Semiclassical theory of weak values

Tanaka, Atushi

doi:10.1016/s0375-9601(02)00384-5

Cited by 21 publications

(20 citation statements)

References 31 publications

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“…The connection between macroscopic "classical" properties and weak values has already been suggested in the literature [1,52,53]. In this section we give further evidence of this connection by showing the correspondence of the QAWV framework in the classical limit.…”

Section: Classical Correspondence Of Qawv Frameworksupporting

confidence: 69%

Quantum averages of weak values

2005

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We re-examine the status of the weak value of a quantum mechanical observable as an objective physical concept, addressing its physical interpretation and general domain of applicability. We show that the weak value can be regarded as a definite mechanical effect on a measuring probe specifically designed to minimize the back-reaction on the measured system. We then present a new framework for general measurement conditions (where the back-reaction on the system may not be negligible) in which the measurement outcomes can still be interpreted as quantum averages of weak values. We show that in the classical limit, there is a direct correspondence between quantum averages of weak values and posterior expectation values of classical dynamical properties according to the classical inference framework.

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Section: Classical Correspondence Of Qawv Frameworksupporting

confidence: 69%

Quantum averages of weak values

2005

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“…thanks to the equality (7). We thus find that, unlike the previous case where both the pre-and post-selections are made by position eingenstates, in the present double slit case the weak trajectory becomes complex in general, starting with the pure imaginary value x w (0) = −ix i tan m x f xi T and ending with the real value x w (T ) = x f (see FIG.…”

Section: The Double Slit Experimentsmentioning

confidence: 50%

“…The point is that the (renormalized) weak trajectory yields a definite function of time such that it can be regarded as some trajectory, and the question whether it coincides with the classical one or not is secondary. However, once the trajectory is established, then it should be interesting to investigate the characteristic feature of the weak trajectory compared to the classical one, as has been done in [7,8] for the case of selections where semiclassical approximation is valid.…”

Section: Weak Trajectory and Which-path Informationmentioning

confidence: 99%

“…When the given process consists of the pre-and postselections given either by position eigenstates or by welllocalized (Gaussian) states, the weak trajectory forms a curve with the two ends specified by the selections. The interest in this case is then to see how the trajectory deviates from the classical one, which has been analyzed earlier in [7,8,10]. In contrast, in our study we are interested in situations where the selections are performed not by those (semi)classical states but by genuinely quantum states, that is, by superposed states for which no particular position is assignable to the particle, at one of the ends at least.…”

Section: Introductionmentioning

confidence: 99%

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Quantum trajectories based on the weak value

Mori¹,

Tsutsui²

2015

Progress of Theoretical and Experimental Physics

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The notion of the trajectory of an individual particle is strictly inhibited in quantum mechanics because of the uncertainty principle. Nonetheless, the weak value, which has been proposed as a novel and measurable quantity definable to any quantum observable, can offer a possible description of trajectory on account of its statistical nature. In this paper, we explore the physical significance provided by this "weak trajectory" by considering various situations where interference takes place simultaneously with the observation of particles, that is, in prototypical quantum situations for which no classical treatment is available. These include the double slit experiment and Lloyd's mirror, where in the former case it is argued that the real part of the weak trajectory describes an average over the possible classical trajectories involved in the process, and that the imaginary part is related to the variation of interference. It is shown that this average interpretation of the weak trajectory holds universally under the complex probability defined from the given transition process. These features remain essentially unaltered in the case of Lloyd's mirror where interference occurs with a single slit.

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“…has not been given any clear answer, we refer to a study conducted from another standpoint. A decade ago, Tanaka pointed out that a semiclassical trajectory identified using SPA can be regarded as a time series of weak values 55 . Therefore, when we remember that semiclassical hopping trajectories can be identified using SPAs, the semiclassical hopping trajectory has the potential to become physically realistic through successive weak measurements.…”

Section: Nonadiabatic Semiclassical Kernel With Overlap Integralsmentioning

confidence: 99%

Semiclassical quantization of nonadiabatic systems with hopping periodic orbits

Fujii

Yamashita

2015

The Journal of Chemical Physics

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We present a semiclassical quantization condition, i.e., quantum-classical correspondence, for steady states of nonadiabatic systems consisting of fast and slow degrees of freedom (DOFs) by extending Gutzwiller's trace formula to a nonadiabatic form. The quantum-classical correspondence indicates that a set of primitive hopping periodic orbits, which are invariant under time evolution in the phase space of the slow DOF, should be quantized. The semiclassical quantization is then applied to a simple nonadiabatic model and accurately reproduces exact quantum energy levels. In addition to the semiclassical quantization condition, we also discuss chaotic dynamics involved in the classical limit of nonadiabatic dynamics.

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Semiclassical theory of weak values

Cited by 21 publications

References 31 publications

Quantum averages of weak values

Quantum averages of weak values

Quantum trajectories based on the weak value

Semiclassical quantization of nonadiabatic systems with hopping periodic orbits

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