Adiabatic Limit Research Articles

Determination of electron screening potential of 6Li(p, [formula omitted])3He reaction using Multi Layer Perceptron based neural network

Understanding nuclear reactions between light-charged nuclei in the sub-Coulomb energy region is crucial for several astrophysical processes. Accurate determination of the reaction cross-section within the astrophysically important Gamow range is challenging due to electron screening. Various methods, including polynomial fits, R-Matrix, and the indirect Trojan Horse Method (THM), have estimated electron screening energies that exceed the adiabatic limit. This study aims to derive the bare astrophysical S-factor for the reaction 6Li(p,α)3He and to extract electron screening energies using Multi-Layer Perceptron-based Artificial Neural Network (ANN) analysis. Experimental S-factors for 6Li(p,α)3He, obtained from the literature, are reanalyzed with the ANN algorithm to determine the energy-dependent S-factor. The bare astrophysical S-factor is calculated from data above 60 keV, where electron screening is negligible. The electron screening potential is then derived by comparing the shielded S-factor with the bare S-factor. The ANN-based analysis yields an electron screening potential of 220 eV, suggesting that ANN could be a viable tool for estimating electron screening potentials in light nuclei reactions.

Nonadiabatic nonlinear non-Hermitian quantized pumping

We analyze a quantized pumping in a nonlinear non-Hermitian photonic system with nonadiabatic driving. The photonic system is made of a waveguide array, where the distances between adjacent waveguides are modulated. It is described by the Su-Schrieffer-Heeger model together with a saturated nonlinear gain term and a linear loss term. A topological interface state between the topological and the trivial phases is stabilized by the combination of a saturated nonlinear gain term and a linear loss term. We study the pumping of the topological interface state. We define the transfer-speed ratio ω/Ω by the ratio of the pumping speed ω of the center of mass of the wave packet to the driving speed Ω of the topological interface. It is quantized topologically as ω/Ω=1 in the adiabatic limit. It remains to be quantized dynamically unless the driving is not too fast even in the nonadiabatic regime. On the other hand, the wave packet collapses and there is no quantized pumping when the driving is too fast. In addition, the stability against disorder is more enhanced by stronger nonlinearity. Published by the American Physical Society 2024

Noise-induced transport in a periodic square-well potential

We investigate a thermal ratchet based on a Brownian particle in a spatially periodic square-well potential driven by a time-dependent square-wave signal. In this model, we rock the Brownian particle between two square-well potentials tilted in opposite directions to induce a net current. Employing the Stratonovich formula and an independent approach using suitable boundary conditions and a normalization condition, we obtain an exact expression for the current in the adiabatic limit, and we observe that there are optimal values of various parameters at which the current can be maximized. In several parameter regimes, our simple non-linear model displays a behavior distinct from some other models of a rocked ratchet. For example, a reversal in the current direction is observed as the square-wave signal’s amplitude or the thermal bath’s temperature is varied. However, under similar conditions, no such current reversal was seen in the case of a periodically rocked Brownian motor in a sawtooth or a smooth potential. Furthermore, unlike the latter type of rocked Brownian motors, the square-well model yields zero current in the deterministic limit, as thermal energy is indispensable for the functioning of the motor.

Adiabatic Limit, Theta Function, and Geometric Quantization

Adiabatic Limit, Theta Function, and Geometric Quantization

Energy landscapes for the quantum approximate optimization algorithm

Variational quantum algorithms (VQAs) have demonstrated considerable potential in solving NP-hard combinatorial problems in the contemporary noisy intermediate-scale quantum (NISQ) era. The quantum approximate optimization algorithm (QAOA) is one such algorithm, used in solving the maximum cut (Max-Cut) problem for a given graph by successive implementation of L quantum circuit layers within a corresponding Trotterized ansatz. The challenge of exploring the cost function of VQAs arising from an exponential proliferation of local minima with increasing circuit depth has been well documented. However, fewer studies have investigated the impact of circuit depth on QAOA performance in finding the correct Max-Cut solution. Here we employ basin-hopping global optimization methods to navigate the energy landscapes for QAOA ansätze for various graphs, and analyze QAOA performance in finding the correct Max-Cut solution. The structure of the solution space is also investigated using discrete path sampling to build databases of local minima and the transition states that connect them, providing insightful visualizations using disconnectivity graphs. We find that the corresponding landscapes generally have a single funnel organization, which makes it relatively straightforward to locate low-lying minima with good Max-Cut solution probabilities. In some cases below the adiabatic limit the second lowest local minimum may even yield a higher solution probability than the global minimum. This important observation has motivated us to develop broader metrics in evaluating QAOA performance, based on collections of minima obtained from basin-hopping global optimization. Hence we establish expectation thresholds in elucidating useful solution probabilities from local minima, an approach that may provide significant gains in elucidating reasonable solution probabilities from local minima. Published by the American Physical Society 2024

Toward Cosmological Simulations of the Magnetized Intracluster Medium with Resolved Coulomb Collision Scale

We present the first results of one extremely high-resolution, nonradiative magnetohydrodynamical cosmological zoom-in simulation of a massive cluster with a virial mass of M vir = 2.0 × 1015 solar masses. We adopt a mass resolution of 4 × 105 M ⊙ with a maximum spatial resolution of around 250 pc in the central regions of the cluster. We follow the detailed amplification process in a resolved small-scale turbulent dynamo in the intracluster medium (ICM) with strong exponential growth until redshift 4, after which the field grows weakly in the adiabatic compression limit until redshift 2. The energy in the field is slightly reduced as the system approaches redshift zero in agreement with adiabatic decompression. The field structure is highly turbulent in the center and shows field reversals on a length scale of a few tens of kiloparsecs and an anticorrelation between the radial and angular field components in the central region that is ordered by small-scale turbulent dynamo action. The large-scale field on megaparsec scales is almost isotropic, indicating that the structure formation process in massive galaxy cluster formation suppresses any memory of both the initial field configuration and the amplified morphology via the turbulent dynamo. We demonstrate that extremely high-resolution simulations of the magnetized ICM are within reach that can simultaneously resolve the small-scale magnetic field structure, which is of major importance for the injection of and transport of cosmic rays in the ICM. This work is a major cornerstone for follow-up studies with an on-the-fly treatment of cosmic rays to model in detail electron-synchrotron and gamma-ray emissions.

Imaginary past of a quantum particle moving on imaginary time

The analytical continuation of classical equations of motion to complex times suggests that a tunneling particle spends in the barrier an imaginary duration i|T|. Does this mean that it takes a finite time to tunnel, or should tunneling be seen as an instantaneous process? It is well known that examination of the adiabatic limit in a small additional AC field points towards |T| being the time it takes to traverse the barrier. However, this is only half the story. We probe the transmitted particle's history, and find that it very little of the field's past behavior, as if the transit time were close to zero. The ensuing contradiction suggests that the question is ill posed, and we explain why. Published by the American Physical Society 2024

Static versus dynamically polarizable environments within the many-body GW formalism.

Continuum- or discrete-polarizable models for the study of optoelectronic processes in embedded subsystems rely mostly on the restriction of the surrounding electronic dielectric response to its low frequency limit. Such a description hinges on the assumption that the electrons in the surrounding medium react instantaneously to any excitation in the central subsystem, thus treating the environment in the adiabatic limit. Exploiting a recently developed embedded GW formalism with an environment described at the fully abinitio level, we assess the merits of the adiabatic limit with respect to an environment where the full dynamics of the dielectric response are considered. Furthermore, we show how to properly take the static limit of the environment's susceptibility by introducing the so-called Coulomb-hole and screened-exchange contributions to the reaction field. As a first application, we consider a C60 molecule at the surface of a C60 crystal, namely, a case where the dynamics of the embedded and embedding subsystems are similar. The common adiabatic assumption, when properly treated, generates errors below 10% on the polarization energy associated with frontier energy levels and associated energy gaps. Finally, we consider a water molecule inside a metallic nanotube, the worst case for the environment's adiabatic limit. The error on the gap polarization energy remains below 10%, even though the error on the frontier orbital polarization energies can reach a few tenths of an electronvolt.

Improving performance of quantum heat engines using modified Otto cycle

The efficiency of a quantum heat engine is maximum when the unitary strokes of the quantum Otto cycle are adiabatic. On the other hand, this may not be always possible due to small energy gaps in the system, especially at the critical point (CP) where the gap between the ground state and the first excited state vanishes and the system gets excited. With the aim to regain this lost adiabaticity, we modify one of the unitary strokes of the Otto cycle by allowing the system to first evolve with a time dependent Hamiltonian as in the case of a usual Otto cycle, followed by an additional evolution with a different time independent Hamiltonian so that the system reaches a less excited state. This will help in increasing the magnitude of the heat absorbed from the hot bath so that the work output and efficiency of the engine can be increased. We demonstrate this method using an integrable model and a non-integrable model as the working medium and discuss the generality and limitations of this method. In the case of a two spin system, the optimal value for the time till which the system needs to be freely evolved is calculated analytically in the adiabatic limit. The results show that implementing this modified unitary stroke significantly improves the work output and efficiency of the engine, especially when it crosses the CP.

Symmetry of the emergent inductance tensor exhibited by magnetic textures

Metals hosting gradually varying spatial magnetic textures are attracting attention as a new class of inductors. Under the application of an alternating current, the spin-transfer-torque effect induces oscillating dynamics of the magnetic texture, which subsequently yields the spin-motive force as a back action, resulting in an inductive voltage response. In general, a second-order tensor representing a material’s response can have an off-diagonal component. However, it is unclear what symmetries the emergent inductance tensor has and also which magnetic textures can exhibit a transverse inductance response. Here, we reveal both analytically and numerically that the emergent inductance tensor should be a symmetric tensor in the so-called adiabatic limit. By considering this symmetric tensor in terms of symmetry operations that a magnetic texture has, we further characterize the magnetic textures in which the transverse inductance response can appear. This finding provides a basis for exploring the transverse response of emergent inductors, which has yet to be discovered.

Energetic perspective on emergent inductance exhibited by magnetic textures in the pinned regime

Spatially varying magnetic textures can exhibit electric-current-induced dynamics as a result of the spin-transfer torque effect. When such a magnetic system is electrically driven, an electric field is generated, which is called the emergent electric field. In particular, when magnetic-texture dynamics are induced under the application of an AC electric current, the emergent electric field also appears in an AC manner, notably, with an out-of-phase time profile, thus exhibiting inductor behavior, often called an emergent inductor. Here we show that the emergent inductance exhibited by magnetic textures in the pinned regime can be explained in terms of the current-induced energy stored in the magnetic system. We numerically find that the inductance values defined from the emergent electric field and the current-induced magnetization-distortion energy, respectively, are in quantitative agreement in the so-called adiabatic limit. Our findings indicate that emergent inductors retain the basic concept of conventional inductors; that is, the energy is stored under the application of electric current.

Gravitoelectric dynamical tides at second post-Newtonian order

We present a gravitoelectric quadrupolar dynamical tidal-interaction Hamiltonian for a compact binary system, that is valid to second order in the post-Newtonian expansion. Our derivation uses the diagrammatic effective field theory approach, and involves Feynman integrals up to two loops, evaluated with the dimensional regularization scheme. We also derive the effective Hamiltonian for adiabatic tides, obtained by taking the appropriate limit of the dynamical effective Hamiltonian, and we check its validity by verifying the complete Poincaré algebra. In the adiabatic limit, we also calculate two gauge-invariant observables, namely, the binding energy for a circular orbit and the scattering angle in a hyperbolic scattering. Our results are important for developing accurate gravitational waveform models for neutron-star binaries for present and future gravitational-wave observatories.

Adiabatic limit for scattering-free waveguiding in space-graded arrays of micro-resonators

We report on the dynamics of graded metamaterials in the context of micro-electromechanical systems (MEMS). Graded metamaterials are known to exhibit space confinement of mechanical energy - or rainbow trapping - in response to a tailored wave speed reduction. Such a behavior, in turn, is controlled by a gradual variation of the resonant characteristics of an array of resonators dressed on a host structure which, as a result, exhibits arbitrarily slow waves. The paper shows quantitatively that there is an adiabatic limit for the rate of change of the grading. Below this limit, the rainbow effect takes place with a negligible scattering of energy, which is otherwise detrimental to practical applications such as harvesting, sensing, and communication. The paper also paves new ways to manipulate wave motion in MEMS through elastic metamaterials.

Nonlinear interaction of electromagnetic wave with electron acoustic wave in plasma

An analysis on the nonlinear interaction of electromagnetic waves with electron acoustic waves is performed in plasma with two different temperature electron fluids in the presence of a neutralizing static ion background. A newly structured Zakharov’s equations are derived employing two fluid two-time scale theory. These coupled Zakharov’s equations describe the weakly nonlinear interaction of em wave perturbation with electron acoustic waves while propagating through plasma. In the low frequency or adiabatic limit, these Zakharov’s equations may be unified to produce a modified NLSE. A solution of the equation, novel in the literature, is derived following the method shown by Kudryashov. In a resonant regime, the modified NLSE reduces to NLSE. Though a stable solution exists for both cases, instability analysis shows caviton instability may arise. The threshold value of the electric field, at which instability sets in, is virtually zero for the resonant region whereas, apart from that region there is a threshold value of the electric field, determined by the frequency difference of em wave and electron plasma wave. Experimental observations support these results. This study is relevant for laser-plasma interaction and astrophysical and space plasma.

Warm-Started QAOA with Custom Mixers Provably Converges and Computationally Beats Goemans-Williamson's Max-Cut at Low Circuit Depths

We generalize the Quantum Approximate Optimization Algorithm (QAOA) of Farhi et al. (2014) to allow for arbitrary separable initial states with corresponding mixers such that the starting state is the most excited state of the mixing Hamiltonian. We demonstrate this version of QAOA, which we call QAOA−warmest, by simulating Max-Cut on weighted graphs. We initialize the starting state as a warm−start using 2 and 3-dimensional approximations obtained using randomized projections of solutions to Max-Cut's semi-definite program, and define a warm-start dependent custommixer. We show that these warm-starts initialize the QAOA circuit with constant-factor approximations of 0.658 for 2-dimensional and 0.585 for 3-dimensional warm-starts for graphs with non-negative edge weights, improving upon previously known trivial (i.e., 0.5 for standard initialization) worst-case bounds at p=0. These factors in fact lower bound the approximation achieved for Max-Cut at higher circuit depths, since we also show that QAOA-warmest with any separable initial state converges to Max-Cut under the adiabatic limit as p→∞. However, the choice of warm-starts significantly impacts the rate of convergence to Max-Cut, and we show empirically that our warm-starts achieve a faster convergence compared to existing approaches. Additionally, our numerical simulations show higher quality cuts compared to standard QAOA, the classical Goemans-Williamson algorithm, and a warm-started QAOA without custom mixers for an instance library of 1148 graphs (upto 11 nodes) and depth p=8. We further show that QAOA-warmest outperforms the standard QAOA of Farhi et al. in experiments on current IBM-Q and Quantinuum hardware.

Causal perturbative QFT and white noise

In this paper, we present the Bogoliubov’s causal perturbative QFT, which includes only one refinement: the creation-annihilation operators at a point, i.e. for a specific momentum, are mathematically interpreted as the Hida operators from the white noise analysis. We leave the rest of the theory completely unchanged. This allows avoiding infrared — and ultraviolet — divergences in the transition to the adiabatic limit for interacting fields. We present here the analysis of the causal axioms for the scattering operator with the Hida operators as the creation-annihilation operators.

Quadratic gravity potentials in de Sitter spacetime from Feynman diagrams

We employ a manifestly covariant formalism to compute the tree-level amputated Green’s function of non-minimally coupled scalar fields in quadratic gravity in a de Sitter background. We study this Green’s function in the adiabatic limit, and construct the classical Newtonian potential. At short distances, the flat-spacetime Yukawa potential is reproduced, while the curvature gives rise to corrections to the potential at large distances. Beyond the Hubble radius, the potential vanishes identically, in agreement with the causal structure of de Sitter spacetime. For sub-Hubble distances, we investigate whether the modifications to the potential reproduce Modified Newtonian Dynamics.

High-harmonic generation in spin and charge current pumping at ferromagnetic or antiferromagnetic resonance in the presence of spin–orbit coupling

One of the cornerstone effects in spintronics is spin pumping by dynamical magnetization that is steadily precessing (around, for example, the z-axis) with frequency ω 0 due to absorption of low-power microwaves of frequency ω 0 under the resonance conditions and in the absence of any applied bias voltage. The two-decades-old ‘standard model’ of this effect, based on the scattering theory of adiabatic quantum pumping, predicts that component of spin current vector is time-independent while and oscillate harmonically in time with a single frequency ω 0 whereas pumped charge current is zero in the same adiabatic limit. Here we employ more general approaches than the ‘standard model’, namely the time-dependent nonequilibrium Green’s function (NEGF) and the Floquet NEGF, to predict unforeseen features of spin pumping: namely precessing localized magnetic moments within a ferromagnetic metal (FM) or antiferromagnetic metal (AFM), whose conduction electrons are exposed to spin–orbit coupling (SOC) of either intrinsic or proximity origin, will pump both spin and charge I(t) currents. All four of these functions harmonically oscillate in time at both even and odd integer multiples of the driving frequency ω 0. The cutoff order of such high harmonics increases with SOC strength, reaching in the one-dimensional FM or AFM models chosen for demonstration. A higher cutoff can be achieved in realistic two-dimensional (2D) FM models defined on a honeycomb lattice, and we provide a prescription of how to realize them using 2D magnets and their heterostructures.

A [3]-catenane non-autonomous molecular motor model: Geometric phase, no-pumping theorem, and energy transduction.

We study a model of a synthetic molecular motor-a [3]-catenane consisting of two small macrocycles mechanically interlocked with a bigger one-subjected to time-dependent driving using stochastic thermodynamics. The model presents nontrivial features due to the two interacting small macrocycles but is simple enough to be treated analytically in limiting regimes. Among the results obtained, we find a mapping into an equivalent [2]-catenane that reveals the implications of the no-pumping theorem stating that to generate net motion of the small macrocycles, both energies and barriers need to change. In the adiabatic limit (slow driving), we fully characterize the motor's dynamics and show that the net motion of the small macrocycles is expressed as a surface integral in parameter space, which corrects previous erroneous results. We also analyze the performance of the motor subjected to step-wise driving protocols in the absence and presence of an applied load. Optimization strategies for generating large currents and maximizing free energy transduction are proposed. This simple model provides interesting clues into the working principles of non-autonomous molecular motors and their optimization.

Incoherent nonadiabatic to coherent adiabatic transition of electron transfer in colloidal quantum dot molecules

Electron transfer is a fundamental process in chemistry, biology, and physics. One of the most intriguing questions concerns the realization of the transitions between nonadiabatic and adiabatic regimes of electron transfer. Using colloidal quantum dot molecules, we computationally demonstrate how the hybridization energy (electronic coupling) can be tuned by changing the neck dimensions and/or the quantum dot sizes. This provides a handle to tune the electron transfer from the incoherent nonadiabatic regime to the coherent adiabatic regime in a single system. We develop an atomistic model to account for several states and couplings to the lattice vibrations and utilize the mean-field mixed quantum-classical method to describe the charge transfer dynamics. Here, we show that charge transfer rates increase by several orders of magnitude as the system is driven to the coherent, adiabatic limit, even at elevated temperatures, and delineate the inter-dot and torsional acoustic modes that couple most strongly to the charge transfer dynamics.