Search Results (222)

We present novel proofs of the Riemann hypothesis by extending the standard complex Riemann zeta function into a quaternionic algebraic framework. Utilizing λ-regularization, we construct a symmetrized form that ensures analytic continuation and restores critical-line reflection symmetry, a key structural property of the Riemann ξ(s) function. This formulation reveals that all nontrivial zeros of the zeta function must lie along the critical line Re(s) = 1/2, offering a constructive and algebraic resolution to this fundamental conjecture. Our method is built on convexity and symmetrical principles that generalize naturally to higher-dimensional hypercomplex spaces. We also explore the broader implications of this framework in quantum statistical physics. In particular, the λ-regularized quaternionic zeta function governs thermodynamic properties and phase transitions in Bose–Einstein condensates. This quaternionic extension of the zeta function encodes oscillatory behavior and introduces critical hypersurfaces that serve as higher-dimensional analogues of the classical critical line. By linking the spectral features of the zeta function to measurable physical phenomena, our work uncovers a profound connection between analytic number theory, hypercomplex geometry, and quantum field theory, suggesting a unified structure underlying prime distributions and quantum coherence. Full article

This article examines a hybrid generation of cryptographic keys, whose novelty lies in the fusion of a multiscale subkey generation with prime sieve and subkeys inspired by quantum mechanics. It combines number theory with techniques emulated and inspired by quantum mechanics, also based on two demons capable of dynamically modifying the cryptographic model. The integration is structured through the JDL. In fact, a specific information fusion model is used to improve security. As a result, the resulting key depends not only on the individual components, but also on the fusion path itself, allowing for dynamic and cryptographically agile configurations that remain consistent with quantum mechanics-inspired logic. The proposed approach, called quantum and prime information fusion (QPIF), couples a simulated quantum entropy source, derived from the numerical solution of the Schrödinger equation, with a multiscale prime number sieve to construct multilevel cryptographic keys. The multiscale sieve, based on recent advances, is currently among the fastest available. Designed to be compatible with classical computing environments, the method aims to contribute to cryptography from a different perspective, particularly during the coexistence of classical and quantum computers. Among the five key generation algorithms implemented here, the ultra-optimised QRNG offers the most effective trade-off between performance and randomness. The results are validated using standard NIST statistical tests. This hybrid framework can also provide a conceptual and practical basis for future work on PQC aimed at addressing the challenges posed by the quantum computing paradigm. Full article

We propose Observer-Linked Branching (OLB), a mathematically rigorous extension of quantum theory in which an observer’s cognitive commitment actively modulates collapse dynamics at macroscopic scales. The OLB framework rests on four axioms, employing a norm-preserving nonlinear Schrödinger evolution and Lüders-type projection triggered by crossing a cognitive commitment threshold. Our expanded formalism provides five main contributions: (1) deriving Lie symmetries of the observer–environment interaction Hamiltonian; (2) embedding OLB into the Consistent Histories and path-integral formalisms; (3) multi-agent network simulations demonstrating intentional synchronisation toward shared macroscopic outcomes; (4) detailed statistical power analyses predicting measurable biases (up to ~5%) in practical experiments involving traffic delays, quantum random number generators, and financial market sentiment; and (5) examining the conceptual, ethical, and neuromorphic implications of intent-driven reality selection. Full reproducibility is ensured via the provided code notebooks and raw data tables in the appendices. While the theoretical predictions are precisely formulated, empirical validation is ongoing, and no definitive field results are claimed at this stage. OLB thus offers a rigorous, norm-preserving and falsifiable framework to empirically test whether cognitive engagement modulates macroscopic quantum outcomes in ways consistent with—but extending—standard quantum predictions. Full article

Longstanding anomalies in the Cosmic Microwave Background (CMB), including the low quadrupole moment and hemispherical power asymmetry, have recently been linked to an underlying parity asymmetry. We show here how this parity asymmetry naturally arises within a quantum framework that explicitly incorporates the construction of a geometric quantum vacuum based on parity ($\mathcal{P}$) and time-reversal ($\mathcal{T}$) transformations. This framework restores unitarity in quantum field theory in curved spacetime (QFTCS). When applied to inflationary quantum fluctuations, this unitary QFTCS formalism predicts parity asymmetry as a natural consequence of cosmic expansion, which inherently breaks time-reversal symmetry. Observational data strongly favor this unitary QFTCS approach, with a Bayes factor, the ratio of marginal likelihoods associated with the model given the data $p\left(M|D\right)$, exceeding 650 times that of predictions from the standard inflationary framework. This Bayesian approach contrasts with the standard practice in the CMB community, which evaluates $p\left(D|M\right)$, the likelihood of the data under the model, which undermines the importance of low-ℓ physics. Our results, for the first time, provide compelling evidence for the quantum gravitational origins of CMB parity asymmetry on large scales. Full article

In his foundational work on classical and quantum electrodynamics, Stueckelberg introduced an external evolution parameter, $\tau$, in order to overcome difficulties associated with the problem of time in relativity. Stueckelberg particle trajectories are described by the evolution of spacetime events under the monotonic advance of $\tau$, the basis for the Feynman–Stueckelberg interpretation of particle–antiparticle interactions. An event is a solution to $\tau$-parameterized equations of motion, which, under simple conditions, including the elimination of pair processes, can be reparameterized by the proper time of motion. The $4+1$ formalism in general relativity (GR) extends this framework to provide field equations for a $\tau$-dependent local metric ${\gamma }_{\mu \nu }(x,\tau )$ induced by these Stueckelberg trajectories, leading to $\tau$-parameterized geodesic equations in an evolving spacetime. As in standard GR, the linearized theory for weak fields leads to a wave equation for the local metric induced by a given matter source. While previous attempts to solve the wave equation have produced a metric with the expected features, the resulting geodesic equations for a test particle lead to unreasonable trajectories. In this paper, we discuss the difficulties associated with the wave equation and set up the more general ADM-like $4+1$ evolution equations, providing an initial value problem for the metric induced by a given source. As in the familiar $3+1$ formalism, the metric can be found as a perturbation to an exact solution for the metric induced by a known source. Here, we propose a metric, ansatz, with certain expected properties; obtain the source that induces this metric; and use them as the initial conditions in an initial value problem for a general metric posed as a perturbation to the ansatz. We show that the ansatz metric, its associated source, and the geodesic equations for a test particle behave as required for such a model, recovering Newtonian gravitation in the nonrelativistic limit. We then pose the initial value problem to obtain more general solutions as perturbations of the ansatz. Full article

In this study, we discuss a series of eight energy scales, some of which are our own speculations, and fit the logarithms of these energies as a straight line versus a quantity related to the dimensionalities of action terms in a way to be defined in the article. These terms in the action are related to the energy scales in question. So, for example, the dimensionality of the Einstein–Hilbert action coefficient is one related to the Planck scale. In fact, we suppose that, in the cases described with quantum field theory, there is, for each of our energy scales, a pair of associated terms in the Lagrangian density, one “kinetic” and one “mass or current” term. To plot the energy scales, we use the ratio of the dimensionality of, say, the “non-kinetic” term to the dimensionality of the “kinetic” one. For an explanation of our phenomenological finding that the logarithm of the energies depends, as a straight line, on the dimensionality defined integer q, we give an ontological—i.e., it really exists in nature in our model—“fluctuating lattice” with a very broad distribution of, say, the link size a. We take the Gaussian in the logarithm, $ln\left(a\right)$. A fluctuating lattice is very natural in a theory with general relativity, since it corresponds to fluctuations in the gauge depth of the field of general relativity. The lowest on our energy scales are intriguing, as they are not described by quantum field theory like the others but by actions for a single particle or single string, respectively. The string scale fits well with hadronic strings, and the particle scale is presumably the mass scale of Standard Model group monopoles, the bound state of a couple of which might be the dimuon resonance (or statistical fluctuation) found in LHC with a mass of 28 GeV. Full article

We review the derivation of the Boltzmann equation and its cosmological applications in this paper. A novel derivation of the Boltzmann equation, especially the collision term, is discussed in detail in the language of quantum field theory without any assumption of a finite temperature system. We also discuss the integrated Boltzmann equation, incorporating the temperature parameter as an extension of the standard equation. Among a number of its cosmological applications, we mainly target two familiar examples, the dynamics of the dark matter abundance through the freeze-out/in process and a baryogenesis scenario. The formulations in those systems are briefly discussed with techniques in their calculations. Full article

Research at the intersection of quantum gravity and quantum information theory has seen significant success in describing the emergence of spacetime and gravity from quantum states whose entanglement entropy approximately obeys an area law. In a different direction, the Kaluza–Klein proposal aims to recover gauge symmetries by means of dimensional reduction in higher-dimensional gravitational theories. Integrating both of these, gravitational and gauge degrees of freedom in $3+1$ dimensions may be obtained upon dimensional reduction in higher-dimensional emergent gravity. To this end, we show that entangled systems of two and three qubits can be associated with $5+1$- and $9+1$-dimensional spacetimes, respectively, which are reduced to $3+1$ dimensions upon singling out a preferred complex direction. Depending on the interpretation of the residual symmetry, either the Standard Model gauge group, $SU\left(3\right)\times SU\left(2\right)\times U\left(1\right)/{\mathbb{Z}}_6$, or the symmetry of Minkowski spacetime together with the gauge symmetry of a right-handed ‘half-generation’ of fermions can be recovered. Thus, there seems to be a natural way to accommodate the chirality of the weak force in the given construction. This motivates a picture in which spacetime emerges from the area law contribution to the entanglement entropy, while gauge and matter degrees of freedom are obtained due to area-law-violating terms. Furthermore, we highlight the possibility of using this construction in quantum simulations of Standard Model fields. Full article

We pose and address the radical question of whether quantum mechanics, known for its firm internal structure and enormous empirical success, carries in itself the genomes of larger quantum theories that have higher internal intricacy and phenomenological versatility. In other words, we consider, at the basic level of closed quantum systems and regardless of interpretational aspects, whether standard quantum theory (SQT) harbors quantum theories with context-based deformed principles or structures, having definite predictive power within much broader scopes. We answer this question in the affirmative following complementary evidence and reasoning arising from quantum-computation-based quantum simulation and fundamental, general, and abstract rationales within the frameworks of information theory, fundamental or functional emergence, and participatory agency. In this light, as we show, one is led to the recently proposed experience-centric quantum theory (ECQT), which is a larger and richer theory of quantum behaviors with drastically generalized quantum dynamics. ECQT allows the quantum information of the closed quantum system’s developed state history to continually contribute to defining and updating the many-body interactions, the Hamiltonians, and even the internal elements and “particles” of the total system. Hence, the unitary evolutions are continually impacted and become guidable by the agent system’s experience. The intrinsic interplay of unitarity and non-Markovianity in ECQT brings about a host of diverse behavioral phases, which concurrently infuse closed and open quantum system characteristics, and it even surpasses the theory of open systems in SQT. From a broader perspective, a focus of our investigation is the existence of the quantum interactome—the interactive landscape of all coexisting, independent, context-based quantum theories that emerge from inferential participatory agencies—and its predictive phenomenological utility. Full article

The exact response theory based on the Dissipation Function applies to general dynamical systems and has yielded excellent results in various applications. In this article, we propose a method to apply it to quantum mechanics. In many quantum systems, it has not yet been possible to overcome the perturbative approach, and the most developed theory is the linear one. Extensions of the exact response theory developed in the field of nonequilibrium molecular dynamics could prove useful in quantum mechanics, as perturbations of small systems or far-from-equilibrium states cannot always be taken as small perturbations. Here, we introduce a quantum analogue of the classical Dissipation Function. We then derive a quantum expression for the exact calculation of time-dependent expectation values of observables, in a form analogous to that of the classical theory. We restrict our analysis to finite-dimensional Hilbert spaces, for the sake of simplicity, and we apply our method to specific examples, like qubit systems, for which exact results can be obtained by standard techniques. This way, we prove the consistency of our approach with the existing methods, where they apply. Although not required for open systems, we propose a self-adjoint version of our Dissipation Operator, obtaining a second equivalent expression of response, where the contribution of an anti-self-adjoint operator appears. We conclude by using new formalism to solve the Lindblad equations, obtaining exact results for a specific case of qubit decoherence, and suggesting possible future developments of this work. Full article

In the framework of quasi-Hermitian quantum mechanics, the eligible operators of observables may be non-Hermitian, $A_j\ne A_j^{†}$, $j=1,2,\dots ,K$. In principle, the standard probabilistic interpretation of the theory can be re-established via a reconstruction of physical inner-product metric $\mathsf{\Theta }\ne I$, guaranteeing the quasi-Hermiticity $A_j^{†}\mathsf{\Theta }=\mathsf{\Theta }{A}_j$. The task is easy at $K=1$ because there are many eligible metrics $\mathsf{\Theta }=\mathsf{\Theta }\left(A_1\right)$. In our paper, the next case with $K=2$ is analyzed. The criteria of the existence of a shared metric, $\mathsf{\Theta }=\mathsf{\Theta }(A_1,A_2)$, are presented and discussed. Full article

In this study, we employed density functional theory (DFT), a standard method in quantum chemistry, to investigate the structural intricacies of thioether-linked naphthalene-based liquid-crystal dimers. The theoretical analysis included the calculation of the molecular bend angle, a crucial factor influencing the formation of the twist–bend nematic (N_TB) phase, as well as other molecular parameters such as transition dipole moments, bond lengths, and bond energies. These calculations allowed for the determination of the probable conformations and the computation of their vibrational spectra, which are essential for interpreting experimental spectra. Connecting these insights, we identified stable conformations and observed differences in the spectra between the conventional nematic (N) and N_TB phases. The combined DFT calculations and infrared absorbance measurements allowed us to investigate the structure and intermolecular interactions of molecules in the N and N_TB phases of the dimers. Notably, significant changes in average absorbance were detected in the experimental spectra in the N_TB phase. During the transition from the N phase to the N_TB phase, a clear decrease in absorbance for longitudinal dipoles and an increase for transverse dipoles were observed. This phenomenon suggests that longitudinal dipoles are antiparallel, while transverse dipoles are parallel. To verify the influence of nearest-neighbor interactions, DFT calculations were conducted on a system comprising several neighboring molecules. Full article

Alzheimer’s disease (AD), one of the neurodegenerative disorders, afflicts negatively across the whole world. Due to its complex etiology, no available treatments are disease-altering. This study aimed to explore isolated saponins profiles from Platycodon grandiflorum in the binding pockets of six target proteins of AD using computational and quantum chemistry simulations. Initially, saponin compounds were docked to AD enzymes, such as GSK-3β and synapsin I, II, and III. The subsequent research from MD simulations of the best three docked compounds (polygalacin D2, polygalacin D, and platycodin D) suggested that their profiles match with the binding of standard active drugs like ifenprodil and donepezil to the six enzymes. Moreover, analyzing DFT quantum calculations of top-scoring compounds fully unravels their electronic and quantum properties and potential in anti-AD. The subtle differences between polygalacin D and D2, and platycodin D, were studied at the level of theory DFT/B3LYP, showing that the electron-donating effect of the hydroxy ethyl group in platycodin D rendering this compound of moderate electrophilicity and reactivity. Polygalacin D2 diglucoside substituent in position-2 contributed to its best binding and intermolecular interactions more than polygalacin D and prosapogenin D, which acted as the negative decoy drug. Full article

This manuscript introduces a comprehensive framework for augmenting classical statistical methodologies through the targeted integration of core quantum mechanical principles—specifically superposition, entanglement, measurement, wavefunctions, and density matrices. By concentrating on these foundational concepts instead of the whole expanse of quantum theory, we propose “quantum-inspired” models that address persistent shortcomings in conventional statistical approaches. In particular, five pivotal distributions (normal, binomial, Poisson, Student’s t, and chi-square) are reformulated to incorporate interference terms, phase factors, and operator-based transformations, thereby facilitating the representation of multimodal data, phase-sensitive dependencies, and correlated event patterns—characteristics that are frequently underrepresented in purely real-valued, classical frameworks. Furthermore, ten quantum-inspired statistical principles are delineated to guide practitioners in systematically adapting quantum mechanics for traditional inferential tasks. These principles are illustrated through domain-specific applications in finance, cryptography (distinct from direct quantum cryptography applications), healthcare, and climate modeling, demonstrating how amplitude-based confidence measures, density matrices, and measurement analogies can enrich standard statistical models by capturing more nuanced correlation structures and enhancing predictive performance. By unifying quantum constructs with established statistical theory, this work underscores the potential for interdisciplinary collaboration and paves the way for advanced data analysis tools capable of addressing high-dimensional, complex, and dynamically evolving datasets. Complete R code ensures reproducibility and further exploration. Full article

In spite of its unbroken PT symmetry, the popular imaginary cubic oscillator Hamiltonian $H^{\left(IC\right)}=p^2+\mathrm{i}{x}^3$ does not satisfy all of the necessary postulates of quantum mechanics. This failure is due to the “intrinsic exceptional point” (IEP) features of $H^{\left(IC\right)}$ and, in particular, to the phenomenon of a high-energy asymptotic parallelization of its bound-state-mimicking eigenvectors. In this paper, it is argued that the operator $H^{\left(IC\right)}$ (and the like) can only be interpreted as a manifestly unphysical, singular IEP limit of a hypothetical one-parametric family of certain standard quantum Hamiltonians. For explanation, ample use is made of perturbation theory and of multiple analogies between IEPs and conventional Kato’s exceptional points. Full article