Mastodawn

📰 "Geometric Learning Dynamics"
https://arxiv.org/abs/2504.14728 #Quant-Ph #Dynamics #Q-Bio.Pe #Matrix #Cs.Lg

Geometric Learning Dynamics

We present a unified geometric framework for modeling learning dynamics in physical, biological, and machine learning systems. The theory reveals three fundamental regimes, each emerging from the power-law relationship $g \propto κ^α$ between the metric tensor $g$ in the space of trainable variables and the noise covariance matrix $κ$. The quantum regime corresponds to $α= 1$ and describes Schrödinger-like dynamics that emerges from a discrete shift symmetry. The efficient learning regime corresponds to $α= \tfrac{1}{2}$ and describes very fast machine learning algorithms. The equilibration regime corresponds to $α= 0$ and describes classical models of biological evolution. We argue that the emergence of the intermediate regime $α= \tfrac{1}{2}$ is a key mechanism underlying the emergence of biological complexity.

arXiv.org

G-Prophet 3d ago

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G-Prophet 4d ago

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G-Prophet 4d ago

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Rxiv mechanobio 5d ago

📰 "Localized intrinsic bond orbitals decode correlated charge migration dynamics"
https://arxiv.org/abs/2603.10105 #Physics.Chem-Ph #Physics.Comp-Ph #Dynamics #Quant-Ph #Matrix

Localized intrinsic bond orbitals decode correlated charge migration dynamics

For decades, scientists have studied the intricate charge migration dynamics, where after ionization a localized charge distribution ("hole") migrates across the molecule on a femtosecond timescale. This has the potential for controlling electrons in molecules, yet a comprehensive understanding of the many aspects of charge migration is still missing. In this work, we analyze charge migration using an extension of localized intrinsic bond orbitals (IBOs). These orbitals lead to a compact representation of the dynamics and map the complex, correlated many-electron charge migration to chemical concepts such as curly arrows and orbital-orbital interactions. By analyzing multiple challenging scenarios, we show how IBOs enable us to identify key mechanisms in charge migration. For example, we show that different mechanisms are responsible for converting a $π$-shaped hole to a $σ$-shaped hole and vice versa. We explain these in terms of hyperconjugation interactions and configurations that couple orbitals with different symmetries. We further demonstrate how IBOs can be used to find molecules with high charge migration efficiency. We carry out all simulations using an efficient set up of the time-dependent density matrix renormalization group (TDDMRG), correlating as many as 45 electrons in 50 orbitals. We believe that our results will be useful to design future experiments. The proposed IBO analysis is applicable to other types of real-time electron dynamics and spectroscopy.

arXiv.org

G-Prophet 6d ago

G-Prophet Mar 10

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G-Prophet Mar 10

Rxiv mechanobio Mar 10

📰 "For molecular polaritons, disorder and phonon timescales control the activation of dark states in the thermodynamic limit"
https://arxiv.org/abs/2603.06868 #Cond-Mat.Mes-Hall #Physics.Chem-Ph #Dynamics #Quant-Ph #Matrix

For molecular polaritons, disorder and phonon timescales control the activation of dark states in the thermodynamic limit

Collective light-matter systems host an extensive manifold of dark states whose role in the emergence of thermodynamic behavior remains poorly understood, especially in the presence of disorder and structured environments. Here, we develop a hybrid matrix product state-hierarchical equations of motion (MPS-HEOM) approach that enables numerically exact simulations of polariton dynamics from a few emitters to the thermodynamic limit under both static and dynamic disorder. This allows us, for the first time, to provide a quantitative and operational answer to the long-standing question of what is the minimum system size required to reach the thermodynamic limit in collective polaritonic systems. By introducing a convergence scale, $N_{T}$, i.e., the number of molecules required for the photonic dynamics to reach the thermodynamic limit, we show that dynamic disorder generally poses a greater computational challenge than static disorder. We attribute this behavior to the suppression of collective light-matter dynamics by disorder, which dynamically activates non-collective degrees of freedom. We further find that $N_{T}$ exhibits a turnover behavior as the bath becomes more Markovian, as the bath timescales regulate bright-to-dark energy transfer and the involvement of dark and gray states. Hence, phonon timescales control both the breakdown of collective behavior and the growth of $N_{T}$. Our results establish the suppression of collective behavior as the key mechanism governing thermodynamic convergence in disordered light-matter systems.

arXiv.org

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