Symmetrization of the nuclear wavefunctions defined by the quantum trajectory dynamics

Gu, Bing; Rassolov, Vitaly A.; Garashchuk, Sophya

doi:10.1007/s00214-016-2021-7

Cited by 4 publications

(3 citation statements)

References 30 publications

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“…of bosons and fermions, one finds that the distance between the fermions as they separate is larger than that of bosons—another reflection of the bunching and anti-bunching phenomenon [ 8 , 9 ]. Some researchers have even tried to describe the repulsion of fermions in terms of an artificial repulsive potential—the “Pauli potential” [ 10 , 11 , 12 , 13 , 14 ]. In statistical mechanics, this situation leads to the so-called statistical interparticle potential which is temperature-dependent since it is related to what is known as the mean thermal wavelength or thermal de Broglie wavelength [ 15 ].…”

Section: Introductionmentioning

confidence: 99%

The Influence of the Symmetry of Identical Particles on Flight Times

Miret‐Artés

Dumont

Rivlin

et al. 2021

Entropy

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In this work, our purpose is to show how the symmetry of identical particles can influence the time evolution of free particles in the nonrelativistic and relativistic domains as well as in the scattering by a potential δ-barrier. For this goal, we consider a system of either two distinguishable or indistinguishable (bosons and fermions) particles. Two sets of initial conditions have been studied: different initial locations with the same momenta, and the same locations with different momenta. The flight time distribution of particles arriving at a `screen’ is calculated in each case from the density and flux. Fermions display broader distributions as compared with either distinguishable particles or bosons, leading to earlier and later arrivals for all the cases analyzed here. The symmetry of the wave function seems to speed up or slow down the propagation of particles. Due to the cross terms, certain initial conditions lead to bimodality in the fermionic case. Within the nonrelativistic domain, and when the short-time survival probability is analyzed, if the cross term becomes important, one finds that the decay of the overlap of fermions is faster than for distinguishable particles which in turn is faster than for bosons. These results are of interest in the short time limit since they imply that the well-known quantum Zeno effect would be stronger for bosons than for fermions. Fermions also arrive earlier and later than bosons when they are scattered by a δ-barrier. Although the particle symmetry does affect the mean tunneling flight time, in the limit of narrow in momentum initial Gaussian wave functions, the mean times are not affected by symmetry but tend to the phase time for distinguishable particles.

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Section: Introductionmentioning

confidence: 99%

The Influence of the Symmetry of Identical Particles on Flight Times

Miret‐Artés

Dumont

Rivlin

et al. 2021

Entropy

View full text Add to dashboard Cite

show abstract

“…Some researchers have tried to describe the repulsion of fermions in terms of an artificial repulsive potential -the "Pauli potential". [10][11][12][13][14] In statistical mechanics, this situation leads to the so-called statistical interparticle potential which is temperature-dependent since it is related to what is known as the mean thermal wavelength or thermal de Broglie wavelength. [15] One then speaks about statistical attraction and repulsion for bosons and fermions, respectively.…”

Section: Introductionmentioning

confidence: 99%

The influence of the symmetry of identical particles on flight times

Miret-Artés,

Dumont,

Rivlin

et al. 2021

Preprint

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In this work, our purpose is to show how the symmetry of identical particles can influence the time evolution of free particles in the nonrelativistic and relativistic domains. For this goal, we consider a system of either two distinguishable or indistinguishable (bosons and fermions) particles. Two classes of initial conditions have been studied: different initial locations with the same momenta, and the same locations with different momenta. The flight time distribution of particles arriving at a 'screen' is calculated in each case. Fermions display broader distributions as compared with either distinguishable particles or bosons, leading to earlier and later arrivals for all the cases analyzed here. The symmetry of the wave function seems to speed up or slow down propagation of particles.Due to the cross terms, certain initial conditions lead to bimodality in the fermionic case. Within the nonrelativistic domain and when the short-time survival probability is analyzed, if the cross term becomes important, one finds that the decay of the overlap of fermions is faster than for distinguishable particles which in turn is faster than for bosons. These results are of interest in the short time limit since they imply that the well-known quantum Zeno effect would be stronger for bosons than for fermions. Fermions also arrive earlier than bosons when they are scattered by a delta barrier. Furthermore, the particle symmetry does not affect the mean tunneling flight time and it is given by the phase time for the distinguishable particle.

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“…As a possible strategy to avoid the exponential scaling with the dimensionality of the system, there is growing interest in the hydrodynamic or quantum trajectory formulation of the time-dependent Schrödinger equation (TDSE). [19][20][21][22][23][24][25][26][27][28] Quantum trajectories (QTs) offer the most efficient representation of the time-dependent wavefunction because their distribution follows the time-dependent probability. The main numerical difficulty stems from the approximation to the quantum potential that arises in this representation.…”

Section: Introductionmentioning

confidence: 99%

Partial hydrodynamic representation of quantum molecular dynamics

Franco

2017

The Journal of Chemical Physics

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A hybrid method is proposed to propagate system-bath quantum dynamics that use both basis functions and coupled quantum trajectories. In it, the bath is represented with an ensemble of Bohmian trajectories while the system degrees of freedom are accounted through reduced density matrices. By retaining the Hilbert space structure for the system, the method is able to capture interference processes that are challenging to describe in Bohmian dynamics due to singularities that these processes introduce in the quantum potential. By adopting quantum trajectories to represent the bath, the method beats the exponential scaling of the computational cost with the bath size. This combination makes the method suitable for large-scale ground and excited state fully quantum molecular dynamics simulations. Equations of motion for the quantum trajectories and reduced density matrices are derived from the Schrödinger equation and a computational algorithm to solve these equations is proposed. Through computations in two-dimensional model systems, the method is shown to offer an accurate description of subsystem observables and of quantum decoherence, which is difficult to obtain when the quantum nature of the bath is ignored. The scaling of the method is demonstrated using a model with 21 degrees of freedom. The limit of independent trajectories is recovered when the mass of bath degrees of freedom is much larger than the one of the system, in agreement with mixed quantum-classical descriptions.

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Symmetrization of the nuclear wavefunctions defined by the quantum trajectory dynamics

Cited by 4 publications

References 30 publications

The Influence of the Symmetry of Identical Particles on Flight Times

The Influence of the Symmetry of Identical Particles on Flight Times

The influence of the symmetry of identical particles on flight times

Partial hydrodynamic representation of quantum molecular dynamics

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