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1. Single-chain simulation of Ising density functional theory for weak polyelectrolytes

   https://doi.org/10.1063/5.0175561  

   Gallegos, Alejandro; Müller, Marcus; Wu, Jianzhong (December 2023, The Journal of Chemical Physics)

   Conventional theories of weak polyelectrolytes are either computationally prohibitive to account for the multidimensional inhomogeneity of polymer ionization in a liquid environment or oversimplistic in describing the coupling effects of ion-explicit electrostatic interactions and long-range intrachain correlations. To bridge this gap, we implement the Ising density functional theory (iDFT) for ionizable polymer systems using the single-chain-in-mean-field algorithm. The single-chain-in-iDFT (sc-iDFT) shows significant improvements over conventional mean-field methods in describing segment-level dissociation equilibrium, specific ion effects, and long-range intrachain correlations. With an explicit consideration of the fluctuations of polymer configurations and the position-dependent ionization of individual polymer segments, sc-iDFT provides a faithful description of the structure and thermodynamic properties of inhomogeneous weak polyelectrolyte systems across multiple length scales. 

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2. Noise-resilient phase transitions and limit-cycles in coupled Kerr oscillators

   https://doi.org/10.1088/1367-2630/ad2414  

   Alaeian, H; Soriente, M; Najafi, K; Yelin, S F (February 2024, New Journal of Physics)

   Abstract In recent years, there has been considerable focus on exploring driven-dissipative quantum systems, as they exhibit distinctive dissipation-stabilized phases. Among themdissipative time crystalis a unique phase emerging as a shift from disorder or stationary states to periodic behaviors. However, understanding the resilience of these non-equilibrium phases against quantum fluctuations remains unclear. This study addresses this query within a canonical parametric quantum optical system, specifically, a multi-mode cavity with self- and cross-Kerr non-linearity. Using mean-field (MF) theory we obtain the phase diagram and delimit the parameter ranges that stabilize a non-stationary limit-cycle phase. Leveraging the Keldysh formalism, we study the unique spectral features of each phase. Further, we extend our analyses beyond the MF theory by explicitly accounting for higher-order correlations through cumulant expansions. Our findings unveil insights into the modifications of the open quantum systems phases, underscoring the significance of quantum correlations in non-equilibrium steady states. Importantly, our results conclusively demonstrate the resilience of the non-stationary phase against quantum fluctuations, rendering it a dissipation-induced genuine quantum synchronous phase. 

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3. Phase-space methods for neutrino oscillations: Extension to multibeams

   https://doi.org/10.1103/PhysRevD.110.103027  

   Lacroix, Denis; Bauge, Angel; Yilmaz, Bulent; Mangin-Brinet, Mariane; Roggero, Alessandro; Balantekin, A Baha (November 2024, Physical Review D)

   The phase-space approach (PSA), which was originally introduced in Lacroix [] to describe neutrino flavor oscillations for interacting neutrinos emitted from stellar objects is extended to describe arbitrary numbers of neutrino beams. The PSA is based on mapping the quantum fluctuations into a statistical treatment by sampling initial conditions followed by independent mean-field evolution. A new method is proposed to perform this sampling that allows treating an arbitrary number of neutrinos in each neutrino beams. We validate the technique successfully and confirm its predictive power on several examples where a reference exact calculation is possible. We show that it can describe many-body effects, such as entanglement and dissipation induced by the interaction between neutrinos. Due to the complexity of the problem, exact solutions can only be calculated for rather limited cases, with a limited number of beams and/or neutrinos in each beam. The PSA approach considerably reduces the numerical cost and provides an efficient technique to accurately simulate arbitrary numbers of beams. Examples of PSA results are given here, including up to 200 beams with time-independent or time-dependent Hamiltonians. We anticipate that this approach will be useful to bridge exact microscopic techniques with more traditional transport theories used in neutrino oscillations. It will also provide important reference calculations for future quantum computer applications where other techniques are not applicable to classical computers. Published by the American Physical Society2024 

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4. Influence of inhomogeneous stochasticity on the falsifiability of mean-field theories and examples from accretion disc modelling

   https://doi.org/10.1093/mnras/stab2403  

   Zhou, Hongzhe; Blackman, Eric G (September 2021, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT Despite spatial and temporal fluctuations in turbulent astrophysical systems, mean-field theories can be used to describe their secular evolution. However, observations taken over time scales much shorter than dynamical time scales capture a system in a single state of its turbulence ensemble. Comparing with mean-field theory can falsify the latter only if the theory is additionally supplied with a quantified precision. The central limit theorem provides appropriate estimates to the precision only when fluctuations contribute linearly to an observable and with constant coherent scales. Here, we introduce an error propagation formula that relaxes both limitations, allowing for non-linear functional forms of observables and inhomogeneous coherent scales and amplitudes of fluctuations. The method is exemplified in the context of accretion disc theories, where inhomogeneous fluctuations in the surface temperature are propagated to the disc emission spectrum – the latter being a non-linear and non-local function of the former. The derived precision depends non-monotonically on emission frequency. Using the same method, we investigate how binned spectral fluctuations in telescope data change with the spectral resolving power. We discuss the broader implications for falsifiability of a mean-field theory. 

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5. Machine learning electronic structure methods based on the one-electron reduced density matrix

   https://doi.org/10.1038/s41467-023-41953-9  

   Shao, Xuecheng; Paetow, Lukas; Tuckerman, Mark E.; Pavanello, Michele (December 2023, Nature Communications)

   Abstract The theorems of density functional theory (DFT) establish bijective maps between the local external potential of a many-body system and its electron density, wavefunction and, therefore, one-particle reduced density matrix. Building on this foundation, we show that machine learning models based on the one-electron reduced density matrix can be used to generate surrogate electronic structure methods. We generate surrogates of local and hybrid DFT, Hartree-Fock and full configuration interaction theories for systems ranging from small molecules such as water to more complex compounds like benzene and propanol. The surrogate models use the one-electron reduced density matrix as the central quantity to be learned. From the predicted density matrices, we show that either standard quantum chemistry or a second machine-learning model can be used to compute molecular observables, energies, and atomic forces. The surrogate models can generate essentially anything that a standard electronic structure method can, ranging from band gaps and Kohn-Sham orbitals to energy-conserving ab-initio molecular dynamics simulations and infrared spectra, which account for anharmonicity and thermal effects, without the need to employ computationally expensive algorithms such as self-consistent field theory. The algorithms are packaged in an efficient and easy to use Python code, QMLearn, accessible on popular platforms. 

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