Related papers: Perturbatively corrected ring-polymer instanton ra…
Marcus-Levich-Jortner (MLJ) theory is one of the most commonly used methods for including nuclear quantum effects into the calculation of electron-transfer rates and for interpreting experimental data. It divides the molecular problem into…
This paper presents a learning-based control strategy for non-linear throttle valves with an asymmetric hysteresis, leading to a near-optimal controller without requiring any prior knowledge about the environment. We start with a carefully…
Perturbation theory (PT) might be one of the most powerful and fruitful tools for both physicists and chemists, which evoked an explosion of applications with the blooming of atomic and subatomic physics. Even though PT is well-used today,…
We consider specific quantum mechanical model problems for which perturbation theory fails to explain physical properties like the eigenvalue spectrum even qualitatively, even if the asymptotic perturbation series is augmented by…
Many reactions in chemistry and biology involve multiple electronic states, rendering them nonadiabatic in nature. These reactions can be formally described using Fermi's golden rule (FGR) in the weak-coupling limit. Nonadiabatic instanton…
Non-perturbatively generated effective potentials play an extremely useful and often critical role in string and inflationary model building. These potentials are typically computed by methods that assume the system is in equilibrium. For…
A consistent theory of the ground state energy and its splitting due to the process of tunneling for the Lipkin model is presented. For the functional integral in terms of the spin coherent states for the partition function of the model we…
Recently, there has been renewed interest in studies of criticality in the spin quantum Hall effect, realized in the Altland-Zirnbauer symmetry class C of disordered, noninteracting fermions in two spatial dimensions. In our study, we…
We introduce Reliable Policy Iteration (RPI) and Conservative RPI (CRPI), variants of Policy Iteration (PI) and Conservative PI (CPI), that retain tabular guarantees under function approximation. RPI uses a novel Bellman-constrained…
Accurate simulations of molecules require high-level electronic-structure theory in combination with rigorous methods for approximating the quantum dynamics. Machine-learning approaches can significantly reduce the computational expense of…
We extend the worldline instanton technique to compute the vacuum pair production rate for spatially inhomogeneous electric background fields, with the spatial inhomogeneity being genuinely two or three dimensional, both for the magnitude…
The decay rates of quasistable states in quantum field theories are usually calculated using instanton methods. Standard derivations of these methods rely in a crucial way upon deformations and analytic continuations of the physical…
This paper proposes a spectral-based tuning method for proportional-integral (PI) controllers in integrating-plus-dead-time (IPDT) systems. The design objective is to achieve unified exponential decay for both reference tracking and…
In this work, we develop a perturbation theory to analyze resonant states near a bound state in the continuum (BIC) in photonic crystal slabs. The theory allows us to rigorously determine the asymptotic behavior of $Q$-factor and the…
The tunneling decay event of a metastable state in a fully connected quantum spin model can be simulated efficiently by path integral quantum Monte Carlo (QMC) [Isakov $et~al.$, Phys. Rev. Lett. ${\bf 117}$, 180402 (2016).]. This is because…
We derive the non-perturbative corrections to the free energy of the two-matrix model in terms of its algebraic curve. The eigenvalue instantons are associated with the vanishing cycles of the curve. For the (p,q) critical points our…
This paper presents a novel Direct Integration Theorem (DIT), derived as a non-trivial corollary of the classical Central Slice Theorem (CST). The DIT provides a mathematically consistent transition from the continuous to the discrete…
We address the calculation of microcanonical reaction rates for processes involving significant nuclear quantum effects using ring-polymer molecular dynamics (RPMD), both with and without electronically non-adiabatic transitions. After…
Artificial neural networks are used to fit a potential energy surface. We demonstrate the benefits of using not only energies, but also their first and second derivatives as training data for the neural network. This ensures smooth and…
A general and rigorous methodology to compute the quantum equilibrium isotope effect is described. Unlike standard approaches, ours does not assume separability of rotational and vibrational motions and does not make the harmonic…