Applied Bohmian mechanics

Benseny, Albert; Albareda, Guillermo; Sanz, Ángel S.; Mompart, J.; Oriols, X.

doi:10.1140/epjd/e2014-50222-4

Cited by 103 publications

(156 citation statements)

References 412 publications

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“…It will be important for us when we begin to derive the Schrödinger equation. For that reason we need to derive the quantum potential, which is a main term underlying Bohmian quantum mechanics [44,45,48,49].…”

Section: Description Of Motion Of a Fluid With The Hydrogen Ionsmentioning

confidence: 99%

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Quantum consciousness in warm, wet and noisy brain

Sbitnev

2016

Mod. Phys. Lett. B

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The emergence of quantum consciousness stems from dynamic flows of hydrogen ions in brain liquid. This liquid contains vast areas of the fourth phase of water with hexagonal packing of its molecules, the so-called exclusion zone (EZ) of water. The hydrogen ion motion on such hexagonal lattices shows as the hopping of the ions forward and the holes (vacant places) backward, caused by the Grotthuss mechanism. By supporting this motion using external infrasound sources, one may achieve the appearance of the superfluid state of the EZ water. Flows of the hydrogen ions are described by the modified Navier-Stokes equation. It, along with the continuity equation, yields the nonlinear Schrödinger equation, which describes the quantum effects of these flows, such as the tunneling at long distances or the interference on gap junctions.

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Section: Description Of Motion Of a Fluid With The Hydrogen Ionsmentioning

confidence: 99%

“…The gradient ∇(Q + U 2,1 ) enclosed by curly bracket (c) determines a generalized force of Newton's second law [49,58] in the Bohmian mechanics due to presence of the quantum potential Q. This force is caused by both the quantum potential Q( r, t) and the imposed external potential U 2,1 ( r, t).…”

Section: Transition To the Schrödinger Equationmentioning

confidence: 99%

Quantum consciousness in warm, wet and noisy brain

Sbitnev

2016

Mod. Phys. Lett. B

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“…Starting with Ψ(R 1 , R 2 , t = 0), we first sample its probability density with trajectories 13,38 and then propagate eq 5 together with the Hermitian limit of eq 3. Figures 4a and 5a show snapshots at different times of the one-particle reduced nuclear probability density, computed as ρ 1 (R 1 , t) = ∫ dR 2 |Ψ(R 1 , R 2 , t)| 2 from the solution of eq 1 (in black solid line), and computed as…”

Section: The Journal Of Physical Chemistry Lettersmentioning

confidence: 99%

Conditional Born–Oppenheimer Dynamics: Quantum Dynamics Simulations for the Model Porphine

Albareda

Bofill

Tavernelli

et al. 2015

J. Phys. Chem. Lett.

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We report a new theoretical approach to solve adiabatic quantum molecular dynamics halfway between wave function and trajectory-based methods. The evolution of a N-body nuclear wave function moving on a 3N-dimensional Born− Oppenheimer potential-energy hyper-surface is rewritten in terms of single-nuclei wave functions evolving nonunitarily on a 3-dimensional potential-energy surface that depends parametrically on the configuration of an ensemble of generally defined trajectories. The scheme is exact and, together with the use of trajectory-based statistical techniques, can be exploited to circumvent the calculation and storage of many-body quantities (e.g., wave function and potential-energy surface) whose size scales exponentially with the number of nuclear degrees of freedom. As a proof of concept, we present numerical simulations of a 2-dimensional model porphine where switching from concerted to sequential double proton transfer (and back) is induced quantum mechanically. O n the basis of the Born−Huang expansion of the molecular wave function, 1 an exact description of adiabatic molecular dynamics requires the propagation of a nuclear wavepacket on the ground-state Born−Oppenheimer potential-energy surface (gs-BOPES). This propagation scheme is, somehow, computationally doubly prohibitive. Besides the computational burden associated with the propagation of the (many-body) nuclear wave function, the calculation of the gs-BOPES constitutes, per se, a time-independent problem that grows exponentially with the number of electrons and nuclei. In this respect, two main classes of computational methods have emerged depending on whether the knowledge of the gs-BOPES is required in the full configuration space, that is, fullquantum methods, 2,3 or only at certain reduced number of points, namely trajectory-based or direct methods.4,5 While methods for computing the energy of any configuration of nuclei have become quicker and more accurate, full-quantum dynamics calculations still become rapidly unfeasible for large molecules. Alternatively, direct dynamics notably reduce the computational cost of the simulations by avoiding partially, sometimes completely, the calculation of the full gs-BOPES (this can be done, for instance, by the use of reaction-path Hamiltonians 6,7 ). Nuclear quantum effects, however, can be hardly included systematically in this second class of methods. Up to date, only quantum-trajectory methods have the particularity of being able to describe all nuclear quantum effects (just as full-quantum methods) and being on-the-fly simultaneously.8−11 Unfortunately, these methods have serious problems in dealing with the so-called quantum potential, which gathers, by definition, all quantum information on the system. The mathematical structure of the quantum potential depends on the inverse of the quantum probability density, and thus, its manipulation entails serious instability problems. 12−14We report here an exact theoretical approach to solve adiabatic quantum molecular dynamics based o...

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“…Analogously, this geometrical nature has also been observed in nonclassical light. This naturally leads to the issue of Bohmian chaos [48], which is absent in all cases analyzed here, because vortices need to be evolving in time.…”

Section: Final Remarksmentioning

confidence: 99%

Nonclassical polarization dynamics in classical-like states

Luis

Sanz

2015

Phys. Rev. A

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Quantum polarization is investigated by means of a trajectory picture based on the Bohmian formulation of quantum mechanics. Relevant examples of classical-like two-mode field states are thus examined, namely, Glauber and SU(2) coherent states. Although these states are often regarded as classical, the analysis here shows that the corresponding electric-field polarization trajectories display topologies very different from those expected from classical electrodynamics. Rather than incompatibility with the usual classical model, this result demonstrates the dynamical richness of quantum motions, determined by local variations of the system quantum phase in the corresponding (polarization) configuration space, absent in classical-like models. These variations can be related to the evolution in time of the phase, but also to its dependence on configurational coordinates, which is the crucial factor to generate motion in the case of stationary states like those considered here. In this regard, for completeness these results are compared with those obtained from nonclassical NOON states.

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Applied Bohmian mechanics

Cited by 103 publications

References 412 publications

Quantum consciousness in warm, wet and noisy brain

Quantum consciousness in warm, wet and noisy brain

Conditional Born–Oppenheimer Dynamics: Quantum Dynamics Simulations for the Model Porphine

Nonclassical polarization dynamics in classical-like states

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