Collapse dynamics and Hilbert-space stochastic processes

AbstractSpontaneous collapse models of state vector reduction represent a possible solution to the quantum measurement problem. In the present paper we focus our attention on the Ghirardi–Rimini–Weber (GRW) theory and the corresponding continuous localisation models in the form of a Brownian-driven motion in Hilbert space. We consider experimental setups in which a single photon hits a beam splitter and is subsequently detected by photon detector(s), generating a superposition of photon-detector quantum states. Through a numerical approach we study the dependence of collapse times on the physical features of the superposition generated, including also the effect of a finite reaction time of the measuring apparatus. We find that collapse dynamics is sensitive to the number of detectors and the physical properties of the photon-detector quantum states superposition.

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The quantum beam splitter revisited without a vacuum state

Revista Mexicana de Física E ◽

10.31349/revmexfise.19.010210 ◽

2022 ◽

Vol 19 (1 Jan-Jun) ◽

Author(s):

Alexander Nahmad ◽

Damian P San-Roman-Alerigi ◽

Edna Magdalena Hernández González ◽

Erick Barrios ◽

Gustavo Armendariz Peña ◽

...

Keyword(s):

Beam Splitter ◽

Single Photon ◽

Vacuum State ◽

Quantum States ◽

Wave Functions ◽

Quantum Interferometer ◽

Quantum Wave ◽

Photon States

In this article we explain in a new light two fundamental concepts ofquantum optics, the quantum beam splitter and the quantum interferometer, in termsof two state quantum wave functions. This method is consistent with the concept ofentanglement, and hence the algebra needed to describe them is reduced to additionsand products of the components of the quantum states. Furthermore, under thepremises of this method it is possible to study quantum states of greater complexity,like those arising from the addition and products of single photon states.

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Realizable Single Photon Beam Splitter Based on Classical-Assisted Cyclic Transition of InGaAs/GaAs Quantum Dot Coupled to the T-Splitter Silver Nanowire

Plasmonics ◽

10.1007/s11468-021-01459-w ◽

2021 ◽

Author(s):

Myong-Chol Ko ◽

Nam-Chol Kim ◽

Su-Ryon Ri ◽

Ju-Song Ryom ◽

Song-Gun Kim ◽

...

Keyword(s):

Quantum Dot ◽

Beam Splitter ◽

Single Photon ◽

Silver Nanowire ◽

Photon Beam ◽

Cyclic Transition ◽

Gaas Quantum Dot

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An attractive numerical algorithm for solving nonlinear Caputo–Fabrizio fractional Abel differential equation in a Hilbert space

Advances in Difference Equations ◽

10.1186/s13662-021-03428-3 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Mohammed Al-Smadi ◽

Nadir Djeddi ◽

Shaher Momani ◽

Shrideh Al-Omari ◽

Serkan Araci

Keyword(s):

Differential Equation ◽

Hilbert Space ◽

Reproducing Kernel ◽

Numerical Approach ◽

Accurate Solution ◽

Stability And Convergence ◽

Type Model ◽

Schmidt Orthogonalization ◽

And Performance ◽

Abel Differential Equation

AbstractOur aim in this paper is presenting an attractive numerical approach giving an accurate solution to the nonlinear fractional Abel differential equation based on a reproducing kernel algorithm with model endowed with a Caputo–Fabrizio fractional derivative. By means of such an approach, we utilize the Gram–Schmidt orthogonalization process to create an orthonormal set of bases that leads to an appropriate solution in the Hilbert space $\mathcal{H}^{2}[a,b]$ H 2 [ a , b ] . We investigate and discuss stability and convergence of the proposed method. The n-term series solution converges uniformly to the analytic solution. We present several numerical examples of potential interests to illustrate the reliability, efficacy, and performance of the method under the influence of the Caputo–Fabrizio derivative. The gained results have shown superiority of the reproducing kernel algorithm and its infinite accuracy with a least time and efforts in solving the fractional Abel-type model. Therefore, in this direction, the proposed algorithm is an alternative and systematic tool for analyzing the behavior of many nonlinear temporal fractional differential equations emerging in the fields of engineering, physics, and sciences.

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