Experience and Understanding

Miller, David

doi:10.1007/978-1-349-20550-9_2

Cited by 180 publications

(316 citation statements)

References 1 publication

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“…The primary difference is that our model does not restrict tunneling only to the "corner to corner" (or corner to edge) path, but allows for tunneling in the "comer to comer" direction every time the component of the motion along this direction experiences a classical turning point. We also note that this "comer to comer" tunneling direction is also very similar to that yielded in some applications of "rigorous" semiclassical theories, i.e., classical S-matrix theory 23 and the instanton mode1. 24 • 25 4.…”

Section: Choice Of Tile Tunneling Pathsupporting

confidence: 77%

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Reaction Dynamics in Polyatomic Molecular Systems: Some Approaches for Constructing Potential Energy Surfaces and Incorporating Quantum Effects in Classical Trajectory Simulations

Miller

1992

Molecular Aspects of Biotechnology: Computational Models and Theories

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Section: Choice Of Tile Tunneling Pathsupporting

confidence: 77%

“…Calculations based on the more rigorous classical S-matrix 23 and "instanton" 24.25 theories show that the optimum tunneling path is relatively straight in the tunneling region.…”

Section: General (Non-separable) Casementioning

confidence: 99%

Reaction Dynamics in Polyatomic Molecular Systems: Some Approaches for Constructing Potential Energy Surfaces and Incorporating Quantum Effects in Classical Trajectory Simulations

Miller

1992

Molecular Aspects of Biotechnology: Computational Models and Theories

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“…The instanton trajectory is a PO in the inverted potential −V and, in a path integral formalism, it is directly related to the tunneling of a particle through the barrier. 19,20,31,54,55 We use the potential…”

Section: B Determining Instanton Trajectories In 2dmentioning

confidence: 99%

Variational principle for the determination of unstable periodic orbits and instanton trajectories at saddle points

2017

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The complexity of arbitray dynamical systems and chemical reactions, in particular, can often be resolved if only the appropriate periodic orbit-in the form of a limit cycle, dividing surface, instanton trajectories or some other related structure-can be uncovered. Determining such a periodic orbit, no matter how beguilingly simple it appears, is often very challenging. We present a method for the direct construction of unstable periodic orbits and instanton trajectories at saddle points by means of Lagrangian descriptors. Such structures result from the minimization of a scalarvalued phase space function without need for any additional constraints or knowledge. We illustrate the approach for two-degree of freedom systems at a rank-1 saddle point of the underlying potential energy surface by constructing both periodic orbits at energies above the saddle point as well as instanton trajectories below the saddle point energy.

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“…The semiclassical approximation proceeds by replacing the quantum-mechanical Green's function by its semiclassical limit G SC : 11,22 …”

Section: ͑4͒mentioning

confidence: 99%

“…[10][11][12][13][14][15][16][17][18][19] We recall that Eq. ͑14͒ employs the semiclassical Green's function, or Fourier-Laplace transform of the Van Vleck propagator, 22,9 for the motion in the interior of the billiard structure. No additional approximation has been made up to this point.…”

Section: Semiclassical Approximationsmentioning

confidence: 99%

Gauge-invariant theory for semiclassical magnetotransport through ballistic microstructures

1999

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Within the semiclassical theory of magnetotransport through ballistic cavities, fluctuations in the transmission amplitude and in the conductance originate from the Aharonov-Bohm phase of directed areas. We formulate the semiclassical transmission amplitude in gauge-invariant form. The gauge invariant phases can be visualized in terms of areas enclosed by classical paths, which consist of the real path connecting the entrance point to the exit point and a virtual path leading back to the entrance point. We implement this method on different levels of a semiclassical description of magnetotransport with applications to magnetoconductance fluctuations and correlations. The validity of the semiclassical theories is analyzed. ͓S0163-1829͑99͒10903-2͔

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Experience and Understanding

Cited by 180 publications

References 1 publication

Reaction Dynamics in Polyatomic Molecular Systems: Some Approaches for Constructing Potential Energy Surfaces and Incorporating Quantum Effects in Classical Trajectory Simulations

Reaction Dynamics in Polyatomic Molecular Systems: Some Approaches for Constructing Potential Energy Surfaces and Incorporating Quantum Effects in Classical Trajectory Simulations

Variational principle for the determination of unstable periodic orbits and instanton trajectories at saddle points

Gauge-invariant theory for semiclassical magnetotransport through ballistic microstructures

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