A quantum-classical bracket from
                    <i>p</i>
                    -mechanics

Kisil, Vladimir V.

doi:10.1209/epl/i2005-10324-7

Cited by 30 publications

(60 citation statements)

References 17 publications

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“…For instance, in cosmology it leads to problems in accounting for the local anisotropy in the early universe [20]. Many other coupling schemes for hybrid classical-quantum systems have been proposed in the literature [6,8,12,[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. As shown in Ref.…”

Section: Introductionmentioning

confidence: 99%

Statistical consistency of quantum-classical hybrids

Salcedo

2012

Phys. Rev. A

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Section: Introductionmentioning

confidence: 99%

Statistical consistency of quantum-classical hybrids

Salcedo

2012

Phys. Rev. A

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“…Then the study of their statistics will follow the usual steps for purely classical or purely quantum ensembles. In this respect, it should be noted that other approaches to MQCD (not based on Ehrenfest equations) exist [19,20,21], and to their corresponding statistics [22,23], however it has been found that the formulation of well defined quantum-classical brackets (i.e., satisfying the Jacobi identity and Leibniz derivation rule) is a difficult issue [24,25,26,27]. On the contrary, as shown below, and as a result of the fact that the evolution of a quantum system can be formulated in terms of Hamilton equations similar to those of a classical system [4,28], we will not have difficulties in a rigorous formulation of the Ehrenfest dynamics in terms of Poisson brackets.…”

Section: Introductionmentioning

confidence: 99%

Statistics and Nosé formalism for Ehrenfest dynamics

Alonso¹,

Castro²,

Clemente-Gallardo³

et al. 2011

J. Phys. A: Math. Theor.

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Abstract. Quantum dynamics (i.e., the Schrödinger equation) and classical dynamics (i.e., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. In this paper we first show that the hybrid quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for Ehrenfest dynamics. Then, the existence of a well defined Poisson bracket allows to arrive to a Liouville equation for a statistical ensemble of Ehrenfest systems. The study of a generic toy model shows that the evolution produced by Ehrenfest dynamics is ergodic and therefore the only constants of motion are functions of the Hamiltonian. The emergence of the canonical ensemble characterized by the Boltzmann distribution follows after an appropriate application of the principle of equal a priori probabilities to this case. Once we know the canonical distribution of a Ehrenfest system, it is straightforward to extend the formalism of Nosé (invented to do constant temperature Molecular Dynamics by a non-stochastic method) to our Ehrenfest formalism. This work also provides the basis for extending stochastic methods to Ehrenfest dynamics.

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“…We remark that this paper can be considered as belonging to the domain emergent quantum mechanics, see, e.g., recent papers of Elze [1][2][3], Rusov et al [4], or Kisil [5] (in fact, such traditional domains of research as Bohmian mechanics or SED [6,7] can also be considered as domains of emergent quantum mechanics; on the other hand, the semiclassical model, although it is close to PCSFT (as a field model), is not a part of emergent quantum mechanics, since here matter is still described by conventional quantum formalism).…”

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confidence: 99%

Prequantum Classical Statistical Field Theory: Schrödinger Dynamics of Entangled Systems as a Classical Stochastic Process

Khrennikov

2009

Found Phys

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The idea that quantum randomness can be reduced to randomness of classical fields (fluctuating at time and space scales which are essentially finer than scales approachable in modern quantum experiments) is rather old. Various models have been proposed, e.g., stochastic electrodynamics or the semiclassical model. Recently a new model, so called prequantum classical statistical field theory (PCSFT), was developed. By this model a "quantum system" is just a label for (so to say "prequantum") classical random field. Quantum averages can be represented as classical field averages. Correlations between observables on subsystems of a composite system can be as well represented as classical correlations. In particular, it can be done for entangled systems. Creation of such classical field representation demystifies quantum entanglement. In this paper we show that quantum dynamics (given by Schrödinger's equation) of entangled systems can be represented as the stochastic dynamics of classical random fields. The "effect of entanglement" is produced by classical correlations which were present at the initial moment of time, cf. views of Albert Einstein.

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A quantum-classical bracket from p -mechanics

Cited by 30 publications

References 17 publications

Statistical consistency of quantum-classical hybrids

Statistical consistency of quantum-classical hybrids

Statistics and Nosé formalism for Ehrenfest dynamics

Prequantum Classical Statistical Field Theory: Schrödinger Dynamics of Entangled Systems as a Classical Stochastic Process

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