Journal articles: 'Post-Hamiltonian systems'

1

Cheng, Xu-Hui, and Guo-Qing Huang. "A Comparison between Second-Order Post-Newtonian Hamiltonian and Coherent Post-Newtonian Lagrangian in Spinning Compact Binaries." Symmetry 13, no. 4 (April 1, 2021): 584. http://dx.doi.org/10.3390/sym13040584.

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In relativistic celestial mechanics, post-Newtonian (PN) Lagrangian and PN Hamiltonian formulations are not equivalent to the same PN order as our previous work in PRD (2015). Usually, an approximate Lagrangian is used to discuss the difference between a PN Hamiltonian and a PN Lagrangian. In this paper, we investigate the dynamics of compact binary systems for Hamiltonians and Lagrangians, including Newtonian, post-Newtonian (1PN and 2PN), and spin–orbit coupling and spin–spin coupling parts. Additionally, coherent equations of motion for 2PN Lagrangian are adopted here to make the comparison with Hamiltonian approaches and approximate Lagrangian approaches at the same condition and same PN order. The completely opposite nature of the dynamics shows that using an approximate PN Lagrangian is not convincing. Hence, using the coherent PN Lagrangian is necessary for obtaining an exact result in the research of dynamics of compact binary at certain PN order. Meanwhile, numerical investigations from the spinning compact binaries show that the 2PN term plays an important role in causing chaos in the PN Hamiltonian system.

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Jaranowski, Piotr, and Gerhard Schäfer. "Radiative 3.5 post-Newtonian ADM Hamiltonian for many-body point-mass systems." Physical Review D 55, no. 8 (April 15, 1997): 4712–22. http://dx.doi.org/10.1103/physrevd.55.4712.

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Luo, Junjie, Jie Feng, Hong-Hao Zhang, and Weipeng Lin. "Contrasting the Implicit Method in Incoherent Lagrangian and the Correction Map Method in Hamiltonian." Symmetry 15, no. 7 (July 11, 2023): 1401. http://dx.doi.org/10.3390/sym15071401.

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The equations of motion for a Lagrangian mainly refer to the acceleration equations, which can be obtained by the Euler–Lagrange equations. In the post-Newtonian Lagrangian form of general relativity, the Lagrangian systems can only maintain a certain post-Newtonian order and are incoherent Lagrangians since the higher-order terms are omitted. This truncation can cause some changes in the constant of motion. However, in celestial mechanics, Hamiltonians are more commonly used than Lagrangians. The conversion from Lagrangianto Hamiltonian can be achieved through the Legendre transformation. The coordinate momentum separable Hamiltonian can be computed by the symplectic algorithm, whereas the inseparable Hamiltonian can be used to compute the evolution of motion by the phase-space expansion method. Our recent work involves the design of a multi-factor correction map for the phase-space expansion method, known as the correction map method. In this paper, we compare the performance of the implicit algorithm in post-Newtonian Lagrangians and the correction map method in post-Newtonian Hamiltonians. Specifically, we investigate the extent to which both methods can uphold invariance of the motion’s constants, such as energy conservation and angular momentum preservation. Ultimately, the results of numerical simulations demonstrate the superior performance of the correction map method, particularly with respect to angular momentum conservation.

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Blümlein, J., A. Maier, P. Marquard, and G. Schäfer. "Fourth post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach." Nuclear Physics B 955 (June 2020): 115041. http://dx.doi.org/10.1016/j.nuclphysb.2020.115041.

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WU, XIN, and JI ZHOU HE. "POST-STABILIZATION OF INVARIANTS AND APPLICATION TO NUMERICAL ANALYSIS OF CHAOS FOR SOME 3-DIMENSIONAL SYSTEMS." International Journal of Modern Physics C 17, no. 11 (November 2006): 1613–28. http://dx.doi.org/10.1142/s0129183106010066.

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This research relates to a numerical integrator with post-stabilization of several constraints for an autonomous dynamical system. A generally analytical approach shows that the total energy correction is not valid in most cases, while post-stabilization of each independent energy is. As a typical test example, we consider a non-integrable Hamiltonian system of three degrees of freedom, which can be split into two independent pieces, one 1D harmonic oscillator and another 2D non-integrable system, by using a transformation of variables. Phase portraits on Poincaré sections about the 2D system manifest that our analysis is reasonable. In addition, a problem how to compute Lyapunov exponents in constrained systems is proposed. As a suggestion, it is best to stabilize all constraints involving each energy integral and its corresponding variation in order to avoid spurious Lyapunov exponents. Because an appropriately larger time step is acceptable in this sense, it is not expensive to use the fast Lyapunov indicators to describe the global dynamics of phase space for the 3D system, where regions of chaos and order are clearly identified.

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Alba, Vincenzo, Bruno Bertini, Maurizio Fagotti, Lorenzo Piroli, and Paola Ruggiero. "Generalized-hydrodynamic approach to inhomogeneous quenches: correlations, entanglement and quantum effects." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 11 (November 1, 2021): 114004. http://dx.doi.org/10.1088/1742-5468/ac257d.

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Abstract We give a pedagogical introduction to the generalized hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems. We review recent applications of the theory, focusing in particular on two classes of problems: bipartitioning protocols and trap quenches, which represent two prototypical examples of broken translational symmetry in either the system initial state or post-quench Hamiltonian. We report on exact results that have been obtained for generic time-dependent correlation functions and entanglement evolution, and discuss in detail the range of applicability of the theory. Finally, we present some open questions and suggest perspectives on possible future directions.

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Luo, Junjie, Jie Feng, Hong-Hao Zhang, and Weipeng Lin. "Performance of different correction maps in the extended phase-space method for spinning compact binaries." Monthly Notices of the Royal Astronomical Society 518, no. 4 (December 8, 2022): 6132–40. http://dx.doi.org/10.1093/mnras/stac3494.

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ABSTRACT Since the first detection of gravitational waves by the LIGO/VIRGO team, the related research field has attracted more attention. The spinning compact binaries system, as one of the gravitational-wave sources for broad-band laser interferometers, has been widely studied by related researchers. In order to analyse the gravitational wave signals using matched filtering techniques, reliable numerical algorithms are needed. Spinning compact binaries systems in post-Newtonian (PN) celestial mechanics have an inseparable Hamiltonian. The extended phase-space algorithm is an effective solution for the problem of this system. We have developed correction maps for the extended phase-space method in our previous work, which significantly improves the accuracy and stability of the method with only a momentum scale factor. In this paper, we will add more scale factors to modify the numerical solution in order to minimize the errors in the constants of motion. However, we find that these correction maps will result in a large energy bias in the subterms of the Hamiltonian in chaotic orbits, whose potential and kinetic energy, etc. are calculated inaccurately. We develop a new correction map to reduce the energy bias of the subterms of the Hamiltonian, which can instead improve the accuracy of the numerical solution and also provides a new idea for the application of the manifold correction in other algorithms.

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8

Blümlein, J., A. Maier, P. Marquard, and G. Schäfer. "The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: Potential contributions." Nuclear Physics B 965 (April 2021): 115352. http://dx.doi.org/10.1016/j.nuclphysb.2021.115352.

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9

Rañada, Manuel F. "Quasi-bi-Hamiltonian structures, complex functions and superintegrability: the Tremblay–Turbiner–Winternitz (TTW) and the Post–Winternitz (PW) systems." Journal of Physics A: Mathematical and Theoretical 50, no. 31 (July 7, 2017): 315206. http://dx.doi.org/10.1088/1751-8121/aa7951.

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10

Lu, D., and X. Zhang. "Transient stability analysis and control of power systems with considering flux decay by energy function approach." Bulletin of the Polish Academy of Sciences: Technical Sciences 60, no. 1 (March 1, 2012): 3–8. http://dx.doi.org/10.2478/v10175-012-0001-1.

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Transient stability analysis and control of power systems with considering flux decay by energy function approach In this paper, transient stability of power systems with structure preserving models is considered. A Hamiltonian function which can be regarded as a Lyapunov function for the system is proposed. Based on this, the influence of flux decay dynamics, especially during a fault, on transient stability is analyzed. With the increase of load power, the variation of stability boundary in the rotor angle/E'q plane is shown. The Energy-based excitation control, aiming at injecting additional damping into the post-fault system may reduce the critical clearing time (CCT). This can be demonstrated by the comparison of different flux decay dynamics in the fault-on condition, and the reason is illustrated by the relationship between rotor angle/E'q and the stability boundary. An improved control strategy is proposed and applied to increase the CCT. Simulation results verify that improvement is obtained both in transient stability and dynamic performance.

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11

Granade, Christopher, Christopher Ferrie, Ian Hincks, Steven Casagrande, Thomas Alexander, Jonathan Gross, Michal Kononenko, and Yuval Sanders. "QInfer: Statistical inference software for quantum applications." Quantum 1 (April 25, 2017): 5. http://dx.doi.org/10.22331/q-2017-04-25-5.

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Characterizing quantum systems through experimental data is critical to applications as diverse as metrology and quantum computing. Analyzing this experimental data in a robust and reproducible manner is made challenging, however, by the lack of readily-available software for performing principled statistical analysis. We improve the robustness and reproducibility of characterization by introducing an open-source library, QInfer, to address this need. Our library makes it easy to analyze data from tomography, randomized benchmarking, and Hamiltonian learning experiments either in post-processing, or online as data is acquired. QInfer also provides functionality for predicting the performance of proposed experimental protocols from simulated runs. By delivering easy-to-use characterization tools based on principled statistical analysis, QInfer helps address many outstanding challenges facing quantum technology.

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12

Lu, Yanzhao, Zhifan Wang, and Fan Wang. "Intermediate Hamiltonian Fock-space coupled-cluster theory for excitation energies, double ionization potentials, and double electron attachments with spin–orbit coupling." Journal of Chemical Physics 156, no. 11 (March 21, 2022): 114111. http://dx.doi.org/10.1063/5.0076462.

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The intermediate Hamiltonian Fock-space coupled-cluster methods at the singles and doubles level (IHFSCCSD) for excitation energies in the (1p, 1h) sector, double ionization potentials in the (0p, 2h) sector, and double electron attachments in the (2p, 0h) sector of the Fock space are implemented based on the CCSD method with spin–orbit coupling (SOC) included in the post-Hartree–Fock treatment using a closed-shell reference in this work. The active space is chosen to contain those orbitals that have the largest contribution to principal ionized or electron-attached states obtained from the equation-of-motion coupled-cluster calculations. Both time-reversal symmetry and spatial symmetry are exploited in the implementation. Our results show that the accuracy of IHFSCCSD results is closely related to the active space, and the sufficiency of the active space can be assessed from the percentage of transitions within the active space. In addition, unreasonable results may be encountered when the ionized or electron-attached states with a somewhat larger contribution from double excitations are included to determine the active space and cluster operators in the (0p, 1h) or (1p, 0h) sector of the Fock space. A larger active space may be required to describe SO splitting reliably than that in the scalar-relativistic calculations in some cases. The IHFSCCSD method with SOC developed in this work can provide reliable results for heavy-element systems when a sufficient active space built upon the principal ionization potential/electron affinity states is adopted.

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13

Martí, J. G., and C. Beaugé. "Stellar scattering and the formation of hot Jupiters in binary systems." International Journal of Astrobiology 14, no. 2 (April 14, 2014): 313–20. http://dx.doi.org/10.1017/s147355041400007x.

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AbstractHot Jupiters (HJs) are usually defined as giant Jovian-size planets with orbital periods P⩽10 days. Although they lie close to the star, several have finite eccentricities and significant misalignment angle with respect to the stellar equator, leading to ~20% of HJs in retrograde orbits. More than half, however, seem consistent with near-circular and planar orbits. In recent years, two mechanisms have been proposed to explain the excited and misaligned subpopulation of HJs: Lidov–Kozai migration and planet–planet scattering. Although both are based on completely different dynamical phenomena, at first hand they appear to be equally effective in generating hot planets. Nevertheless, there has been no detailed analysis comparing the predictions of both mechanisms, especially with respect to the final distribution of orbital characteristics. In this paper, we present a series of numerical simulations of Lidov–Kozai trapping of single planets in compact binary systems that suffered a close fly-by of a background star. Both the planet and the binary component are initially placed in coplanar orbits, although the inclination of the impactor is assumed random. After the passage of the third star, we follow the orbital and spin evolution of the planet using analytical models based on the octupole expansion of the secular Hamiltonian. We also include tidal effects, stellar oblateness and post-Newtonian perturbations. The present work aims at the comparison of the two mechanisms (Lidov–Kozai and planet–planet scattering) as an explanation for the excited and inclined HJs in binary systems. We compare the results obtained through this paper with results in Beaugé & Nesvorný (2012), where the authors analyse how the planet–planet scattering mechanisms works in order to form this hot Jovian-size planets. We find that several of the orbital characteristics of the simulated HJs are caused by tidal trapping from quasi-parabolic orbits, independent of the driving mechanism (planet–planet scattering or Lidov–Kozai migration). These include both the 3-day pile-up and the distribution in the eccentricity versus semimajor axis plane. However, the distribution of the inclinations shows significant differences. While Lidov–Kozai trapping favours a more random distribution (or even a preference for near polar orbits), planet–planet scattering shows a large portion of bodies nearly aligned with the equator of the central star. This is more consistent with the distribution of known hot planets, perhaps indicating that scattering may be a more efficient mechanism for producing these bodies.

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14

Christlmaier, Evelin Martine, Daniel Kats, Ali Alavi, and Denis Usvyat. "Full configuration interaction quantum Monte Carlo treatment of fragments embedded in a periodic mean field." Journal of Chemical Physics 156, no. 15 (April 21, 2022): 154107. http://dx.doi.org/10.1063/5.0084040.

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We present an embedded fragment approach for high-level quantum chemical calculations on local features in periodic systems. The fragment is defined as a set of localized orbitals (occupied and virtual) corresponding to a converged periodic Hartree–Fock solution. These orbitals serve as the basis for the in-fragment post-Hartree–Fock treatment. The embedding field for the fragment, consisting of the Coulomb and exchange potential from the rest of the crystal, is included in the fragment’s one-electron Hamiltonian. As an application of the embedded fragment approach, we investigate the performance of full configuration interaction quantum Monte Carlo (FCIQMC) with the adaptive shift. As the orbital choice, we use the natural orbitals from the distinguishable cluster method with singles and doubles. FCIQMC is a stochastic approximation to the full CI method and can be routinely applied to much larger active spaces than the latter. This makes this method especially attractive in the context of open shell defects in crystals, where fragments of adequate size can be rather large. As a test case, we consider dissociation of a fluorine atom from a fluorographane surface. This process poses a challenge for high-level electronic structure models as both the static and dynamic correlations are essential here. Furthermore, the active space for an adequate fragment (32 electrons in 173 orbitals) is already quite large even for FCIQMC. Despite this, FCIQMC delivers accurate dissociation and total energies.

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15

Kotyczka, Paul, and Laurent Lefèvre. "Discrete-time port-Hamiltonian systems based on Gauss-Legendre collocation ⁎ ⁎P. Kotyczka received financial support as a part-time post-doctoral researcher (03/17–08/17) from the DFG-ANR funded project INFI-DHEM (no ANR-16-CE92-0028) and by a part-time visiting fellowship of Grenoble INP in summer term 2017. The work makes also part of the project KO 4750/1-1, funded by the German Research Foundation (DFG)." IFAC-PapersOnLine 51, no. 3 (2018): 125–30. http://dx.doi.org/10.1016/j.ifacol.2018.06.035.

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16

Jaranowski, Piotr, and Gerhard Schäfer. "Towards the fourth post-Newtonian Hamiltonian for two-point-mass systems." Physical Review D 86, no. 6 (September 11, 2012). http://dx.doi.org/10.1103/physrevd.86.061503.

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17

Chung, Ming-Zhi, Yu-tin Huang, Jung-Wook Kim, and Sangmin Lee. "Complete Hamiltonian for spinning binary systems at first post-Minkowskian order." Journal of High Energy Physics 2020, no. 5 (May 2020). http://dx.doi.org/10.1007/jhep05(2020)105.

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Mandal, Manoj K., Pierpaolo Mastrolia, Raj Patil, and Jan Steinhoff. "Gravitational spin-orbit Hamiltonian at NNNLO in the post-Newtonian framework." Journal of High Energy Physics 2023, no. 3 (March 17, 2023). http://dx.doi.org/10.1007/jhep03(2023)130.

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Abstract We present the result of the spin-orbit interaction Hamiltonian for binary systems of rotating compact objects with generic spins, up to N3LO corrections within the post-Newtonian expansion. The calculation is performed by employing the effective field theory diagrammatic approach, and it involves Feynman integrals up to three loops, evaluated within the dimensional regularization scheme. We apply canonical transformations to eliminate the non-physical divergences and spurious logarithmic behaviours of the Hamiltonian, and use the latter to derive the gauge-invariant binding energy and the scattering angle, in special kinematic regimes.

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19

Bern, Zvi, Clifford Cheung, Radu Roiban, Chia-Hsien Shen, Mikhail P. Solon, and Mao Zeng. "Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order." Physical Review Letters 122, no. 20 (May 24, 2019). http://dx.doi.org/10.1103/physrevlett.122.201603.

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20

Ledvinka, Tomáš, Gerhard Schäfer, and Jiří Bičák. "Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation." Physical Review Letters 100, no. 25 (June 23, 2008). http://dx.doi.org/10.1103/physrevlett.100.251101.

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Mandal, Manoj K., Pierpaolo Mastrolia, Raj Patil, and Jan Steinhoff. "Gravitational quadratic-in-spin Hamiltonian at NNNLO in the post-Newtonian framework." Journal of High Energy Physics 2023, no. 7 (July 14, 2023). http://dx.doi.org/10.1007/jhep07(2023)128.

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Abstract We present the result of the quadratic-in-spin interaction Hamiltonian for binary systems of rotating compact objects with generic spins, up to N3LO corrections within the post-Newtonian expansion. The calculation is performed by employing the effective field theory diagrammatic approach, and it involves Feynman integrals up to three loops, evaluated within the dimensional regularization scheme. The gauge-invariant binding energy and the scattering angle, in special kinematic regimes and spin configurations, are explicitly derived. The results extend our earlier study on the spin-orbit interaction effects.

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22

Yoshida, Ryuhei, Erik Lotstedt, and Kaoru Yamanouchi. "Quantum computing of Hückel molecular orbitals of π-electron systems." Journal of Chemical Physics, April 26, 2022. http://dx.doi.org/10.1063/5.0086489.

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In order to demonstrate an applicability of quantum computing to fundamental electronic structure problems of molecules, we describe the Hückel Hamiltonian matrix in terms of quantum gates and obtain the orbital energies of fundamental π-electron molecules (C2H4, C3H4, C4H4, C4H6, and C6H6 ) using a superconducting-qubit type quantum computer ( ibm_kawasaki) with a post-selection error mitigation method. We show that the orbital energies are obtained with sufficiently high accuracy and small uncertainties and that characteristic features of the electronic structure of the π-electron molecules can be extracted by quantum computing in a straightforward manner.

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23

Blümlein, J., A. Maier, P. Marquard, and G. Schäfer. "The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach." Nuclear Physics B, July 2022, 115900. http://dx.doi.org/10.1016/j.nuclphysb.2022.115900.

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Henry, Quentin, Guillaume Faye, and Luc Blanchet. "Hamiltonian for tidal interactions in compact binary systems to next-to-next-to-leading post-Newtonian order." Physical Review D 102, no. 12 (December 29, 2020). http://dx.doi.org/10.1103/physrevd.102.124074.

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25

SREEDHARAN, APARNA, Sridevi Kuriyattil, and Sebastian Wuester. "Hyper-entangling mesoscopic bound states." New Journal of Physics, August 2, 2023. http://dx.doi.org/10.1088/1367-2630/acec91.

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Abstract We predict hyper-entanglement generation by binary scattering of mesoscopic bound states, considering solitary waves in Bose-Einstein condensates containing thousands of identical Bosons. For it to occur, the underlying many-body Hamiltonian must not be integrable, and the pre-collision quantum state of the solitons needs to be fragmented.Under these conditions, we show that the post-collision state will be hyper-entangled in spatial degrees of freedom and atom number within solitons, for realistic parameters. The effect links aspects of non-linear systems and quantum-coherence and the entangled post-collision state challenges present entanglement criteria for identical particles. Our results are based on simulations of colliding quantum solitons in a quintic interaction model beyond the mean-field, using the truncated Wigner approximation.

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Jones, Michael A., Harish J. Vallury, Charles D. Hill, and Lloyd C. L. Hollenberg. "Chemistry beyond the Hartree–Fock energy via quantum computed moments." Scientific Reports 12, no. 1 (May 28, 2022). http://dx.doi.org/10.1038/s41598-022-12324-z.

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AbstractQuantum computers hold promise to circumvent the limitations of conventional computing for difficult molecular problems. However, the accumulation of quantum logic errors on real devices represents a major challenge, particularly in the pursuit of chemical accuracy requiring the inclusion of electronic correlation effects. In this work we implement the quantum computed moments (QCM) approach for hydrogen chain molecular systems up to H$$_6$$ 6 . On a superconducting quantum processor, Hamiltonian moments, $$\langle H^p\rangle$$ ⟨ H p ⟩ are computed with respect to the Hartree–Fock state, which are then employed in Lanczos expansion theory to determine an estimate for the ground-state energy which incorporates electronic correlations and manifestly improves on the direct energy measurement. Post-processing purification of the raw QCM data takes the estimate below the Hartree–Fock energy to within 99.9% of the exact electronic ground-state energy for the largest system studied, H$$_6$$ 6 . Calculated dissociation curves indicate precision at about 10mH for this system and as low as 0.1mH for molecular hydrogen, H$$_2$$ 2 , over a range of bond lengths. In the context of stringent precision requirements for chemical problems, these results provide strong evidence for the error suppression capability of the QCM method, particularly when coupled with post-processing error mitigation. While calculations based on the Hartree–Fock state are tractable to classical computation, these results represent a first step towards implementing the QCM method in a quantum chemical trial circuit. Greater emphasis on more efficient representations of the Hamiltonian and classical preprocessing steps may enable the solution of larger systems on near-term quantum processors.

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Kälin, Gregor, and Rafael A. Porto. "Post-Minkowskian effective field theory for conservative binary dynamics." Journal of High Energy Physics 2020, no. 11 (November 2020). http://dx.doi.org/10.1007/jhep11(2020)106.

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Abstract We develop an Effective Field Theory (EFT) formalism to solve for the conservative dynamics of binary systems in gravity via Post-Minkowskian (PM) scattering data. Our framework combines a systematic EFT approach to compute the deflection angle in the PM expansion, together with the ‘Boundary-to-Bound’ (B2B) dictionary introduced in [1, 2]. Due to the nature of scattering processes, a remarkable reduction of complexity occurs both in the number of Feynman diagrams and type of integrals, compared to a direct EFT computation of the potential in a PM scheme. We provide two illustrative examples. Firstly, we compute all the conservative gravitational observables for bound orbits to 2PM, which follow from only one topology beyond leading order. The results agree with those in [1, 2], obtained through the ‘impetus formula’ applied to the classical limit of the one loop amplitude in Cheung et al. [3]. For the sake of comparison we reconstruct the conservative Hamiltonian to 2PM order, which is equivalent to the one derived in [3] from a matching calculation. Secondly, we compute the scattering angle due to tidal effects from the electric- and magnetic-type Love numbers at leading PM order. Using the B2B dictionary we then obtain the tidal contribution to the periastron advance. We also construct a Hamiltonian including tidal effects at leading PM order. Although relying on (relativistic) Feynman diagrams, the EFT formalism developed here does not involve taking the classical limit of a quantum amplitude, neither integrals with internal massive fields, nor additional matching calculations, nor spurious (‘super-classical’) infrared singularities. By construction, the EFT approach can be automatized to all PM orders.

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Sabín, Carlos. "Digital quantum simulation of quantum gravitational entanglement with IBM quantum computers." EPJ Quantum Technology 10, no. 1 (February 8, 2023). http://dx.doi.org/10.1140/epjqt/s40507-023-00161-6.

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AbstractWe report the digital quantum simulation of a hamiltonian involved in the generation of quantum entanglement by gravitational means. In particular, we focus on a pair of quantum harmonic oscillators, whose interaction via a quantum gravitational field generates single-mode squeezing in both modes at the same time, a non-standard process in quantum optics. We perform a boson-qubit mapping and a digital gate decomposition specific for IBM quantum devices. We use error mitigation and post-selection to achieve high-fidelity, accessing a parameter regime out of direct experimental reach.

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Mniszewski, Susan M., Pavel A. Dub, Sergei Tretiak, Petr M. Anisimov, Yu Zhang, and Christian F. A. Negre. "Reduction of the molecular hamiltonian matrix using quantum community detection." Scientific Reports 11, no. 1 (February 18, 2021). http://dx.doi.org/10.1038/s41598-021-83561-x.

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AbstractQuantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree–Fock methods as future advances in quantum hardware become available.

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Weng, Guorong, Rushil Mallarapu, and Vojtech Vlcek. "Embedding vertex corrections in GW self-energy: theory, implementation, and outlook." Journal of Chemical Physics, March 23, 2023. http://dx.doi.org/10.1063/5.0139117.

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The vertex function (Γ) within the Green's function formalism encapsulates information about all higher-order electron-electron interactions beyond those mediated by density fluctuations. Herein, we present an efficient approach that embeds vertex corrections in the one-shot GW correlation self-energy for isolated and periodic systems. The vertex-corrected self-energy is constructed through the proposed separation-propagation-recombination procedure: the electronic Hilbert space is separated into an active space and its orthogonal complement denoted as the "rest;" the active component is propagated by a space-specific effective Hamiltonian different from the rest. The vertex corrections are introduced by a rescaled time-dependent nonlocal exchange interaction. The direct Γ correction to the self-energy is further updated by adjusting the rescaling factor in a self-consistent post-processing circle. Our embedding method is tested mainly on donor-acceptor charge-transfer systems. The embedded vertex effects consistently and significantly correct the quasiparticle energies of the gap-edge states. The fundamental gap is generally improved by 1-3 eV upon the one-shot $GW$ approximation. Furthermore, we provide an outlook for applications of (embedded) vertex corrections in calculations of extended solids.

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Blümlein, J., A. Maier, P. Marquard, and G. Schäfer. "Erratum to: The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach [Nucl. Phys. B 983 (2022) 115900]." Nuclear Physics B, October 2022, 115991. http://dx.doi.org/10.1016/j.nuclphysb.2022.115991.

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Cao, Kaiyuan, Ming Zhong, and Peiqing Tong. "Dynamical quantum phase transition in periodic quantum Ising chains." Journal of Physics A: Mathematical and Theoretical, July 21, 2022. http://dx.doi.org/10.1088/1751-8121/ac8324.

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Abstract The dynamical quantum phase transitions (DQPTs) after a sudden quench in periodic quantum Ising chains (QICs) are studied. We obtain the formulas of the Loschmidt echo and the Fisher zeros of the Loschmidt amplitude in the periodic QIC. It’s found that for the quench across the quantum phase transitions(QPTs), the periodic QICs have richer DQPTs than that in the homogeneous QIC, and the number of critical times of the DQPTs are dependent on the specifical parameter of the preand post-quench Hamiltonian. For instance, in the period-two QIC, there is one critical time for the quench from the FM phase to the PM phase, and three critical times for the quench from the PM phase to the FM phase. In the period-three QIC, there may have three or four critical times for the quench from FM phase to the PM phase, but may have two or three critical times for the quench from PM to the FM phase. The reason is that the periodic QICs have multiple quasiparticle excitation spectra, and the Fisher zeros of the periodic systems consist of several separated branches, which is different from that in the homogeneous QIC. For different quenches across the QPTs, different branches will intersect with the imaginary axis, which correspond to different critical times. Our conclusion also provides insight in the property of the DQPT in the inhomogeneous systems.

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33

O'Brien, Jack, Hasan Ahmadian Baghbaderani, Frederico Orlandini Keller, Nora M. Dempsey, Laura H. Lewis, and Plamen Stamenov. "Hardware, Methodology and Applications of 2⁺D Backscatter Mössbauer Spectroscopy with Simultaneous X-ray and γ-ray Detection." Measurement Science and Technology, October 17, 2023. http://dx.doi.org/10.1088/1361-6501/ad044b.

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Abstract A unique method is presented for the acquisition and analysis of 57Fe backscatter Mössbauer spectra with simultaneous detection of the resonant 14.4 keV γ-rays and characteristic 6.4 keV x-rays, using a Multi-Parameter Analyser (MPA) constructed on the basis of commercial Analogue to Digital Converters (ADCs) and custom-built high-speed digital latches. The system allows for the simultaneous registration of Doppler-modulated velocities and photon energies, with up to 4096 and 8192 digital channels respectively. This arrangement is in contrast to most related systems, which detect at a single energy window per detector. Samples of arbitrary atomic structure, morphology and surface topography can be studied without altering the setup or the analysis procedure, provided that the samples are at least micrometre sized. The hardware and software that are used to acquire data with minimal dead time are described and the custom and self-contained methods for post-measurement energy discrimination, background correction and velocity-axis folding are discussed. The data are fit using a general Hamiltonian model for the nuclear energy levels of 57Fe and a quantum mechanical description of the angular momentum coupling is utilised, with consideration of the crystalline and chemical disorder of the sample under examination. Three examples of distinct magnetic systems, with thicknesses ranging from 5 µm to 6 mm, that were studied using this method are presented, these are: an amorphous CoFeB-based ribbon with ultra-soft coercivity for high-frequency applications, magnetically hard Nd-Fe-B thick films on Si substrates, examined in both pre- and post-annealed states, and a sample from the nickel-rich iron meteorite NWA 6259 that contains the atomically ordered, elevated coercivity, L10 phase, tetrataenite.The wide applicability and usefulness of this method is thus demonstrated on three distinct sample morphologies that required little to no surface preparation prior to examination.

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Winkler, Ludwig, Klaus-Robert Mueller, and Huziel E. Sauceda. "High-fidelity Molecular Dynamics Trajectory Reconstruction with Bi-Directional Neural Networks." Machine Learning: Science and Technology, May 11, 2022. http://dx.doi.org/10.1088/2632-2153/ac6ec6.

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Abstract Molecular dynamics simulations are a cornerstone in science, enabling the investigation of a system's thermodynamics all the way to analyzing intricate molecular interactions. In general, creating extended molecular trajectories can be a computationally expensive process, for example, when running ab-initio simulations. Hence, repeating such calculations to either obtain more accurate thermodynamics or to get a higher resolution in the dynamics generated by a fine-grained quantum interaction can be time- and computational resource-consuming. In this work, we explore different machine learning (ML) methodologies to increase the resolution of molecular dynamics trajectories on-demand within a post-processing step. As a proof of concept, we analyze the performance of bi-directional neural networks such as neural ODEs, Hamiltonian networks, recurrent neural networks and LSTMs, as well as the uni-directional variants as a reference, for molecular dynamics simulations (here: the MD17 dataset). We have found that Bi-LSTMs are the best performing models; by utilizing the local time-symmetry of thermostated trajectories they can even learn long-range correlations and display high robustness to noisy dynamics across molecular complexity. Our models can reach accuracies of up to 10-4 Å in trajectory interpolation, which leads to the faithful reconstruction of several unseen high-frequency molecular vibration cycles. This renders the comparison between the learned and reference trajectories indistinguishable. The results reported in this work can serve (1) as a baseline for larger systems, as well as (2) for the construction of better MD integrators.

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Journal articles on the topic 'Post-Hamiltonian systems'

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