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Bacciagaluppi, Guido

doi:10.1023/a:1021622603864

Cited by 29 publications

(17 citation statements)

References 36 publications

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“…The fundamental goal of stochastic quantization (Bacciagaluppi, 1999;Belavkin, 2003;de la Peña and Cetto, 1996;Gaioli et al, 1997;Hooft, 1997;Namiki, 1982Namiki, , 2000Olavo, 2000;Torres and Figueiredo, 2003) is to reproduce the whole content of quantum mechanics by means of classical equations subjected to random perturbations. Presently, there remains the controversy about the physical origin of the noise, which is supposed to arise, for instance, from a fluctuating metrics or from fluctuations of the vacuum electromagnetic field.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Quantization of Time-Dependent Systems by the Haba and Kleinert Method

Haas

2005

Int J Theor Phys

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The stochastic quantization method recently developed by Haba and Kleinert is extended to non-autonomous mechanical systems, in the case of the time-dependent harmonic oscillator. In comparison with the autonomous case, the quantization procedure involves the solution of a nonlinear, auxiliary equation. Using a rescaling transformation, the Schrödinger equation for the time-dependent harmonic oscillator is obtained after averaging of a classical stochastic differential equation.KEY WORDS: stochastic quantization; time-dependent harmonic oscillator; Schrödinger equation; classical simulation of quantum systems.

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Section: Introductionmentioning

confidence: 99%

Stochastic Quantization of Time-Dependent Systems by the Haba and Kleinert Method

Haas

2005

Int J Theor Phys

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“…Such ambiguities may potentially be relevant too for possible empirical predictions concerning non-equilibrium. Note that similar ambiguities arise in for example the context of Nelson's stochastic mechanics [48,49]. Nelson's mechanics [50,51] can be regarded as a modification of the de Broglie-Bohm theory in which the deterministic de Broglie-Bohm dynamics is replaced by a diffusion process (though Nelson himself wanted to derive the wavefunction and Schrödinger's dynamics from the stochastic process instead of assuming them independently).…”

Section: Resultsmentioning

confidence: 99%

Quantum non-equilibrium and relaxation to equilibrium for a class of de Broglie–Bohm-type theories

Colin

Struyve

2010

New J. Phys.

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The de Broglie-Bohm theory is about non-relativistic point-particles that move deterministically along trajectories. The theory reproduces the predictions of standard quantum theory, given that the distribution of particles over an ensemble of systems, all described by the same wavefunction ψ, equals the quantum equilibrium distribution |ψ| 2 . Numerical simulations by Valentini and Westman have illustrated that non-equilibrium particle distributions may relax to quantum equilibrium after some time. Here we consider non-equilibrium distributions and their relaxation properties for a particular class of trajectory theories, first studied in detail by Deotto and Ghirardi, that are empirically equivalent to the de Broglie-Bohm theory in quantum equilibrium. For the examples of such theories that we consider, we find a speed-up of the relaxation compared to the ordinary de Broglie-Bohm theory. Hence non-equilibrium predictions that depend strongly on relaxation properties, such as those studied recently by Valentini, may vary for different trajectory theories. As such these theories might be experimentally distinguishable.

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“…Beyond that, Bell's jump rule (3) itself permits generalization [18], providing additional freedom over which trajectory probability assignments may vary. The import of this freedom for mechanism identification remains to be determined.…”

Section: Remarks and Conclusionmentioning

confidence: 99%

“…An application to the problem of population transfer for a model 7-level system is given in §4, which illustrates the usefulness of mechanism information in understanding control processes. We then show how the beable approach leads to the laboratory working relations (17) and (18), which make it possible to identify some basic aspects of control mechanisms directly from experimental data. We illustrate this process in §6 on simulated experimental data for the model 7-level system.…”

Section: Introductionmentioning

confidence: 99%

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Bell trajectories for revealing quantum control mechanisms

Dennis

Rabitz

2003

Phys. Rev. A

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The dynamics induced while controlling quantum systems by optimally shaped laser pulses have often been difficult to understand in detail. A method is presented for quantifying the importance of specific sequences of quantum transitions involved in the control process. The method is based on a "beable" formulation of quantum mechanics due to John Bell that rigorously maps the quantum evolution onto an ensemble of stochastic trajectories over a classical state space. Detailed mechanism identification is illustrated with a model 7-level system. A general procedure is presented to extract mechanism information directly from closed-loop control experiments. Application to simulated experimental data for the model system proves robust with up to 25% noise.

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Untitled

Cited by 29 publications

References 36 publications

Stochastic Quantization of Time-Dependent Systems by the Haba and Kleinert Method

Stochastic Quantization of Time-Dependent Systems by the Haba and Kleinert Method

Quantum non-equilibrium and relaxation to equilibrium for a class of de Broglie–Bohm-type theories

Bell trajectories for revealing quantum control mechanisms

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