The Experts below are selected from a list of 267 Experts worldwide ranked by ideXlab platform
Raymond Kapral - One of the best experts on this subject based on the ideXlab platform.
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forward backward solution of quantum classical Liouville Equation in the adiabatic mapping basis
Molecular Physics, 2013Co-Authors: Changyu Hsieh, Jeremy Schofield, Raymond KapralAbstract:A forward–backward solution of quantum-classical Liouville Equation in the adiabatic mapping basis is constructed. The trajectory dynamics of this solution admits an interpretation that is different from that in the quantum subsystem basis and allows one to establish a connection between mean-field and surface-hopping algorithms within the quantum-classical Liouville Equation framework. This adiabatic formulation also suggests hybrid simulation schemes that combine aspects of mean-field and surface-hoping dynamics.
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Analysis of the quantum-classical Liouville Equation in the mapping basis
The Journal of chemical physics, 2010Co-Authors: Ali Nassimi, Sara Bonella, Raymond KapralAbstract:The quantum-classical Liouville Equation provides a description of the dynamics of a quantum subsystem coupled to a classical environment. Representing this Equation in the mapping basis leads to a continuous description of discrete quantum states of the subsystem and may provide an alternate route to the construction of simulation schemes. In the mapping basis the quantum-classical Liouville Equation consists of a Poisson bracket contribution and a more complex term. By transforming the evolution Equation, term-by-term, back to the subsystem basis, the complex term (excess coupling term) is identified as being due to a fraction of the back reaction of the quantum subsystem on its environment. A simple approximation to quantum-classical Liouville dynamics in the mapping basis is obtained by retaining only the Poisson bracket contribution. This approximate mapping form of the quantum-classical Liouville Equation can be simulated easily by Newtonian trajectories. We provide an analysis of the effects of neg...
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Analysis of the quantum-classical Liouville Equation in the mapping basis
The Journal of chemical physics, 2010Co-Authors: Ali Nassimi, Sara Bonella, Raymond KapralAbstract:The quantum-classical Liouville Equation provides a description of the dynamics of a quantum subsystem coupled to a classical environment. Representing this Equation in the mapping basis leads to a continuous description of discrete quantum states of the subsystem and may provide an alternate route to the construction of simulation schemes. In the mapping basis the quantum-classical Liouville Equation consists of a Poisson bracket contribution and a more complex term. By transforming the evolution Equation, term-by-term, back to the subsystem basis, the complex term (excess coupling term) is identified as being due to a fraction of the back reaction of the quantum subsystem on its environment. A simple approximation to quantum-classical Liouville dynamics in the mapping basis is obtained by retaining only the Poisson bracket contribution. This approximate mapping form of the quantum-classical Liouville Equation can be simulated easily by Newtonian trajectories. We provide an analysis of the effects of neglecting the presence of the excess coupling term on the expectation values of various types of observables. Calculations are carried out on nonadiabatic population and quantum coherence dynamics for curve crossing models. For these observables, the effects of the excess coupling term enter indirectly in the computation and good estimates are obtained with the simplified propagation.
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QUANTUM-CLASSICAL WIGNER-Liouville Equation
Ukrainian Mathematical Journal, 2005Co-Authors: Raymond Kapral, Alessandro SergiAbstract:We consider a quantum system that is partitioned into a subsystem and a bath. Starting from the Wigner transform of the von Neumann Equation for the quantum-mechanical density matrix of the entire system, the quantum-classical Wigner-Liouville Equation is obtained in the limit where the masses M of the bath particles are large as compared with the masses m of the subsystem particles. The structure of this Equation is discussed and it is shown how the abstract operator form of the quantum-classical Liouville Equation is obtained by taking the inverse Wigner transform on the subsystem. Solutions in terms of classical trajectory segments and quantum transition or momentum jumps are described.
Ali Nassimi - One of the best experts on this subject based on the ideXlab platform.
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Analysis of the quantum-classical Liouville Equation in the mapping basis
The Journal of chemical physics, 2010Co-Authors: Ali Nassimi, Sara Bonella, Raymond KapralAbstract:The quantum-classical Liouville Equation provides a description of the dynamics of a quantum subsystem coupled to a classical environment. Representing this Equation in the mapping basis leads to a continuous description of discrete quantum states of the subsystem and may provide an alternate route to the construction of simulation schemes. In the mapping basis the quantum-classical Liouville Equation consists of a Poisson bracket contribution and a more complex term. By transforming the evolution Equation, term-by-term, back to the subsystem basis, the complex term (excess coupling term) is identified as being due to a fraction of the back reaction of the quantum subsystem on its environment. A simple approximation to quantum-classical Liouville dynamics in the mapping basis is obtained by retaining only the Poisson bracket contribution. This approximate mapping form of the quantum-classical Liouville Equation can be simulated easily by Newtonian trajectories. We provide an analysis of the effects of neg...
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Analysis of the quantum-classical Liouville Equation in the mapping basis
The Journal of chemical physics, 2010Co-Authors: Ali Nassimi, Sara Bonella, Raymond KapralAbstract:The quantum-classical Liouville Equation provides a description of the dynamics of a quantum subsystem coupled to a classical environment. Representing this Equation in the mapping basis leads to a continuous description of discrete quantum states of the subsystem and may provide an alternate route to the construction of simulation schemes. In the mapping basis the quantum-classical Liouville Equation consists of a Poisson bracket contribution and a more complex term. By transforming the evolution Equation, term-by-term, back to the subsystem basis, the complex term (excess coupling term) is identified as being due to a fraction of the back reaction of the quantum subsystem on its environment. A simple approximation to quantum-classical Liouville dynamics in the mapping basis is obtained by retaining only the Poisson bracket contribution. This approximate mapping form of the quantum-classical Liouville Equation can be simulated easily by Newtonian trajectories. We provide an analysis of the effects of neglecting the presence of the excess coupling term on the expectation values of various types of observables. Calculations are carried out on nonadiabatic population and quantum coherence dynamics for curve crossing models. For these observables, the effects of the excess coupling term enter indirectly in the computation and good estimates are obtained with the simplified propagation.
J.-c. Yera - One of the best experts on this subject based on the ideXlab platform.
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Vortex solutions of the Liouville Equation
arXiv: High Energy Physics - Theory, 1998Co-Authors: Peter A. Horvathy, J.-c. YeraAbstract:The most general vortex solution of the Liouville Equation (which arises in non-relativistic Chern-Simons theory) is associated with rational functions, $f(z)=P(z)/Q(z)$ where $P(z)$ and $Q(z)$ are both polynomials, $°P
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Vortex Solutions of the Liouville Equation
Letters in Mathematical Physics, 1998Co-Authors: Peter A. Horvathy, J.-c. YeraAbstract:The most general vortex solution of the Liouville Equation (which arises in nonrelativistic Chern–Simons theory) is associated with rational functions, f(z)=P(z) ∖Q∥z), where P(z) and Q(z) are both polynomials, deg P
Sara Bonella - One of the best experts on this subject based on the ideXlab platform.
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Analysis of the quantum-classical Liouville Equation in the mapping basis
The Journal of chemical physics, 2010Co-Authors: Ali Nassimi, Sara Bonella, Raymond KapralAbstract:The quantum-classical Liouville Equation provides a description of the dynamics of a quantum subsystem coupled to a classical environment. Representing this Equation in the mapping basis leads to a continuous description of discrete quantum states of the subsystem and may provide an alternate route to the construction of simulation schemes. In the mapping basis the quantum-classical Liouville Equation consists of a Poisson bracket contribution and a more complex term. By transforming the evolution Equation, term-by-term, back to the subsystem basis, the complex term (excess coupling term) is identified as being due to a fraction of the back reaction of the quantum subsystem on its environment. A simple approximation to quantum-classical Liouville dynamics in the mapping basis is obtained by retaining only the Poisson bracket contribution. This approximate mapping form of the quantum-classical Liouville Equation can be simulated easily by Newtonian trajectories. We provide an analysis of the effects of neg...
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Analysis of the quantum-classical Liouville Equation in the mapping basis
The Journal of chemical physics, 2010Co-Authors: Ali Nassimi, Sara Bonella, Raymond KapralAbstract:The quantum-classical Liouville Equation provides a description of the dynamics of a quantum subsystem coupled to a classical environment. Representing this Equation in the mapping basis leads to a continuous description of discrete quantum states of the subsystem and may provide an alternate route to the construction of simulation schemes. In the mapping basis the quantum-classical Liouville Equation consists of a Poisson bracket contribution and a more complex term. By transforming the evolution Equation, term-by-term, back to the subsystem basis, the complex term (excess coupling term) is identified as being due to a fraction of the back reaction of the quantum subsystem on its environment. A simple approximation to quantum-classical Liouville dynamics in the mapping basis is obtained by retaining only the Poisson bracket contribution. This approximate mapping form of the quantum-classical Liouville Equation can be simulated easily by Newtonian trajectories. We provide an analysis of the effects of neglecting the presence of the excess coupling term on the expectation values of various types of observables. Calculations are carried out on nonadiabatic population and quantum coherence dynamics for curve crossing models. For these observables, the effects of the excess coupling term enter indirectly in the computation and good estimates are obtained with the simplified propagation.
Eitan Geva - One of the best experts on this subject based on the ideXlab platform.
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a derivation of the mixed quantum classical Liouville Equation from the influence functional formalism
Journal of Chemical Physics, 2004Co-Authors: Qiang Shi, Eitan GevaAbstract:We show that the mixed quantum-classical Liouville Equation is equivalent to linearizing the forward-backward action in the influence functional. Derivations are provided in terms of either the diabatic or adiabatic basis sets. An application of the mixed quantum-classical Liouville Equation for calculating the memory kernel of the generalized quantum master Equation is also presented. The accuracy and computational feasibility of such an approach is demonstrated in the case of a two-level system nonlinearly coupled to an anharmonic bath.