Time-extended measurement of the position of a particle

Roig, Francesc S.

doi:10.1103/physreva.73.042106

Cited by 5 publications

(19 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This means that information concerning the position of the particle has been "transferred" from the state of the particle to the state of the pointer, as is to be expected to occur after a position measurement. The result summarized in equation (11), connecting the displacement of the pointer's location after a position measurement of finite time duration with the average initial and final positions of the particle, has been discussed by Roig [18] using an approach based on path integrals, which is different from the one followed in the present work, based on the evolution of the mean values of selected observables.…”

Section: A Free Particlementioning

confidence: 98%

“…as described in equation (23), which corresponds to equation (18) with λ 5 = 0. Due to the particle-pointer interaction the system evolves to a final state with λ 5 = 0, corresponding to a non-separable Gaussian wave packet.…”

Section: B Initial Conditionsmentioning

confidence: 99%

“…From this point of view the particle (with coordinate x) plays the role of the measuring apparatus, while the pointer (with coordinate Q) is the system being measured. The amount of entanglement E generated by an instantaneous (T → 0) measurement process (with the initial state of the particle-pointer system given by the Gaussian wave packet ansatz (18)) is depicted in Figure 1 as a function of (a) ∆ x with fixed values of ∆ Q = 0.1, 1, 10, and (b) ∆ Q with ∆ x = 0.1, 1, 10. It transpires from Figure 1, that for given values of ∆ Q , E increases with ∆ x from zero to the maximum value given by 1.…”

Section: Particle-pointer Entanglementmentioning

confidence: 99%

“…The particle (of mass m) interacts with another particle of mass M (the "pointer") that represents the measuring apparatus. The particle-pointer composite system is governed by the Hamiltonian [18] …”

Section: Introductionmentioning

confidence: 99%

“…A useful tool for analyzing the conceptual issues associated with this point of view is given by the celebrated von Neumann model for quantum measurements [17][18][19]. In this model the measuring apparatus is characterized by one, single relevant coordinate Q (the "pointer" coordinate).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Entanglement and the process of measuring the position of a quantum particle

2015

View full text Add to dashboard Cite

Section: A Free Particlementioning

confidence: 98%

Section: B Initial Conditionsmentioning

confidence: 99%

Section: Particle-pointer Entanglementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Entanglement and the process of measuring the position of a quantum particle

2015

View full text Add to dashboard Cite

Decoherent histories for a particle coupled to a von Neumann apparatus

Roig

2014

Preprint

Self Cite

View full text Add to dashboard Cite

Using the Gell-Mann and Hartle formalism of generalized quantum mechanics of closed systems, we study coarse-grained decoherent histories. The system under consideration is one-dimensional and consists of a particle coupled to a von Neumann apparatus that measures its position. The particle moves in a quadratic potential; in particular we consider a driven harmonic oscillator. The real line is divided into intervals of the same length, and coarse-grained histories are defined by the arithmetic average of the initial and final position of the particle to be within one of these intervals. The position of the pointer correlates with this arithmetic average. In addition a constant term is added to this average, which is a result of the presence of a driving force on the oscillator. We investigate decoherence for such histories via the decoherence functional for the particle-apparatus. An exact expression for this functional has been derived. If the particle or the pointer of the apparatus is in an exact position state initially, then exact decoherence ensues, and the relative probability for such histories is obtained. If the initial state of the particle, which is centered at some arbitrary point in the x-axis, is narrow compared to the width of the intervals on the x-axis, then we obtain approximate decoherence. The same result follows if the initial state of the pointer is narrow. In these two situations, we evaluate expressions for the decoherence functional qualitatively and quantitatively. In the latter case we obtain the first two terms in an expansion in powers of the width of the initial state of the particle or the pointer respectively. Approximate relative probabilities can be assigned in this case, and we have obtained an expansion up to second order in powers of the width of the initial state for an expression for an upper bound of these probabilities.

show abstract

Decoherence in the classical limit of histories of a particle coupled to a von Neumann apparatus

Roig¹

2016

Preprint

Self Cite

View full text Add to dashboard Cite

Using the Gell-Mann and Hartle formalism of generalized quantum mechanics of closed systems, we study the classical limit of coarse-grained spacetime histories and their decoherence. The system under consideration is one-dimensional and consists of a particle coupled to a von Neumann apparatus that performs a measurement of the position of the particle during the finite time interval during which the histories of this system take place. We consider two cases: a free particle and a harmonic oscillator. The real line is divided into intervals of the same length, and coarse-grained histories are defined by the time average of the position of the particle on a given Feynman path to be within one of these intervals. The position of the pointer in each Feynman path correlates with this time average. The class operators for this system have been evaluated, and the decoherence functional shows that these coarse-grained histories do not decohere, not even when initially either the particle or the pointer is in an eigenstate of position. Decoherence is obtained only when the classical limit is taken. Qualitative arguments for decoherence in the classical limit are presented for the case of a general particle potential.

show abstract

Time-extended measurement of the position of a particle

Cited by 5 publications

References 23 publications

Entanglement and the process of measuring the position of a quantum particle

Entanglement and the process of measuring the position of a quantum particle

Decoherent histories for a particle coupled to a von Neumann apparatus

Decoherence in the classical limit of histories of a particle coupled to a von Neumann apparatus

Contact Info

Product

Resources

About