomatization

Reconstructions of quantum theory: methodology and the role of axiomatization

Uncertainty relation and the constrained quadratic programming

The uncertainty relation is a fundamental concept in quantum theory, plays a pivotal role in various quantum information processing tasks. In this study, we explore the additive uncertainty relation pertaining to two or more observables, in terms of their variance, by utilizing the generalized Gell-Mann representation in qudit systems. We find that the tight state-independent lower bound of the variance sum can be characterized as a quadratic programming problem with nonlinear constraints in optimization theory. As illustrative examples, we derive analytical solutions for these quadratic programming problems in lower-dimensional systems, which align with the state-independent lower bounds. Additionally, we introduce a numerical algorithm tailored for solving these quadratic programming instances, highlighting its efficiency and accuracy. The advantage of our approach lies in its potential ability to simultaneously achieve the optimal value of the quadratic programming problem with nonlinear constraints but also precisely identify the extremal state where this optimal value is attained. This enables us to establish a tight state-independent lower bound for the sum of variances, and further identify the extremal state at which this lower bound is realized.