Search Results (120)

Traditional brain emulation approaches often rely on classical computational models that inadequately capture the stochastic, nonlinear, and potentially coherent features of biological neural systems. In this position paper, we introduce NeuroQ a quantum-inspired framework grounded in stochastic mechanics, particularly Nelson’s formulation. By reformulating the FitzHugh–Nagumo neuron model with structured noise, we derive a Schrödinger-like equation that encodes membrane dynamics in a quantum-like formalism. This formulation enables the use of quantum simulation strategies—including Hamiltonian encoding, variational eigensolvers, and continuous-variable models—for neural emulation. We outline a conceptual roadmap for implementing NeuroQ on near-term quantum platforms and discuss its broader implications for neuromorphic quantum hardware, artificial consciousness, and time-symmetric cognitive architectures. Rather than demonstrating a working prototype, this work aims to establish a coherent theoretical foundation for future research in quantum brain emulation. Full article

A reduced representation of a dynamical system helps us to understand what the true degrees of freedom of that system are and thus what the possible instabilities are. Here we extend previous work on barotropic flows to the more general non-barotropic flow case and study the implications for variational analysis and conserved quantities of topological significance such as circulation and helicity. In particular we introduce a four-function Eulerian variational principle of non-barotropic flows, which has not been described before. Also new conserved quantities of non-barotropic flows related to the topological velocity field, topological circulation and topological helicity, including a local version of topological helicity, are introduced. The variational formalism given in terms of a Lagrangian density allows us to introduce canonical momenta and hence a Hamiltonian formalism. Full article

A formalism for the systematic construction of integrable non-autonomous deformations of soliton hierarchies is presented. The theory is formulated as an initial value problem (IVP) for an associated Frobenius integrability condition on a Lie algebra. It is shown that this IVP has a formal solution, and within the framework of two particular subalgebras of the hereditary Lie algebra, the explicit forms of this formal solution are derived. Finally, this formalism is applied to the Korteveg-de Vries, dispersive water waves and Ablowitz–Kaup–Newell–Segur soliton hierarchies. The zero-curvature representations and Hamiltonian structures of the considered non-autonomous soliton hierarchies are also provided. 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

We address the problem of routing quantum and classical information from one sender to many possible receivers in a network. By employing the formalism of quantum walks, we describe the dynamics on a discrete structure based on a complete graph, where the sites naturally provide a basis for encoding the quantum state to be transmitted. Upon tuning a single phase or weight in the Hamiltonian, we achieve near-unitary routing fidelity, enabling the selective delivery of information to designated receivers for both classical and quantum data. The structure is inherently scalable, accommodating an arbitrary number of receivers. The routing time is largely independent of the network’s dimension and input state, and the routing performance is robust under static and dynamic noise, at least for a short time. Full article

The Stroh sextic formalism, developed by Stroh, offers a compelling framework for representing the equilibrium equations in anisotropic elasticity. This approach has proven particularly effective for studying multilayered structures and time-harmonic problems, owing to its ability to seamlessly integrate physical constraints into the analysis. By recognizing that the Stroh formalism aligns with the canonical Hamiltonian structure, this work extends its application to Biot’s poroelasticity, focusing on scenarios where the solid material is incompressible and there is no fluid pressure gradient. The study introduces a novel Hamiltonian-based approach to analyze such systems, offering deeper insights into the interplay between solid incompressibility and fluid–solid coupling. A key novelty lies in the derivation of canonical equations under these constraints, enabling clearer interpretations of reversible poroelastic behavior. However, the framework assumes perfectly drained conditions and neglects dissipative effects, which limits its applicability to fully realistic scenarios involving energy loss or complex fluid dynamics. Despite this limitation, the work provides a foundational step toward understanding constrained poroelastic systems and paves the way for future extensions to more general cases, including dissipative and nonlinear regimes. Full article

Entropic Dynamics (ED) provides a framework that allows the reconstruction of the formalism of quantum mechanics by insisting on ontological and epistemic clarity and adopting entropic methods and information geometry. Our present goal is to extend the ED framework to account for spin. The result is a realist $\psi$-epistemic model in which the ontology consists of a particle described by a definite position plus a discrete variable that describes Pauli’s peculiar two-valuedness. The resulting dynamics of probabilities is, as might be expected, described by the Pauli equation. What may be unexpected is that the generators of transformations—Hamiltonians and angular momenta, including spin, are all granted clear epistemic status. To the old question, ‘what is spinning?’ ED provides a crisp answer: nothing is spinning. Full article

This review discusses two triatomic Hamiltonians and their applications to some non-adiabatic spectroscopic and collision problems. Carter and Handy in 1984 presented the first Hamiltonian in bond lengths–bond angle coordinates, that is here applied for studying the NO₂ spectroscopy: vibronic states, internal dynamics, and interaction with the radiation due to the $\tilde{\mathrm{X}}$²A′(A₁)−$\tilde{\mathrm{A}}$²A′(B₂) conical intersection. The second Hamiltonian was reported by Tennyson and Sutcliffe in 1983 in Jacobi coordinates and is here employed in the study of the Kr + OH(A²Σ⁺) electronic quenching due to conical intersection and Renner–Teller interactions among the 1²A′, 2²A′, and 1²A″ electronic species. Within the non-relativistic approximation and the expansion method in diabatic electronic representations, the formalism is exact and allows a unified study of various non-adiabatic interactions between electronic states. The rotation, inversion, and nuclear permutation symmetries are considered for defining rovibronic representations, which are symmetry adapted for ABC and AB₂ molecules, and the matrix elements of the Hamiltonians are then computed. Full article

Purpose in systems is considered to be beyond the purview of science since it is thought to be intrinsically personal. However, just as Claude Shannon was able to define an impersonal measure of information, so we formally define the (impersonal) ‘entropic purpose’ of an information system (using the theoretical apparatus of Quantitative Geometrical Thermodynamics) as the line integral of an entropic “purposive” Lagrangian defined in hyperbolic space across the complex temporal plane. We verify that this Lagrangian is well-formed: it has the appropriate variational (Euler-Lagrange) behaviour. We also discuss the teleological characteristics of such variational behaviour (featuring both thermodynamically reversible and irreversible temporal measures), so that a “Principle of Least (entropic) Purpose” can be adduced for any information-producing system. We show that entropic purpose is (approximately) identified with the information created by the system: an empirically measurable quantity. Exploiting the relationship between the entropy production of a system and its energy Hamiltonian, we also show how Landauer’s principle also applies to the creation of information; any purposive system that creates information will also dissipate energy. Finally, we discuss how ‘entropic purpose’ might be applied in artificial intelligence contexts (where degrees of system ‘aliveness’ need to be assessed), and in cybersecurity (where this metric for ‘entropic purpose’ might be exploited to help distinguish between people and bots). Full article

The covariant Hamilton–Jacobi formulation of electrodynamics is systematically derived from the first-order (Palatini-like) Lagrangian. This derivation utilizes the De Donder–Weyl covariant Hamiltonian formalism with constraints incroporating generalized Dirac brackets of forms and the associated polysymplectic reduction, which ensure manifest covariance and consistency with the field dynamics. It is also demonstrated that the canonical Hamilton–Jacobi equation in variational derivatives and the Gauss law constraint are derived from the covariant De Donder–Weyl Hamilton–Jacobi formulation after space + time decomposition. Full article

The spin Hall effect for the model Hamiltonian of graphene with Rashba spin–orbit coupling is analyzed by means of a recently derived quantum kinetic theory of the linear response for multi-band electron systems. The latter expresses the interband part of the density matrix in terms of the intraband occupation numbers, which can be obtained as solutions of a Boltzmann transport equation. The analysis, which, in the case of the model here considered, can be carried out in a completely analytical way, thus provides an effective pedagogical illustration of the general theory. While our results agree with those previously obtained with alternative approaches for the same model, our comparatively simpler and more physically transparent derivation illustrates the advantages of our formalism when dealing with non trivial multi-band Hamiltonians. Full article

To investigate the gravitational effects of massive objects on a typical observer, we studied the dynamics of a test particle following ${\mathrm{BMS}}_3$ geodesics. We constructed the ${\mathrm{BMS}}_3$ framework using the canonical phase space formalism and the corresponding Hamiltonian. We focused on analyzing these effects at fine scales of spacetime, which led us to quantization of the phase space. By deriving and studying the solutions of the quantum equations of motion for the test particle, we obtained its energy spectrum and explored the behavior of its wave function. These findings offer a fresh perspective on gravitational interactions in the context of quantum mechanics, providing an alternative approach to traditional quantum field theory analyses. Full article

In this work, we study the time-dependent behavior of quantum correlations of a system of an inverted oscillator governed by out-of-equilibrium dynamics using the well-known Schwinger–Keldysh formalism in the presence of quantum mechanical quench. Considering a generalized structure of a time-dependent Hamiltonian for an inverted oscillator system, we use the invariant operator method to obtain its eigenstate and continuous energy eigenvalues. Using the expression for the eigenstate, we further derive the most general expression for the generating function as well as the out-of-time-ordered correlators (OTOCs) for the given system using this formalism. Further, considering the time-dependent coupling and frequency of the quantum inverted oscillator characterized by quench parameters, we comment on the dynamical behavior, specifically the early, intermediate and late time-dependent features of the OTOC for the quenched quantum inverted oscillator. Next, we study a specific case, where the system of an inverted oscillator exhibits chaotic behavior by computing the quantum Lyapunov exponent from the time-dependent behavior of OTOCs in the presence of the given quench profile. Full article

Concentric multiple nanorings have previously been fabricated and investigated mainly for their different static magnetization states. Here, we present a theoretical analysis for the magnetization dynamics in double nanorings arranged concentrically, where there is coupling across a nonmagnetic spacer due to the long-range dipole–dipole interactions. We employ a microscopic, or Hamiltonian-based, formalism to study the discrete spin waves that exist in the magnetic states where the individual rings may be in either a vortex or an onion state. Numerical results are shown for the frequencies and the spatial amplitudes (with relative phase included) of the spin-wave modes. Cases are considered in which the magnetic materials of the rings are the same (taken to be permalloy) or two different materials such as permalloy and cobalt. The dependence of these properties on the mean radial position of the spacer were studied, showing, in most cases, the existence of two distinct transition fields. The special cases, where the radial spacer width becomes very small (less than 1 nm) were analyzed to study direct interfaces between dissimilar materials and/or effects of interfacial exchange interactions such as Ruderman–Kittel–Kasuya–Yoshida coupling. These spin-wave properties may be of importance for magnetic switching devices and sensors. Full article

This paper presents an analysis of the Hamiltonian formulation for continuous systems with second-order derivatives derived from Dirac’s theory. This approach offers a unique perspective on the equations of motion compared to the traditional Euler–Lagrange formulation. Focusing on Podolsky’s generalized electrodynamics, the Hamiltonian and corresponding equations of motion are derived. The findings demonstrate that both Hamiltonian and Euler–Lagrange formulations yield equivalent results. This study highlights the Hamiltonian approach as a valuable alternative for understanding the dynamics of second-order systems, validated through a specific application within generalized electrodynamics. The novelty of the research lies in developing advanced theoretical models through Hamiltonian formalism for continuous systems with second-order derivatives. The research employs an alternative method to the Euler–Lagrange formulas by applying Dirac’s theory to study the generalized Podolsky electrodynamics, contributing to a better understanding of complex continuous systems. Full article