Invariant Dynamics Research Articles

Fast implementation of controlled-π phase gates and preparation of cluster states with Rydberg superatoms

In this paper, we propose a scheme for rapidly implementing a controlled-π phase gate by combining the Lewis–Riesenfeld invariant and quantum Zeno dynamics. We demonstrate the adiabatic shortcut by using Rydberg superatoms in distant-atom–cavity systems. Furthermore, we utilize the controlled-π phase gate to achieve the preparation of N-particle cluster states. Additionally, the impact of decoherence and operational imperfections is discussed. Numerical simulation demonstrates that the proposed scheme has high fidelities and robustness against both cavity leakage and atomic spontaneous emission.

Focusing Φ⁴₃-model with a Hartree-type Nonlinearity

Lebowitz, Rose, and Speer (1988) initiated the study of focusing Gibbs measures, which was continued by Brydges and Slade (1996), Bourgain (1997, 1999), and Carlen, Fröhlich, and Lebowitz (2016) among others. In this paper, we complete the program on the (non-)construction of the focusing Hartree Gibbs measures in the three-dimensional setting. More precisely, we study a focusing Φ 3 4 \Phi ^4_3 -model with a Hartree-type nonlinearity, where the potential for the Hartree nonlinearity is given by the Bessel potential of order β \beta . We first construct the focusing Hartree Φ 3 4 \Phi ^4_3 -measure for β > 2 \beta > 2 , while we prove its non-normalizability for β > 2 \beta > 2 . Furthermore, we establish the following phase transition at the critical value β = 2 \beta = 2 : normalizability in the weakly nonlinear regime and non-normalizability in the strongly nonlinear regime. We then study the canonical stochastic quantization of the focusing Hartree Φ 3 4 \Phi ^4_3 -measure, namely, the three-dimensional stochastic damped nonlinear wave equation (SdNLW) with a cubic nonlinearity of Hartree-type, forced by an additive space-time white noise, and prove almost sure global well-posedness and invariance of the focusing Hartree Φ 3 4 \Phi ^4_3 -measure for β > 2 \beta > 2 (and β = 2 \beta = 2 in the weakly nonlinear regime). In view of the non-normalizability result, our almost sure global well-posedness result is sharp. In Appendix, we also discuss the (parabolic) stochastic quantization for the focusing Hartree Φ 3 4 \Phi ^4_3 -measure. We also consider the defocusing case. By adapting our argument from the focusing case, we first construct the defocusing Hartree Φ 3 4 \Phi ^4_3 -measure and the associated invariant dynamics for the defocusing Hartree SdNLW for β > 1 \beta > 1 . By introducing further renormalizations at β = 1 \beta = 1 and β = 1 2 \beta = \frac 12 , we extend the construction of the defocusing Hartree Φ 3 4 \Phi ^4_3 -measure for β > 0 \beta > 0 , where the resulting measure is shown to be singular with respect to the reference Gaussian free field for 0 > β ≤ 1 2 0 > \beta \le \frac 12 .

Bosonization of 2+1 dimensional fermions on the surface of topological insulators

Three-dimensional topological insulators can be described by an effective field theory involving two ‘hydrodynamic’ Abelian gauge fields. The action contains a bulk topological BF term and a surface term, called loop model. This describes the massless 2+1 dimensional excitations and provides them with a semiclassical, yet non-trivial conformal invariant dynamics. Given that topological insulators are originally fermionic, this physical setting is ideal for realizing the bosonization of massless fermions in terms of gauge fields. Building on earlier analyses of the loop model, we find that fermions belong to the solitonic spectrum and can be described by Wilson lines, through the generalization of 1+1 dimensional vertex operators. Their correlation functions agree with conformal invariance. The bosonic loop model is then mapped into a fermionic theory by using the general construction of fermionic topological phases described in the literature. It requires the identification of the characteristic one-form ℤ2 symmetry of the bosonic theory and its gauging, which originates the fermion number (−1)F, the spin sectors and the time reversal symmetry obeying T2 = (−1)F. These results are detailed for the effective action and the partition function on the geometry S2 × S1.

Scaling Properties of Liquid Dynamics Predicted from a Single Configuration: Pseudoisomorphs for Harmonic-Bonded Molecules.

Isomorphs are curves in the thermodynamic phase diagram of invariant excess entropy, structure, and dynamics, while pseudoisomorphs are curves of invariant structure and dynamics, but not of the excess entropy. The latter curves have been shown to exist in molecular models with flexible bonds [Olsen, A. E. J. Chem. Phys. 2016, 145, 241103]. We here present three force-based methods to trace out pseudoisomorphs based on a single configuration and test them on the asymmetric dumbbell and 10-bead Lennard-Jones chain models with bonds modeled as harmonic springs. The three methods are based on requiring that particle forces, center-of-mass forces, and torques, respectively, are invariant in reduced units. For each of the two investigated models we identify a method that works well for tracing out pseudoisomorphs, but these methods are not the same. Overall, we find that the more internal degrees of freedom there are in the molecule studied, the less they appear to affect the gross dynamical behavior. Moreover, the "internal" degrees of freedom (including rotation) do not significantly affect the scaling behavior of the dynamical/transport coefficients provided some 'quenching' is performed.

Projection of the Airborne CO2 Concentration by Land/Ocean Absorption Dynamics and Fossil-Fuel Reserve Depletion

The paper has been suggested by the following observations: (1) the atmospheric growth rate of carbon dioxide concentration is smaller than that ascribed to the emission of fossil-fuel combustion and (2) the fossil-fuel reserves are finite. The first observation leads to a simple dynamic model, based on the balance of CO2 land/ocean absorption and anthropogenic emissions, only limited by the depletion of fossil-fuel reserves, in a business-as-usual scenario. The second observation suggests of projecting the past CO2 emissions to the future, by constraining emissions to the limit of reserve availability. Similar projections are available in the literature, but either driven by heuristics or by complex simulation packages. The paper provides a simple and formal method only driven by historical data, their uncertainty and simple models. The method aims to provide CO2 concentration projections, which being constrained by fossil-fuel finite reserve may be in principle employed as bounds to forecasting exercises. The time–invariant dynamics of the land/ocean absorption is the simplification of a more complex set of equations describing carbon dioxide exchange between different reservoirs. Contribution of other greenhouse gases like methane and nitrous oxide has been neglected, since their emissions cannot be projected with the paper methodology. Comparison with recent profiles of the Intergovernmental Panel on Climate Change (IPCC) confirms that the finite-reserve projections of the fossil fuel emissions is close to those of a moderate Shared Socioeconomic Scenario (SSP) like SSP2-4.5—a result in agreement with other authors—but also reveals the limits of the simplified model, when extending the tuned dynamics of the recent mean CO2 exchanges to long-term future. The limits derive from linearity, time invariance, and aggregation assumptions, which allow a more complex model of CO2 exchanges to be simplified and tuned on experimental data.

Scalable, ab initio protocol for quantum simulating SU(N)×U(1) Lattice Gauge Theories

We propose a protocol for the scalable quantum simulation of SU(N)×U(1) lattice gauge theories with alkaline-earth like atoms in optical lattices in both one- and two-dimensional systems. The protocol exploits the combination of naturally occurring SU(N) pseudo-spin symmetry and strong inter-orbital interactions that is unique to such atomic species. A detailed ab initio study of the microscopic dynamics shows how gauge invariance emerges in an accessible parameter regime, and allows us to identify the main challenges in the simulation of such theories. We provide quantitative results about the requirements in terms of experimental stability in relation to observing gauge invariant dynamics, a key element for a deeper analysis on the functioning of such class of theories in both quantum simulators and computers.

High fidelity control of a many-body Tonks-Girardeau gas with an effective mean-field approach

Shortcuts to adiabaticity (STA) are powerful tools that can be used to control quantum systems with high fidelity. They work particularly well for single particle and noninteracting systems which can be described exactly and which possess invariant or self-similar dynamics. However, finding an exact STA for strongly correlated many-body systems can be difficult, as their complex dynamics may not be easily described, especially for larger systems that do not possess self-similar solutions. Here, we design STAs for one-dimensional bosonic gas in the Tonks-Girardeau limit by using a mean-field approach that succinctly captures the strong interaction effects through a quintic nonlinear term in the Schrödinger equation. We show that for the case of the harmonic oscillator with a time-dependent trap frequency the mean-field approach works exactly and recovers the well-known STA from literature. To highlight the robustness of our approach we also show that it works effectively for anharmonic potentials, achieving higher fidelities than other typical control techniques. Published by the American Physical Society 2024

Invariant Charge Carrier Dynamics Using a Non-Planar Non-Fullerene Acceptor across Multiple Processing Solvents.

Conventional non-fullerene acceptors (NFAs) typically have planar structures that can enable improved electron mobility and produce more efficient organic photovoltaic devices. A relatively simple A-D-A'-D-A type NFA specifically designed to match with poly(3-hexylthiophene-2,5-diyl) (P3HT) for green-absorbing agrivoltaic applications has been examined using a variety of techniques: microsecond transient absorption spectroscopy, atomic force microscopy, and photoluminescence. Relatively invariant charge carrier decay dynamics are observed in the blend films across a variety of processing solvents. Raman spectroscopy in conjunction with computational studies reveals that this NFA is non-planar and that multiple conformations are present in films, while preserving the crystalline nature of P3HT. The non-planarity of the NFA therefore creates a dispersive acceptor environment, irrespective of processing solvent, and this leads to the observed relative invariance in charge carrier decay dynamics and high tolerance to morphological variation. The findings presented in this work highlight the potential of non-planar materials as acceptors in organic photovoltaic devices.

The effects of curvature and β on zonally invariant f-plane dynamics

The modification of the dynamics on the f-plane due to the inclusion of the latitudinal variation of the Coriolis frequency, quantified by β, is examined by comparing steady and time-dependent solutions for different values of β, including 0. The comparisons are made for analytic expressions and numerical simulations of the solutions of two physical problems: geostrophic adjustment and Ekman transport. By varying the extent of the meridional domain, L, and the value of β, while keeping the same value of the deformation radius, Rd, we find that the relative change of the Coriolis frequency across L is not a uniformly valid predictor of the effect of β on the dynamics. Instead, the magnitude of this effect varies with the physical problem, the type of dynamics, i.e., steady or time dependent, and with the particular values of β and L. In contrast to the effect of β, the effect of curvature on the zonally invariant f-plane dynamics is negligible in all cases for L≤1200 km and Rd=30 km employed here.

Invariant dynamics in a united-atom model of an ionic liquid.

We study a united-atom model of the ionic liquid 1-butyl-1-methylpyrrolidinium bis(trifluoromethyl)sulfonylamide to determine to what extent there exist curves in the phase diagram along which the microscopic dynamics are invariant when expressed in dimensionless, or reduced, form. The initial identification of these curves, termed isodynes, is made by noting that contours of reduced shear viscosity and reduced self-diffusion coefficient coincide to a good approximation. Choosing specifically the contours of reduced viscosity as nominal isodynes, further simulations were carried out for state points on these, and other aspects of dynamics were investigated to study their degree of invariance. These include the mean-squared displacement, shear-stress autocorrelation function, and various rotational correlation functions. These were invariant to a good approximation, with the main exception being rotations of the anion about its long axis. The dynamical features that are invariant have in common that they are aspects that would be relevant for a coarse-grained description of the system; specifically, removing the most microscopic degrees of freedom in principle leads to a simplification of the potential energy landscape, which allows for the existence of isodynes.

Invariant Gibbs dynamics for the two-dimensional Zakharov-Yukawa system

We study the Gibbs dynamics for the Zakharov-Yukawa system on the two-dimensional torus T2, namely a Schrödinger-wave system with a Zakharov-type coupling (−Δ)γ. We first construct the Gibbs measure in the weakly nonlinear coupling case (0≤γ<1). Combined with the non-construction of the Gibbs measure in the strongly nonlinear coupling case (γ=1) by Oh, Tolomeo, and the author (2020), this exhibits a phase transition at γ=1. We also study the dynamical problem and prove almost sure global well-posedness of the Zakharov-Yukawa system and invariance of the Gibbs measure under the resulting dynamics for the range 0≤γ<13. In this dynamical part, the main step is to prove local well-posedness. Our argument is based on the first order expansion and the operator norm approach via the random matrix/tensor estimate from a recent work Deng, Nahmod, and Yue (2020). In the appendix, we briefly discuss the Hilbert-Schmidt norm approach and compare it with the operator norm approach.

Smoothness of invariant manifolds for stochastic evolution equations with non-dense domain

With the crucial estimation of random Stieltjes-type convolution, the Lyapunov–Perron method allows us to establish the existence of invariant dynamics for stochastic evolution equation with non-dense domain. In this paper, we develop the conditions for [Formula: see text]-smoothness of center manifold for such equation with linear multiplicative noise, unstable manifold and stable set for the one with nonlinear multiplicative noise as well. Our result may apply to a broad range of stochastic systems with non-dense domain beyond Brownian noise.

Concentration of invariant means and dynamics of chain stabilizers in continuous geometries

We prove a concentration inequality for invariant means on topological groups, namely for such adapted to a chain of amenable topological subgroups. The result is based on an application of Azuma’s martingale inequality and provides a method for establishing extreme amenability. Building on this technique, we exhibit new examples of extremely amenable groups arising from von Neumann’s continuous geometries. Along the way, we also answer a question by Pestov on dynamical concentration in direct products of amenable topological groups.

Lie group analysis for obtaining the abundant group invariant solutions and dynamics of solitons for the Lonngren-wave equation

The Lonngren-wave equation (LW Equation), one of the many nonlinear evolution equations (N-EEs) that arise in the field of mathematical physics, is the subject of this study, which uses an extremely strong analytical technique known as “Lie group analysis” to create novel solutions. We obtain a five-dimensional optimal system based on four-dimensional Lie algebra. We compute the group invariant solutions via subalgebras. Our obtained solutions are based on the trigonometric, hyperbolic, and polynomial functions. By varying the parameters, the solutions exhibit wavelike properties that include bright, dark, singular, dark-singular-combined solitons, periodic singular and dark-bright-combined. The physical dynamics of the obtained solutions are explored by the 3D and 2D Mathematica simulations which are explaining the new properties of the model considered in this paper.

Active-matter isomorphs in the size-polydisperse Ornstein–Uhlenbeck Lennard–Jones model

This paper studies size-polydisperse Lennard–Jones systems described by active Ornstein–Uhlenbeck particle (AOUP) dynamics. The focus is on the existence of isomorphs (curves of invariant structure and dynamics) in the model’s three-dimensional phase diagram. Isomorphs are traced out from a single steady-state configuration by means of the configurational-temperature method. Good isomorph invariance of the reduced-unit radial distribution function and the mean-square displacement as a function of time is demonstrated for three uniform-distribution polydispersities, , 23%, and 29%. Comparing to active-matter isomorphs generated by the analytical direct-isomorph-check method, the latter have poorer invariance of the structure, but better invariance of the dynamics. We conclude that both methods can be used to quickly get an overview of the phase diagram of polydisperse AOUP models involving a potential-energy function obeying the hidden-scale-invariance property required for isomorph theory to apply.

Invariant neural dynamics drive commands to control different movements.

It has been proposed that the nervous system has the capacity to generate a wide variety of movements because it reuses some invariant code. Previous work has identified that dynamics of neural populationactivity are similar during different movements, where dynamics refer to how the instantaneous spatialpattern of population activity changes in time. Here, we test whether invariant dynamics of neural populations are actually used to issue the commands that direct movement. Using a brain-machine interface (BMI) that transforms rhesus macaques' motor-cortex activity into commands for a neuroprosthetic cursor, we discovered that the same command is issued with different neural-activity patterns in different movements. However, these different patterns were predictable, as we found that the transitionsbetween activity patterns are governed by the same dynamics across movements. These invariant dynamics are low dimensional, and critically, they align with the BMI, so that they predict the specific component of neural activity that actually issues the next command. We introduce a model of optimal feedback control (OFC) that shows that invariant dynamics can help transform movement feedback into commands, reducing the input that the neural population needs to control movement. Altogether our results demonstrate that invariant dynamics drive commands to control a variety of movements and show how feedback can be integrated with invariant dynamics to issue generalizable commands.

Build a DC to AC Inverter Circuit with IOT Based Load Monitoring

Abstract: The boost inverter or boost DC-AC converter is a new voltage source inverter (VSI) that is suggested in this research. The novel inverter topology's key feature is that, depending on the instantaneous duty cycle, it produces an AC output voltage that is greater than the DC input voltage. This characteristic is not present in the conventional VSI, which consistently generates an AC output instantaneous voltage lower than the DC input voltage. A sliding mode controller is suggested to optimize the boost inverter dynamics while guaranteeing proper functioning under any working circumstance. The primary benefit of sliding mode control over traditional control strategies is its resistance to changes in plant parameters, which results in invariant dynamics and steady-state response in in the best scenario. This study covers operation, analysis, control technique, and experimental outcomes. When an AC voltage greater than the DC link voltage is required, the new inverter is designed to be employed in UPS and AC driver systems without the requirement for a second power conversion stage

Hamiltonian structure of 2D fluid dynamics with broken parity

Isotropic fluids in two spatial dimensions can break parity symmetry and sustain transverse stresses which do not lead to dissipation. Corresponding transport coefficients include odd viscosity, odd torque, and odd pressure. We consider an isotropic Galilean invariant fluid dynamics in the adiabatic regime with momentum and particle density conservation. We find conditions on transport coefficients that correspond to dissipationless and separately to Hamiltonian fluid dynamics. The restriction on the transport coefficients will help identify what kind of hydrodynamics can be obtained by coarse-graining a microscopic Hamiltonian system. Interestingly, not all parity-breaking transport coefficients lead to energy conservation and, generally, the fluid dynamics is energy conserving but not Hamiltonian. We show how this dynamics can be realized by imposing a nonholonomic constraint on the Hamiltonian system.

Configurational temperature in active matter. I. Lines of invariant physics in the phase diagram of the Ornstein-Uhlenbeck model.

This paper shows that the configurational temperature of liquid-state theory, T_{conf}, defines an energy scale, which can be used for adjusting model parameters of active Ornstein-Uhlenbeck particle (AOUP) models in order to achieve approximately invariant structure and dynamics upon a density change. The required parameter changes are calculated from the variation of a single configuration's T_{conf} for a uniform scaling of all particle coordinates. The resulting equationsare justified theoretically for models involving a potential-energy function with hidden scale invariance. The validity of the procedure is illustrated by computer simulations of the Kob-Andersen binary Lennard-Jones AOUP model, showing the existence of lines of approximate invariance of the reduced-unit radial distribution function and time-dependent mean-square displacement.

Flight dynamics model identification of a meso-scale twin-cyclocopter in hover

In this paper the flight dynamics of a 33-gram twin-cyclocopter is analyzed via deriving a Linear Time Invariant (LTI) dynamics model from flight test data. The twin-cyclocopter is a novel micro air vehicle that uses two co-rotating cycloidal rotors to generate thrust and a coaxial nose rotor to counteract the reaction torque and provide additional thrust. During flight tests, perturbation maneuvers were performed about the hovering state to excite different modes and a 3D motion capture system collected attitude and position data. The data was used to extract a bare airframe LTI model linearized about the hovering state using time-domain system identification techniques. The model demonstrated that the roll and yaw modes are gyroscopically coupled with stable high-frequency and low-frequency modes. Comparing the two different yaw control methods: thrust vectoring of the cycloidal rotors and differential torque of the coaxial nose rotor, the former was more effective.