6 research outputs found
Decoherence and Quantum-Classical Master Equation Dynamics
The conditions under which quantum-classical Liouville dynamics may be
reduced to a master equation are investigated. Systems that can be partitioned
into a quantum-classical subsystem interacting with a classical bath are
considered. Starting with an exact non-Markovian equation for the diagonal
elements of the density matrix, an evolution equation for the subsystem density
matrix is derived. One contribution to this equation contains the bath average
of a memory kernel that accounts for all coherences in the system. It is shown
to be a rapidly decaying function, motivating a Markovian approximation on this
term in the evolution equation. The resulting subsystem density matrix equation
is still non-Markovian due to the fact that bath degrees of freedom have been
projected out of the dynamics. Provided the computation of non-equilibrium
average values or correlation functions is considered, the non-Markovian
character of this equation can be removed by lifting the equation into the full
phase space of the system. This leads to a trajectory description of the
dynamics where each fictitious trajectory accounts for decoherence due to the
bath degrees of freedom. The results are illustrated by computations of the
rate constant of a model nonadiabatic chemical reaction.Comment: 13 pages, 6 figures, revision includes: Added references on mixed
quantum-classical Liouville theory, and some minor details that address the
comments of the reviewe
Surface-hopping dynamics and decoherence with quantum equilibrium structure
In open quantum systems decoherence occurs through interaction of a quantum
subsystem with its environment. The computation of expectation values requires
a knowledge of the quantum dynamics of operators and sampling from initial
states of the density matrix describing the subsystem and bath. We consider
situations where the quantum evolution can be approximated by quantum-classical
Liouville dynamics and examine the circumstances under which the evolution can
be reduced to surface-hopping dynamics, where the evolution consists of
trajectory segments evolving exclusively on single adiabatic surfaces, with
probabilistic hops between these surfaces. The justification for the reduction
depends on the validity of a Markovian approximation on a bath averaged memory
kernel that accounts for quantum coherence in the system. We show that such a
reduction is often possible when initial sampling is from either the quantum or
classical bath initial distributions. If the average is taken only over the
quantum dispersion that broadens the classical distribution, then such a
reduction is not always possible.Comment: 11, pages, 8 figure
Quantum-Classical Master Equation Dynamics: An Analysis of Decoherence and Surface-hopping Techniques
In this thesis quantum-classical dynamics is applied to the study of quantum condensed phase processes. This approach is based on the quantum-classical Liouville equation where the dynamics of a small subset of the degrees of freedom are treated quantum mechanically while the remaining degrees of freedom are treated by classical mechanics to a good approximation. We use this approach as it is computationally tractable, and the resulting equation of motion accurately accounts for the quantum and classical dynamics, as well as the coupling between these two components of the system.
By recasting the quantum-classical Liouville equation into the form of a generalized master equation we investigate connections to surface-hopping. The link between these approaches is decoherence arising from interaction of the subsystem with the environment. We derive an evolution equation for the subsystem which contains terms accounting for the effects of the environment. One of these terms involves a memory kernel that accounts for the coherent dynamics. If this term decays rapidly, a Markovian approximation can be made. By lifting the resulting subsystem master equation into the full phase space, we obtain a Markovian master equation that prescribes surface-hopping-like dynamics. Our analysis outlines the conditions under which such a description is valid.
Next, we consider the calculation of the rate constant for a quantum mechanical barrier crossing process. Starting from the reactive-flux autocorrelation function, we derive a quantum-classical expression for the rate kernel. This expression involves quantum-classical evolution of a species operator averaged over the initial quantum equilibrium structure of the system making it possible to compute the rate constant via computer simulation. Using a simple model for a proton transfer reaction we compare the results of the rate calculation obtained by quantum-classical Liouville dynamics with that of master equation dynamics. The master equation provides a good approximation to the full quantum-classical Liouville calculation for our model and a more stable algorithm results due to the elimination of oscillating phase factors in the simulation.
Finally, we make use of the theoretical framework established in this thesis to analyze some aspects of decoherence used in popular surface-hopping techniques.Ph
Second asymptomatic carotid surgery trial (ACST-2) : a randomised comparison of carotid artery stenting versus carotid endarterectomy
Background: Among asymptomatic patients with severe carotid artery stenosis but no recent stroke or transient cerebral ischaemia, either carotid artery stenting (CAS) or carotid endarterectomy (CEA) can restore patency and reduce long-term stroke risks. However, from recent national registry data, each option causes about 1% procedural risk of disabling stroke or death. Comparison of their long-term protective effects requires large-scale randomised evidence.
Methods: ACST-2 is an international multicentre randomised trial of CAS versus CEA among asymptomatic patients with severe stenosis thought to require intervention, interpreted with all other relevant trials. Patients were eligible if they had severe unilateral or bilateral carotid artery stenosis and both doctor and patient agreed that a carotid procedure should be undertaken, but they were substantially uncertain which one to choose. Patients were randomly allocated to CAS or CEA and followed up at 1 month and then annually, for a mean 5 years. Procedural events were those within 30 days of the intervention. Intention-to-treat analyses are provided. Analyses including procedural hazards use tabular methods. Analyses and meta-analyses of non-procedural strokes use Kaplan-Meier and log-rank methods. The trial is registered with the ISRCTN registry, ISRCTN21144362.
Findings: Between Jan 15, 2008, and Dec 31, 2020, 3625 patients in 130 centres were randomly allocated, 1811 to CAS and 1814 to CEA, with good compliance, good medical therapy and a mean 5 years of follow-up. Overall, 1% had disabling stroke or death procedurally (15 allocated to CAS and 18 to CEA) and 2% had non-disabling procedural stroke (48 allocated to CAS and 29 to CEA). Kaplan-Meier estimates of 5-year non-procedural stroke were 2·5% in each group for fatal or disabling stroke, and 5·3% with CAS versus 4·5% with CEA for any stroke (rate ratio [RR] 1·16, 95% CI 0·86-1·57; p=0·33). Combining RRs for any non-procedural stroke in all CAS versus CEA trials, the RR was similar in symptomatic and asymptomatic patients (overall RR 1·11, 95% CI 0·91-1·32; p=0·21).
Interpretation: Serious complications are similarly uncommon after competent CAS and CEA, and the long-term effects of these two carotid artery procedures on fatal or disabling stroke are comparable