Stability of Quantum Eigenstates and Collapse of Superposition of States in a Fluctuating Vacuum: The Madelung Hydrodynamic Approach

Chiarelli, Piero; Chiarelli, Simone

doi:10.24018/ejphysics.2021.3.5.97

Cited by 5 publications

(4 citation statements)

References 26 publications

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“…A similar situation appears in the examples of Makowski [25,26], which are similar to our wavefunctions with two terms given by Equation (9). However, we take constant phases φ 1 and φ 2 , while in Makowski's works, the phases depend on x and y.…”

Section: Bohmian Qubitssupporting

confidence: 75%

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Order, Chaos and Born’s Distribution of Bohmian Particles

Tzemos,

Contopoulos

2023

Particles

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We study order, chaos and ergodicity in the Bohmian trajectories of a 2D quantum harmonic oscillator. We first present all the possible types (chaotic, ordered) of Bohmian trajectories in wavefunctions made of superpositions of two and three energy eigenstates of the oscillator. There is no chaos in the case of two terms and in some cases of three terms. Then, we show the different geometries of nodal points in bipartite Bohmian systems of entangled qubits. Finally, we study multinodal wavefunctions and find that a large number of nodal points does not always imply the dominance of chaos. We show that, in some cases, the Born distribution is dominated by ordered trajectories, something that has a significant impact on the accessibility of Born’s rule P=|Ψ|2 by initial distributions of Bohmian particles with P0≠|Ψ0|2.

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Section: Bohmian Qubitssupporting

confidence: 75%

“…Thus, BQM is characterised as a pilot wave theory [1,2]. A similar approach was the Madelung hydrodynamic approach [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Order, Chaos and Born’s Distribution of Bohmian Particles

Tzemos,

Contopoulos

2023

Particles

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“…Chiarelli and Chiarelli [ 22 ], while exploring the literature on quantum hydrodynamics, observed that quantum hydrodynamic equations can play a critical role in describing emergence of the classical world from the underlying quantum domain. The main problem they approach is; however, the fact that the dependence of the dynamics of systems on mass create disconnections in a smooth passage from quantum superposition to classical domain.…”

Section: Resultsmentioning

confidence: 99%

A Testable Theory for the Emergence of the Classical World

Kauffman

Patra

2022

Entropy

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The transition from the quantum to the classical world is not yet understood. Here, we take a new approach. Central to this is the understanding that measurement and actualization cannot occur except on some specific basis. However, we have no established theory for the emergence of a specific basis. Our framework entails the following: (i) Sets of N entangled quantum variables can mutually actualize one another. (ii) Such actualization must occur in only one of the 2N possible bases. (iii) Mutual actualization progressively breaks symmetry among the 2N bases. (iv) An emerging “amplitude” for any basis can be amplified by further measurements in that basis, and it can decay between measurements. (v) The emergence of any basis is driven by mutual measurements among the N variables and decoherence with the environment. Quantum Zeno interactions among the N variables mediates the mutual measurements. (vi) As the number of variables, N, increases, the number of Quantum Zeno mediated measurements among the N variables increases. We note that decoherence alone does not yield a specific basis. (vii) Quantum ordered, quantum critical, and quantum chaotic peptides that decohere at nanosecond versus femtosecond time scales can be used as test objects. (viii) By varying the number of amino acids, N, and the use of quantum ordered, critical, or chaotic peptides, the ratio of decoherence to Quantum Zeno effects can be tuned. This enables new means to probe the emergence of one among a set of initially entangled bases via weak measurements after preparing the system in a mixed basis condition. (ix) Use of the three stable isotopes of carbon, oxygen, and nitrogen and the five stable isotopes of sulfur allows any ten atoms in the test protein to be discriminably labeled and the basis of emergence for those labeled atoms can be detected by weak measurements. We present an initial mathematical framework for this theory, and we propose experiments.

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“…The additional contribution from an imaginary term to the continuity equation, in our case the additional diffusion term in the Smoluchowski equation, should, therefore, be related to the stochastic force. Hence, our extension of the Madelung picture to include open systems could also be considered in the context of a recent stochastic quantum hydrodynamic model [27,28]. This model relates vacuum fluctuations to dark matter and, thus, provides even connections with cosmological models, thus extending substantially the domain of possible applicability of our approach.…”

Section: Introductionmentioning

confidence: 98%

Complex Quantum Hydrodynamics in Momentum Space with Broken Time-Reversal Symmetry

Schuch

Bonilla-Licea

2023

Symmetry

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Shortly after Schrödinger’s wave mechanics in terms of complex wave functions was published, Madelung formulated this theory in terms of two real hydrodynamic-like equations. This version is also the formal basis of Bohmian mechanics, albeit with a different ontological interpretation. A point of criticism raised by Pauli against Bohmian mechanics is its missing symmetry between position and momentum that is present in classical phase space as well as in the quantum mechanical position and momentum representations. Both Madelung’s quantum hydrodynamics formulation and Bohmian mechanics are usually expressed only in position space. Recently, with the use of complex quantities, we were able to provide a hydrodynamic formulation also in momentum space. In this paper, we extend this formalism to include dissipative systems with broken time-reversal symmetry. In classical Hamiltonian mechanics and conventional quantum mechanics, closed systems with reversible time-evolution are usually considered. Extending the discussion to include open systems with dissipation, another form of symmetry is broken, that under time-reversal. There are different ways of describing such systems; for instance, Langevin and Fokker–Planck-type equations are commonly used in classical physics. We now investigate how these aspects can be incorporated into our complex hydrodynamic description and what modifications occur in the corresponding equations, not only in position, but particularly in momentum space.

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Stability of Quantum Eigenstates and Collapse of Superposition of States in a Fluctuating Vacuum: The Madelung Hydrodynamic Approach

Cited by 5 publications

References 26 publications

Order, Chaos and Born’s Distribution of Bohmian Particles

Order, Chaos and Born’s Distribution of Bohmian Particles

A Testable Theory for the Emergence of the Classical World

Complex Quantum Hydrodynamics in Momentum Space with Broken Time-Reversal Symmetry

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