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Dissipative Continuous Spontaneous Localization (CSL) model.

Smirne A, Bassi A - Sci Rep (2015)

Bottom Line: Here we present the dissipative version of the CSL model, which guarantees a finite energy during the entire system's evolution, thus making a crucial step toward a realistic energy-conserving collapse model.This is achieved by introducing a non-linear stochastic modification of the Schrödinger equation, which represents the action of a dissipative finite-temperature collapse noise.The possibility to introduce dissipation within collapse models in a consistent way will have relevant impact on the experimental investigations of the CSL model, and therefore also on the testability of the quantum superposition principle.

View Article: PubMed Central - PubMed

Affiliation: 1] Dipartimento di Fisica, Università degli Studi di Trieste, Strada Costiera 11, I-34151 Trieste, Italy [2] Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Via Valerio 2, I-34127 Trieste, Italy.

ABSTRACT
Collapse models explain the absence of quantum superpositions at the macroscopic scale, while giving practically the same predictions as quantum mechanics for microscopic systems. The Continuous Spontaneous Localization (CSL) model is the most refined and studied among collapse models. A well-known problem of this model, and of similar ones, is the steady and unlimited increase of the energy induced by the collapse noise. Here we present the dissipative version of the CSL model, which guarantees a finite energy during the entire system's evolution, thus making a crucial step toward a realistic energy-conserving collapse model. This is achieved by introducing a non-linear stochastic modification of the Schrödinger equation, which represents the action of a dissipative finite-temperature collapse noise. The possibility to introduce dissipation within collapse models in a consistent way will have relevant impact on the experimental investigations of the CSL model, and therefore also on the testability of the quantum superposition principle.

No MeSH data available.


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(Left, center) Evolution of the position probability distribution  in the CSL model in one dimension, for one nucleon initially in a balanced superposition of two gaussian states with equal variance σ2 and centered, respectively, in α and −α. The probability distribution is plotted for a single realization of the random noise and at times λt = 0 (black solid line), λt = 0.1 (blue dot-dashed line), λt = 0.3 (red dashed line) and λt = 0.4 (green dotted line), left, and λt = 0.5 (black solid line), λt = 0.6 (blue dot-dashed line), λt = 0.8 (red dashed line) and λt = 0.9 (green dotted line), (center); σ/rC = 0.55 and α/rC = 2.5. (Right) Time evolution of the position variance, , for different realizations of the noise field. We have applied the Euler-Maruyama method4748 to Eq. (1), for  and time step λΔt = 0.01. As discussed in the text, see also Supplementary Information for more details, the rate λ has to be replaced by the rate Γ defined in Eq. (3) if a macroscopic object is taken into account, in accordance with the amplification mechanism.
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f1: (Left, center) Evolution of the position probability distribution in the CSL model in one dimension, for one nucleon initially in a balanced superposition of two gaussian states with equal variance σ2 and centered, respectively, in α and −α. The probability distribution is plotted for a single realization of the random noise and at times λt = 0 (black solid line), λt = 0.1 (blue dot-dashed line), λt = 0.3 (red dashed line) and λt = 0.4 (green dotted line), left, and λt = 0.5 (black solid line), λt = 0.6 (blue dot-dashed line), λt = 0.8 (red dashed line) and λt = 0.9 (green dotted line), (center); σ/rC = 0.55 and α/rC = 2.5. (Right) Time evolution of the position variance, , for different realizations of the noise field. We have applied the Euler-Maruyama method4748 to Eq. (1), for and time step λΔt = 0.01. As discussed in the text, see also Supplementary Information for more details, the rate λ has to be replaced by the rate Γ defined in Eq. (3) if a macroscopic object is taken into account, in accordance with the amplification mechanism.

Mentions: where n is the number of constituents of the body contained in a volume and denotes how many such volumes are held in the macroscopic body. This relation clearly shows the amplification mechanism, which is at the basis of every collapse model. The localization induced by the noise field grows with the size of the system, so that the center of mass of any macroscopic object behaves, for all practical purposes, according to classical mechanics. The peculiar property of the CSL model is the quadratic dependence of the rate Γ on the number of constituents, which is a direct consequence of the action of the noise field on identical particles13. The main features of the CSL model are summarized in Fig. 1, where we represent the time evolution of the position probability distribution of one particle, which is initially in a superposition of two gaussian states. The wavefunction is subject continuously to the action of the noise, which suppresses the superposition between the two gaussians, leading to a gaussian state localized around one of the two initial peaks, in a time scale fixed by the collapse rate, see Fig. 1(left, center). The diffusive nature of the dynamics in the CSL model is clearly illustrated by the time-evolution of the position variance, see Fig. 1(right).


Dissipative Continuous Spontaneous Localization (CSL) model.

Smirne A, Bassi A - Sci Rep (2015)

(Left, center) Evolution of the position probability distribution  in the CSL model in one dimension, for one nucleon initially in a balanced superposition of two gaussian states with equal variance σ2 and centered, respectively, in α and −α. The probability distribution is plotted for a single realization of the random noise and at times λt = 0 (black solid line), λt = 0.1 (blue dot-dashed line), λt = 0.3 (red dashed line) and λt = 0.4 (green dotted line), left, and λt = 0.5 (black solid line), λt = 0.6 (blue dot-dashed line), λt = 0.8 (red dashed line) and λt = 0.9 (green dotted line), (center); σ/rC = 0.55 and α/rC = 2.5. (Right) Time evolution of the position variance, , for different realizations of the noise field. We have applied the Euler-Maruyama method4748 to Eq. (1), for  and time step λΔt = 0.01. As discussed in the text, see also Supplementary Information for more details, the rate λ has to be replaced by the rate Γ defined in Eq. (3) if a macroscopic object is taken into account, in accordance with the amplification mechanism.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4525142&req=5

f1: (Left, center) Evolution of the position probability distribution in the CSL model in one dimension, for one nucleon initially in a balanced superposition of two gaussian states with equal variance σ2 and centered, respectively, in α and −α. The probability distribution is plotted for a single realization of the random noise and at times λt = 0 (black solid line), λt = 0.1 (blue dot-dashed line), λt = 0.3 (red dashed line) and λt = 0.4 (green dotted line), left, and λt = 0.5 (black solid line), λt = 0.6 (blue dot-dashed line), λt = 0.8 (red dashed line) and λt = 0.9 (green dotted line), (center); σ/rC = 0.55 and α/rC = 2.5. (Right) Time evolution of the position variance, , for different realizations of the noise field. We have applied the Euler-Maruyama method4748 to Eq. (1), for and time step λΔt = 0.01. As discussed in the text, see also Supplementary Information for more details, the rate λ has to be replaced by the rate Γ defined in Eq. (3) if a macroscopic object is taken into account, in accordance with the amplification mechanism.
Mentions: where n is the number of constituents of the body contained in a volume and denotes how many such volumes are held in the macroscopic body. This relation clearly shows the amplification mechanism, which is at the basis of every collapse model. The localization induced by the noise field grows with the size of the system, so that the center of mass of any macroscopic object behaves, for all practical purposes, according to classical mechanics. The peculiar property of the CSL model is the quadratic dependence of the rate Γ on the number of constituents, which is a direct consequence of the action of the noise field on identical particles13. The main features of the CSL model are summarized in Fig. 1, where we represent the time evolution of the position probability distribution of one particle, which is initially in a superposition of two gaussian states. The wavefunction is subject continuously to the action of the noise, which suppresses the superposition between the two gaussians, leading to a gaussian state localized around one of the two initial peaks, in a time scale fixed by the collapse rate, see Fig. 1(left, center). The diffusive nature of the dynamics in the CSL model is clearly illustrated by the time-evolution of the position variance, see Fig. 1(right).

Bottom Line: Here we present the dissipative version of the CSL model, which guarantees a finite energy during the entire system's evolution, thus making a crucial step toward a realistic energy-conserving collapse model.This is achieved by introducing a non-linear stochastic modification of the Schrödinger equation, which represents the action of a dissipative finite-temperature collapse noise.The possibility to introduce dissipation within collapse models in a consistent way will have relevant impact on the experimental investigations of the CSL model, and therefore also on the testability of the quantum superposition principle.

View Article: PubMed Central - PubMed

Affiliation: 1] Dipartimento di Fisica, Università degli Studi di Trieste, Strada Costiera 11, I-34151 Trieste, Italy [2] Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Via Valerio 2, I-34127 Trieste, Italy.

ABSTRACT
Collapse models explain the absence of quantum superpositions at the macroscopic scale, while giving practically the same predictions as quantum mechanics for microscopic systems. The Continuous Spontaneous Localization (CSL) model is the most refined and studied among collapse models. A well-known problem of this model, and of similar ones, is the steady and unlimited increase of the energy induced by the collapse noise. Here we present the dissipative version of the CSL model, which guarantees a finite energy during the entire system's evolution, thus making a crucial step toward a realistic energy-conserving collapse model. This is achieved by introducing a non-linear stochastic modification of the Schrödinger equation, which represents the action of a dissipative finite-temperature collapse noise. The possibility to introduce dissipation within collapse models in a consistent way will have relevant impact on the experimental investigations of the CSL model, and therefore also on the testability of the quantum superposition principle.

No MeSH data available.


Related in: MedlinePlus