370 research outputs found
Coupled forward-backward trajectory approach for non-equilibrium electron-ion dynamics
We introduce a simple ansatz for the wavefunction of a many-body system based
on coupled forward and backward-propagating semiclassical trajectories. This
method is primarily aimed at, but not limited to, treating nonequilibrium
dynamics in electron-phonon systems. The time-evolution of the system is
obtained from the Euler-Lagrange variational principle, and we show that this
ansatz yields Ehrenfest mean field theory in the limit that the forward and
backward trajectories are orthogonal, and in the limit that they coalesce. We
investigate accuracy and performance of this method by simulating electronic
relaxation in the spin-boson model and the Holstein model. Although this method
involves only pairs of semiclassical trajectories, it shows a substantial
improvement over mean field theory, capturing quantum coherence of nuclear
dynamics as well as electron-nuclear correlations. This improvement is
particularly evident in nonadiabatic systems, where the accuracy of this
coupled trajectory method extends well beyond the perturbative electron-phonon
coupling regime. This approach thus provides an attractive route forward to the
ab-initio description of relaxation processes, such as thermalization, in
condensed phase systems
Improving the accuracy and efficiency of time-resolved electronic spectra calculations: Cellular dephasing representation with a prefactor
Time-resolved electronic spectra can be obtained as the Fourier transform of
a special type of time correlation function known as fidelity amplitude, which,
in turn, can be evaluated approximately and efficiently with the dephasing
representation. Here we improve both the accuracy of this approximation---with
an amplitude correction derived from the phase-space propagator---and its
efficiency---with an improved cellular scheme employing inverse Weierstrass
transform and optimal scaling of the cell size. We demonstrate the advantages
of the new methodology by computing dispersed time-resolved stimulated emission
spectra in the harmonic potential, pyrazine, and the NCO molecule. In contrast,
we show that in strongly chaotic systems such as the quartic oscillator the
original dephasing representation is more appropriate than either the cellular
or prefactor-corrected methods.Comment: submitte
Capturing Vacuum Fluctuations and Photon Correlations in Cavity Quantum Electrodynamics with Multi-Trajectory Ehrenfest Dynamics
We describe vacuum fluctuations and photon-field correlations in interacting
quantum mechanical light-matter systems, by generalizing the application of
mixed quantum-classical dynamics techniques. We employ the multi-trajectory
implementation of Ehrenfest mean field theory, traditionally developed for
electron-nuclear problems, to simulate the spontaneous emission of radiation in
a model quantum electrodynamical cavity-bound atomic system. We investigate the
performance of this approach in capturing the dynamics of spontaneous emission
from the perspective of both the atomic system and the cavity photon field,
through a detailed comparison with exact benchmark quantum mechanical
observables and correlation functions. By properly accounting for the quantum
statistics of the vacuum field, while using mixed quantum-classical (mean
field) trajectories to describe the evolution, we identify a surprisingly
accurate and promising route towards describing quantum effects in realistic
correlated light-matter systems
Mathematical Methods in Quantum Molecular Dynamics
This report summarizes the 2015 Oberwolfach meeting on mathematical methods in quantum molecular dynamics. Over decades this field has hosted considerable research activity from different disciplines, such as mathematics, chemistry, and physics. The workshop has aimed at bringing together these scientists for mutual benefit
On the Inversion of High Energy Proton
Inversion of the K-fold stochastic autoconvolution integral equation is an
elementary nonlinear problem, yet there are no de facto methods to solve it
with finite statistics. To fix this problem, we introduce a novel inverse
algorithm based on a combination of minimization of relative entropy, the Fast
Fourier Transform and a recursive version of Efron's bootstrap. This gives us
power to obtain new perspectives on non-perturbative high energy QCD, such as
probing the ab initio principles underlying the approximately negative binomial
distributions of observed charged particle final state multiplicities, related
to multiparton interactions, the fluctuating structure and profile of proton
and diffraction. As a proof-of-concept, we apply the algorithm to ALICE
proton-proton charged particle multiplicity measurements done at different
center-of-mass energies and fiducial pseudorapidity intervals at the LHC,
available on HEPData. A strong double peak structure emerges from the
inversion, barely visible without it.Comment: 29 pages, 10 figures, v2: extended analysis (re-projection ratios,
2D
Parallel Implementation of Semiclassical Transition State Theory
This paper presents the parsctst code, an efficient parallel implementation of the semiclassical transition state theory (SCTST) for reaction rate constant calculations. Parsctst is developed starting from a previously presented approach for the computation of the vibrational density of states of fully coupled anharmonic molecules (Nguyen et al. Chem. Phys. Lett. 2010, 499, 915). The parallel implementation makes it practical to tackle reactions involving more than 100 fully coupled anharmonic vibrational degrees of freedom and also includes multidimensional tunneling effects. After describing the pseudocode and demonstrating its computational efficiency, we apply the new code for estimating the rate constant of the proton transfer isomerization reaction of the 2,4,6-tri-tert-butylphenyl to 3,5-di-tert-butylneophyl. Comparison with both theoretical and experimental results is presented. Parsctst code is user-friendly and provides a significant computational time saving compared to serial calculations. We believe that parsctst can boost the application of SCTST as an alternative to the basic transition state theory for accurate kinetics modeling not only in combustion or atmospheric chemistry, but also in organic synthesis, where bigger reactive systems are encountered
Development and application of semiclassical models for strong-field phenomena
Semiclassical models based on classical trajectories for the description of the electron motion in the continuum are a powerful tool of strong-field, ultrafast, and attosecond physics. The semiclassical models allow us to identify the specific mechanism of a phenomenon of interest and visualize it in terms of classical trajectories. Often these models are also computationally simple. In the present work we developed a range of new semiclassical models and applied them to various strong-field phenomena. Among these are: capture of electrons into Rydberg states, sequential multiple ionization, above-threshold ionization of the hydrogen molecule, multielectron effects due to the laser-induced polarization of the atomic ion, and strong-field holography with photoelectrons. We also used the semiclassical simulations to understand the results obtained using quantum optimal control theory, namely, optimization of the high-harmonic yield by shaping of the driving pulse. We developed a method capable of retrieving effective single-active electron potentials, which are required for semiclassical simulations. In this method the single-active electron potential is found as the result of an optimization procedure aimed at reproducing given photoelectron momentum distributions. Finally, we applied deep learning to retrieve the internuclear distance in a molecule ionized by a strong laser pulse from the photoelectron momentum distribution. The results of this thesis will serve as a basis for development of new generation of semiclassical models that are expected to combine accurate description of the ionization step, the ability to account for interference and multielectron effects, and numerical efficiency. The emergence of such models will open new perspectives in the theory of laser-matter interaction
Numerical computation of rare events via large deviation theory
An overview of rare events algorithms based on large deviation theory (LDT)
is presented. It covers a range of numerical schemes to compute the large
deviation minimizer in various setups, and discusses best practices, common
pitfalls, and implementation trade-offs. Generalizations, extensions, and
improvements of the minimum action methods are proposed. These algorithms are
tested on example problems which illustrate several common difficulties which
arise e.g. when the forcing is degenerate or multiplicative, or the systems are
infinite-dimensional. Generalizations to processes driven by non-Gaussian
noises or random initial data and parameters are also discussed, along with the
connection between the LDT-based approach reviewed here and other methods, such
as stochastic field theory and optimal control. Finally, the integration of
this approach in importance sampling methods using e.g. genealogical algorithms
is explored
Quantum Computing for Fusion Energy Science Applications
This is a review of recent research exploring and extending present-day
quantum computing capabilities for fusion energy science applications. We begin
with a brief tutorial on both ideal and open quantum dynamics, universal
quantum computation, and quantum algorithms. Then, we explore the topic of
using quantum computers to simulate both linear and nonlinear dynamics in
greater detail. Because quantum computers can only efficiently perform linear
operations on the quantum state, it is challenging to perform nonlinear
operations that are generically required to describe the nonlinear differential
equations of interest. In this work, we extend previous results on embedding
nonlinear systems within linear systems by explicitly deriving the connection
between the Koopman evolution operator, the Perron-Frobenius evolution
operator, and the Koopman-von Neumann evolution (KvN) operator. We also
explicitly derive the connection between the Koopman and Carleman approaches to
embedding. Extension of the KvN framework to the complex-analytic setting
relevant to Carleman embedding, and the proof that different choices of complex
analytic reproducing kernel Hilbert spaces depend on the choice of Hilbert
space metric are covered in the appendices. Finally, we conclude with a review
of recent quantum hardware implementations of algorithms on present-day quantum
hardware platforms that may one day be accelerated through Hamiltonian
simulation. We discuss the simulation of toy models of wave-particle
interactions through the simulation of quantum maps and of wave-wave
interactions important in nonlinear plasma dynamics.Comment: 42 pages; 12 figures; invited paper at the 2021-2022 International
Sherwood Fusion Theory Conferenc
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