Stochastic Bohmian and Scaled Trajectories

Mousavi, S. V.; Miret‐Artés, Salvador

doi:10.1007/s10701-022-00598-2

Cited by 6 publications

(4 citation statements)

References 80 publications

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“…As before, we are going to work on dimensionless variables. By using the same definitions as given by equations ( 29)- (31), and adding a few more for the scaled functions…”

Section: Preliminariesmentioning

confidence: 99%

“…At this level, it is interesting to point out that this process studied within this theoretical scheme displays decoherence due to the gradual transition from the quantum to the classical regime. This kind of studies has been extended to dissipative and stochastic dynamics in the framework of the CK and the so-called Schrödinger-Langevin or Kostin equations, respectively [28,29,31].…”

Section: Introductionmentioning

confidence: 99%

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Different routes to the classical limit of backflow

Mousavi¹,

Miret‐Artés²

2022

J. Phys. A: Math. Theor.

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Decoherence is a well established process for the emergence of classical mechanics in open quantum systems. However, it can have two different origins or mechanisms depending on the dynamics one is considering, speaking then about intrinsic decoherence for isolated systems and environmental decoherence due to dissipation/fluctuations for open systems. This second mechanism can not be considered for backflow since no thermal fluctuation terms can be added in the formalism in order to keep an important requirement for the occurrence of this effect: only contributions of positive momenta along time should be maintained. The purpose of this work is to analyze the backflow effect in the light of the underlying intrinsic decoherence and the dissipative dynamics. For this goal, we first deal with the Milburn approach where a mean frequency of the unitary evolution steps undergone for the system is assumed. A comparative analysis is carried out in terms of the Lindblad master equation. Second, the so-called quantum-to-classical transition wave equation is analyzed from a linear scaled Schr\"odinger equation which is derived and expressed in terms of a continuous parameter covering from the quantum to the classical regime as well as all in-between dynamical non-classical regimes. This theoretical analysis is inspired by the Wentzel-Kramers-Brillouin approximation. And third, in order to complete our analysis, the transition wave equation formalism is also applied to dissipative backflow within the Caldirola-Kanai approach where the dissipative dynamics comes from an effective Hamiltonian. In all the cases treated here, backflow is gradually suppressed as the intrinsic decoherence process is developing, paying a special attention to the classical limit. The route to classicality is not unique.

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“…As before, we are going to work on dimensionless variables. By using the same definitions as given by equations ( 29)- (31), and adding a few more for the scaled functions…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Different routes to the classical limit of backflow

Mousavi¹,

Miret‐Artés²

2022

J. Phys. A: Math. Theor.

Self Cite

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show abstract

“…By using the same definitions as given by Eqs. ( 29), (30), and (31), and adding a few more for the scaled functions…”

Section: Preliminariesmentioning

confidence: 99%

Different routes to the classical limit of backflow

Mousavi,

Miret-Artes

2022

Preprint

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Decoherence is a well established process for the emergence of classical mechanics in open quantum systems.However, it can have two different origins or mechanisms depending on the dynamics one is considering, speaking then about intrinsic decoherence for isolated systems and environmental decoherence due to dissipation/fluctuations for open systems. This second mechanism can not be considered for backflow since no thermal fluctuation terms can be added in the formalism in order to keep an important requirement for the occurrence of this effect: only contributions of positive momenta along time should be maintained. The purpose of this work is to analyze the backflow effect in the light of the underlying intrinsic decoherence and the dissipative dynamics. For this goal, we first deal with the Milburn approach where a mean frequency of the unitary evolution steps undergone for the system is assumed. A comparative analysis is carried out in terms of the Lindblad master equation. Second, the so-called quantum-to-classical transition wave equation is analyzed from a linear scaled Schrödinger equation which is derived and expressed in terms of a continuous parameter covering from the quantum to the classical regime as well as all in-between dynamical non-classical regimes. This theoretical analysis is inspired by the Wentzel-Kramers-Brillouin approximation. And third, in order to complete our analysis, the transition wave equation formalism is also applied to dissipative backflow within the Caldirola-Kanai approach where the dissipative dynamics comes from an effective Hamiltonian. In all the cases treated here, backflow is gradually suppressed as the intrinsic decoherence process is developing, paying a special attention to the classical limit. The route to classicality is not unique.

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“…Chou applied this wave equation to analyze wave-packet interference [16] and the dynamics of the harmonic and Morse oscillators with complex trajectories [17]. Stochastic Bohmian and scaled trajectories have also been discussed in the literature for open quantum systems [18]. Moreover, if a time-dependent Gaussian ansatz is assumed for the probability density, Bohmian and scaled trajectories are expressed as a sum of a classical trajectory (that is, a particle feature) and a term containing the width of the corresponding wave packet (that is, a wave feature), which has been called the dressing scheme [12].…”

Section: Introductionmentioning

confidence: 99%

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

Mousavi

Miret‐Artés

2023

Symmetry

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In this work, we proposed a smooth transition wave equation from a quantum to classical regime in the framework of von Neumann formalism for ensembles and then obtained an equivalent scaled equation. This led 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, was analyzed.

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Stochastic Bohmian and Scaled Trajectories

Cited by 6 publications

References 80 publications

Different routes to the classical limit of backflow

Different routes to the classical limit of backflow

Different routes to the classical limit of backflow

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

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