Bohm Trajectory Approach to Timing Electrons

Leavens, C.R.

doi:10.1007/3-540-45846-8_5

Cited by 9 publications

(15 citation statements)

References 54 publications

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“…Thus, although quantum trajectories are not experimentally observable 2 , the information extracted from them could be used in a practical fashion in the design or characterization of quantum control experiments involving tunneling (e.g., ionization processes or chemical reactions). In this regard, it is worth mentioning that this idea has also been considered in the literature to determine tunneling times [23] or escape rates for confined multiparticle systems [24].…”

Section: Introductionmentioning

confidence: 99%

Setting up tunneling conditions by means of Bohmian mechanics

Sanz¹,

Miret‐Artés²

2011

J. Phys. A: Math. Theor.

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Abstract. Usually tunneling is established after imposing some matching conditions on the (time-independent) wave function and its first derivative at the boundaries of a barrier. Here an alternative scheme is proposed to determine tunneling and estimate transmission probabilities in time-dependent problems, which takes advantage of the trajectory picture provided by Bohmian mechanics. From this theory a general functional expression for the transmission probability in terms of the system initial state can be reached. This expression is used here to analyze tunneling properties and estimate transmissions in the case of initial Gaussian wave packets colliding with ramp-like barriers.

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Section: Introductionmentioning

confidence: 99%

Setting up tunneling conditions by means of Bohmian mechanics

Sanz¹,

Miret‐Artés²

2011

J. Phys. A: Math. Theor.

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“…These quantum trajectories have been called 'surrealistic' by Englert et al [12] because they appear nonintuitive. Nevertheless, the quantum trajectories have been useful in treating the tunnelling time problem by Leavens and co-workers [13]. The quantum trajectories have also been used to treat quantum chaos in a manner similar to classical chaos [14,15].…”

Section: Introductionmentioning

confidence: 99%

Quantum power in de Broglie–Bohm theory

Kobe¹

2007

J. Phys. A: Math. Theor.

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In the de Broglie-Bohm approach to quantum mechanics for a charged particle in a time-dependent electromagnetic field the time derivative of the energy is equal to the classical power plus a quantum power. We show that the average of the quantum power is zero. The de Broglie-Bohm energy is obtained from the quantum mechanical energy operator, which is the Hamiltonian with the gauge-dependent scalar potential subtracted. The time derivative of the average de Broglie-Bohm energy is shown to be equal to Ehrenfest's theorem for the quantum energy operator.

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“…From the non-crossing property of Bohmian trajectories, Leavens [34] proved that the arrival time distribution is given by the modulus of the probability current density.…”

Section: Resultsmentioning

confidence: 99%

Quantum-Classical Transition for Mixed States: The Scaled Von Neumann Equation

Mousavi¹,

Miret‐Artés²

2023

Preprint

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In this work, we propose a transition wave equation from quantum to classical regime in the framework of the von Neumann formalism for ensembles and then obtain an equivalent scaled equation. This leads us to develop a scaled statistical theory following the well-known Wigner-Moyal approach of quantum mechanics. This scaled nonequilibrium statistical mechanics has in it all the ingredients of the classical and quantum theory described in terms of a continuous parameter displaying all the dynamical regimes in-between the two extreme cases. Finally, a simple application of our scaled formalism consisting of reflection from a mirror by computing various quantities including probability density plots, scaled trajectories and arrival times are analyzed.

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Bohm Trajectory Approach to Timing Electrons

Cited by 9 publications

References 54 publications

Setting up tunneling conditions by means of Bohmian mechanics

Setting up tunneling conditions by means of Bohmian mechanics

Quantum power in de Broglie–Bohm theory

Quantum-Classical Transition for Mixed States: The Scaled Von Neumann Equation

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