In this work, we investigate the effects of a controlled conical geometry on the electric charge transport through a two-dimensional quantum ring weakly coupled to both the emitter and the collector. These mesoscopic systems are known for being able to confine highly mobile electrons in a defined region of matter. In particular, we consider a GaAs device having an average radius of 800 nm in different regimes of subband occupation at non-zero temperature and under the influence of a weak and uniform background magnetic field. Using an adapted Landauer formula for resonant tunneling together with the corresponding energy eigenvalues we explore how the modified surface affects the Van-Hove conductance singularities, the magnetoresistance interference patterns resulting from the Aharonov-Bohm oscillations of different frequencies and the charge transport when an electric potential is applied to the terminals of the device. Magnetoresistance and charge current oscillations depending only on the curvature intensity are reported, providing a new feature that represents an alternative way to optimize the transport through the device by tuning its geometry. • Conical curvature reshapes the transport spectrum of a 2D GaAs quantum ring. • Geometry tunes Van Hove conductance peaks and Aharonov–Bohm interference patterns. • Magnetoresistance exhibits curvature-controlled oscillations, including stable node regimes. • A nearly periodic magnetoresistance modulation with curvature is identified at zero field. • The charge current shows geometry-driven oscillations and a sawtooth-like behavior at high bias.

Abstract We introduce color Heisenberg-Lie (super)algebras graded by the abelian groups Z 3 2 , Z 2 p × Z 3 2 for p = 1 , 2 , 3 , and investigate the properties of their associated multi-particle quantum paraoscillators. In the Rittenberg–Wyler’s color Lie (super)algebras framework the above abelian groups are the simplest ones which induce mixed brackets interpolating commutators and anticommutators. These mixed brackets allow to accommodate two types of parastatistics: one based on the permutation group (beyond bosons and fermions in any space dimension) and an anyonic parastatistics based on the braid group. In both such cases the two broad classes of paraparticles are given by parabosons and parafermions. Mixed-bracket parafermions are created by nilpotent operators; they satisfy a generalized Pauli exclusion principle leading to roots-of-unity truncations in their multi-particle energy spectrum (braided Majorana qubits and their Gentile-type parastatistics are recovered in this color Lie superalgebra setting). Mixed-bracket parabosons do not admit truncations of the spectrum; the minimal detectable signature of their parastatistics is encoded in the measurable probability density of two indistinguishable parabosonic oscillators in a given energy eigenstate.

Calculations of Ground-State Energy Eigenvalues in Hadron Physics with Quantum Simulation

The influence of point-like global monopole topological defects on the fractional energy eigenvalues of the exponential Kratzer–Fues potential model has been evaluated in this study. By solving the radial Schrödinger equation, an improved approximation scheme has been used to check the centrifugal barrier term. The fractional energy solutions obtained are varied with different quantum states, fractional parameters and topological defects, for selected hydrogen-related diatomic molecules. The fractional energy eigenvalues of eKFP are seen to follow a positive shift pattern for the selected diatomic molecules. These phenomena are significantly sponsored by the global effects of the point like global monopole and fractional parameter values considered in the curved space-time. Vibrational energy spectra obtained as a special case in the Minkowski space-time is employed to study some thermochemical functions with temperature variation. Our results can model the experimental data of the thermochemical functions in literature for the selected hydrogen-related diatomic molecules. Negligible deviations computed are within acceptable range and their graphically consideration are presented to support our findings.

The human neocortex is functionally organised at its highest level along a continuous sensory-to-association (AS) hierarchy. This study investigates two questions-how this hierarchy is structurally altered in schizophrenia, and what these alterations imply for neural dynamics and cognitive computation. Using a large fMRI dataset (N = 355), we extracted individual AS gradients via spectral analysis of brain connectivity and quantified hierarchical organisation by the gradient range. Schizophrenia showed a compressed AS hierarchy, indicating reduced functional differentiation. Estimating neural timescale (autocorrelation decay constant) with the Ornstein-Uhlenbeck process, we observed that the most specialised, locally cohesive regions at the gradient extremes exhibit longer timescales, an empirical spatiotemporal mapping that is attenuated in schizophrenia. To probe the computational consequences of this compression, we used the gradients to regularise subject-specific recurrent neural networks (RNNs) trained on working memory tasks. Networks endowed with greater gradient range learned more efficiently, plateaued at lower task loss, and maintained stronger alignment to the prescribed AS hierarchical geometry. Fixed-point linearisation showed that high-range networks settled into more stable neural states during memory delay, evidenced by lower energy and smaller maximal Jacobian eigenvalues. This gradient-regularised RNN framework thereby links large-scale cortical architecture with fixed point stability, providing a computational hypothesis that AS gradient de-differentiation can destabilise neural computations in schizophrenia, convergently supported by empirical timescale flattening along AS gradient and model-based evidence of less stable fixed points.

Abstract A common intuition in introductory physics is that confinement of a charged particle necessarily implies acceleration and hence electromagnetic radiation. In this paper, we examine this intuition by directly comparing the radiative behavior of a charged particle confined to a one-dimensional box within classical and quantum frameworks. While classical electrodynamics predicts unavoidable radiation due to impulsive accelerations at rigid boundaries, quantum mechanics yields a strikingly different result: a charged particle prepared in a stationary energy eigenstate does not radiate. By analyzing expectation values, dipole moments, and Ehrenfest's theorem, we show that identical boundary conditions lead to qualitatively different physical predictions. A quantitative extension involving superposition states demonstrates how radiation reappears when observables become time dependent. The classical-quantum contrast provides a clear pedagogical illustration of the limits of classical intuition and correspondence in confined systems.

ABSTRACT This study introduces a hybrid analytical–machine learning framework for solving the Schrödinger equation with complex potentials. The semi‐inverse variational method is first used to generate highly accurate eigenfunctions and eigenenergies for both 1D radial potentials (Yukawa and Cornell) and a 2D coupled anharmonic oscillator. Based on these rigorous, physics‐consistent results, we train supervised machine learning models; including Random Forest and Neural Network regressors; to predict energy eigenvalues across wide parameter ranges. Both models achieve near‐perfect predictive accuracy (R 2 > 0.999) with errors of only a few millielectronvolts, while preserving fundamental quantum‐mechanical trends. Feature importance analysis confirms that the quantum number n and potential strength parameters dominate the energy scaling, in agreement with theoretical expectations. By integrating variational physics with data‐driven emulation, this hybrid framework reduces computational cost by orders of magnitude; enabling rapid, high‐throughput exploration of quantum systems across dimensions. The approach not only accelerates parameter screening but also serves as a discovery tool, uncovering emergent scaling laws and critical confinement behavior in mixed potentials. This synergy between analytical rigor and machine learning efficiency opens new pathways for quantum simulation, materials design, and the discovery of novel quantum phenomena.

By using the radial Schrödinger equation with the Morse potential in the context of the generalized fractional derivative (GFD), this work provides an important improvement in modelling the vibrational energy spectrum of diatomic molecules. We have used the generalized fractional Nikiforov-Uvarov (GFNU) method to derive an analytical solution for the energy eigenvalues in D-dimensional space by applying the Pekeris-type approximation to the centrifugal term. The proposed model is thoroughly examined across many electronic states, using a diverse set of twenty-two diatomic molecules, including astrophysically important species like SiO[Formula: see text] and TaO, as well as CO, Na[Formula: see text], and AlH. The potential energy curves for the selected diatomic molecules have been produced using the Morse potential with the help of molecular constants. Furthermore, the pure vibrational energy levels for several diatomic molecules have been computed in both classical and fractional models. Our calculated vibrational energies are consistent with the Rydberg-Klein-Rees (RKR) data and previous studies. Additionally, it is seen that the vibrational energy spectra of different diatomic molecules calculated with fitted fractional parameters are improved compared to those obtained in the classical case for modelling the observed RKR data. The analysis of absolute percentage deviations at each level indicates that, for all examined diatomic molecules, the fractional derivative framework produces smaller and more consistent vibrational energy errors compared to the classical limit as the quantum number increases. Consequently, this study provides strong evidence that the GFNU method is a reliable and accurate technique to obtain the pure vibrational energies of various diatomic molecules.

The fluctuation–dissipation theorem (FDT) is a fundamental result in statistical mechanics. It stipulates that, if perturbed out of equilibrium, a system responds at a rate proportional to a thermal-equilibrium property. Applications range from particle diffusion to electrical-circuit noise. To prove the FDT, one must prove that common thermal states obey a symmetry property, the Kubo–Martin–Schwinger (KMS) relation. Energy eigenstates of certain quantum many-body systems were recently proven to obey a KMS relation. The proof relies on the eigenstate thermalization hypothesis (ETH), which explains how such systems thermalize internally. This KMS relation contains a finite-size correction that scales as the inverse system size. Non-Abelian symmetries conflict with the ETH, so a non-Abelian ETH was proposed recently. Using it, we derive a KMS relation for SU(2)-symmetric quantum many-body systems’ energy eigenstates. The finite-size correction scales as usual under certain circumstances but can be polynomially larger in others, we argue. We support the ordinary-scaling result numerically, simulating a Heisenberg chain of 16–24 qubits. The numerics, limited by computational capacity, indirectly support the larger correction. This work helps extend into nonequilibrium physics the effort, recently of interest across quantum physics, to identify how non-Abelian symmetries may alter conventional thermodynamics.

Efficiently estimating energy expectation values of quantum lattice systems on quantum computers is a crucial subroutine for various quantum algorithms, which can lead to significant overhead due to the high measurement shot numbers required. We introduce a measurement strategy tailored to quantum lattice systems and (noisy) energy eigenstates. It is based on a geometric partitioning of the Hamiltonian into local patches and performing the measurements in the eigenbases of those patches. The resulting energy estimator has a smaller variance than the ones of Pauli grouping schemes, which leads to a reduction of the total number of shots. We provide rigorous guarantees for this variance improvement for energy eigenstates, also in the presence of depolarizing noise. As one can choose the subsystem size, one can ensure that measurement circuits remain within implementable depths. In numerical experiments, we demonstrate the shot count reduction for various 2D lattice models, including the transverse field XY and Ising models, as well as the Fermi-Hubbard model. We find sampling improvements of several orders of magnitude already for plaquettes of two by two qubits, where the required readout circuits remain very moderate in depth.

We study the influence of the Aharonov-Bohm quantum phase on a quantum system described by a non-Hermitian Hamiltonian. We show that a non-Hermitian Hamiltonian has real energy eigenvalues which are influenced by the Aharonov-Bohm quantum phase. In addition, we show that persistent currents can arise. Finally, we calculate the revival times in this two-dimensional system and show that they are influenced by Aharonov-Bohm quantum phase.

This study presents a comprehensive analysis of the two-body central-interaction problem in quantum mechanics. We investigate the Schrödinger equation for two particles interacting through a central potential, and derive the radial and angular parts of the wave function. The energy eigenvalues and Eigen functions are obtained for various central potentials, including the Coulomb, harmonic oscillator, and square well potentials.

In quantum mechanics, the Schrieffer–Wolff (SW) transformation (also called quasi-degenerate perturbation theory) is known as an approximative method to reduce the dimension of the Hamiltonian. We present a geometric interpretation of the SW transformation: We prove that it induces a local coordinate chart in the space of Hermitian matrices near a k -fold degeneracy submanifold. Inspired by this result, we establish a `distance theorem': we show that the standard deviation of k neighboring eigenvalues of a Hamiltonian equals the distance of this Hamiltonian from the corresponding k -fold degeneracy submanifold, divided by k . Furthermore, we investigate one-parameter perturbations of a degenerate Hamiltonian, and prove that the standard deviation and the pairwise differences of the eigenvalues lead to the same order of splitting of the energy eigenvalues, which in turn is the same as the order of distancing from the degeneracy submanifold. As applications, we prove the `protection' of Weyl points using the transversality theorem, and infer geometrical properties of certain degeneracy submanifolds based on results from quantum error correction and topological order.

In this work, we solve the Schrödinger equation for a hydrogenic impurity located at the apex of a right circular cone, with the electron constrained to move on the conical surface of semi-aperture angle and subjected to an Aharonov–Bohm magnetic flux along the symmetry axis. Analytical expressions for the energy eigenvalues and normalized radial wave functions are obtained in terms of the principal quantum number n and the angular quantum number m, the magnetic flux , and the cone angle. The Shannon entropy is evaluated in both configuration and momentum spaces for several low-lying states, and its variation with and is analyzed in detail. When the magnetic flux vanishes, pairs of states and share the same entropic behavior; for finite flux, this degeneracy is lifted and the entropies depend explicitly on the state, the cone geometry, and the flux strength. Finally, we verify that the entropic sum fulfills the Bialynicki-Birula–Mycielski bound, providing an information-theoretic consistency check for the model.

In this paper we study transitions of atoms between energy levels of several number-theory-inspired trapping potentials under the effect of time-dependent perturbations. First, we simulate in detail the case of a trap whose single-particle spectrum is given by the prime numbers. We investigate one-body Rabi oscillations and the excitation line shape for two resonantly coupled energy levels, and we show that quantum control is a faster method for state preparation than periodic perturbation. Next, we investigate cascades of such transitions, particularly whether one can construct a quantum system where the existence of a continuous resonant cascade from a given initial energy eigenstate is predicated by the validity of a given statement in number theory. We find that such resonance cascades, in a suitably designed one-body system, can be used to illustrate that the sequence of natural numbers is closed under multiplication. We further present ideas for two more resonance cascade experiments designed to illustrate certain statements within the Diophantus-Brahmagupta-Fibonacci identity and the Goldbach conjecture.

We study the possibility of discriminating between metric theories within the Parametrized Post-Newtonian formalism. In this approach, the two-dimensional quantum state of a massive quantum clock becomes, after propagating at low speed and in a weak gravitational field, a function of the post-Newtonian parameters and thus a signature of a metric theory. To discriminate among metric theories, we resort to quantum-state discrimination strategies such as minimum-error and unambiguous discrimination. In particular, we show that it is possible to refute the hypothesis that a particular metric theory describes spacetime with a single detection event and that it is possible to discriminate with certainty between two different metrics, also with a single detection event. In general, the success probability of the discrimination strategy is a harmonic function of the product of the difference of the proper time corresponding to each quantum clock state, the energy difference between the energy eigenstates of the quantum clock, the propagation length, and speed. It is thus possible to find suitable length and speed scales such that the success probability is close to one by selecting a quantum system with the highest energy difference and the longest natural lifetime. According to this, atomic nuclei such as thorium are considered the most suitable quantum clocks. We also show that the use of a ensemble of quantum clocks leads to a significant increase in the probability of success in discriminating between post-Newtonian parameters that differ by $10^{-5}$. This facilitates achieving a probability of success approaching unity with distances on the scale of several kilometers and velocities approximating one-thousandth of the speed of light for a ensemble of only 10 quantum clocks.

Abstract Twisted cylindrical tubes are important model systems for nanostructures, heterostructures, and curved quantum devices. In this work, we investigate the quantum behavior of an electron confined to a twisted cylindrical surface. By first calculating the strain tensor to obtain the induced surface metric, we employ da Costa’s formalism to derive the geometry-induced quantum potential. This potential modifies the Schrödinger equation even in the absence of external forces, allowing us to determine the bound states and energy eigenvalues. This was made in the linear and non-linear torsion regime. Furthermore, we analyze two distinct scattering problems: (i) scattering within an infinite cylinder containing a twisted section, and (ii) scattering of a free particle incident upon a finite twisted cylinder. Our goal is to understand how geometry and strain influence the properties of analogous untwisted systems. It turns out that both the linear and non-linear twists yield a geometric phase into the wave function, while the da Costa potential is kept unchanged. Consequently, the system supports bound states whose energie spectrum is twist independent. For both scattering problems, we find that the transmission probability is insensitive to torsion, whereas it is significantly affected by the particle angular momentum and the cylinder’s radius, exhibiting distinct oscillatory behavior. These findings suggest relevant implications for engineering quantum devices based on materials with controlled curvature and twist.

Berry monopoles always cancel when summing over a complete set of energy eigenstates. We demonstrate that analogous sum rules exist for geometric phases and their underlying 2-forms in non-adiabatic evolution. Our result has implications for qudit computation as it limits the types of gates that can be implemented by purely geometric means.

Abstract Anomalies in the characteristic x-ray spectra of 3 d transition metals, particularly in lineshape, linewidth, and intensity ratios, have long motivated detailed investigation. We present the first accurate ab initio study of the zinc K β spectrum, using multiconfiguration Dirac–Hartree–Fock. We predict the zinc K β spectrum, including the K β 1 , 3 diagram doublet together with the dominant satellite transition manifolds for the first time, from [ 4 s ] , [ 3 d ] , [ 3 p ] , and [ 3 s ] single shake-off, as well as [ 3 d 2 ] double shake-off. Such features cannot be resolved by experiment as proven by the literature over several decades. We investigate two novel active space approaches. New convergence metrics are questioned and assessed for energy eigenvalues, gauge ratios A L / A V , transition A coefficients, and a newly developed Σ metric. We achieve energy eigenvalue convergence within 0.03 eV, gauge ratios A L / A V within 0.6%, convergence of transition A coefficients within 0.03% to 0.23%, and convergence of the Σ-metric to within 0.1% to 6.1%. Ab initio shake probabilities are used to quantify satellite contributions to experiment for the first time for zinc. Sequential inclusion of satellite components was evaluated in comparison with the most accurate data available, showing that all dominant shake transitions are required for an accurate description. Incorporating these satellites yields excellent agreement with experiment.

Abstract In the quantum infinite square well with hard walls at x = 0 and L the energy eigenvalues are proportional to ϵ n 2 , where ϵ n = n is a dimensionless reduced wave number. We examine how the values of ϵ n are modified by the addition of one or more Dirac delta barriers, scaled so that the probability T for a particle to transmit through the barrier is not dependent on the particle’s energy. If the barriers are placed at rational locations x = iL / D , where D > 1 is an integer common denominator and i is any integer such that 0 < i < D , then ϵ n follows a pattern that repeats every D values. Once the first D values of ϵ n are found, all other values follow from this pattern. Analytical solutions for ϵ n are derived for D = 2 and 3. Numerical solutions for D = 7 are shown to illustrate phenomena such as band structure, defects, and avoided crossings. When the barriers are placed at irrational locations there is no repeating pattern, but a finite sequence of ϵ values can be well-approximated by using results with the barriers placed at rational approximations of the irrational locations. Because this system admits analytical solutions, or numerical solutions obtained with minimal effort, it could serve as the basis for interesting exercises or projects in undergraduate or beginning graduate courses in quantum mechanics.