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Schro ̈dinger dynamics of a two-state system under measurement

Kryukov, Alexey (2024) Schro ̈dinger dynamics of a two-state system under measurement. [Preprint]


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Spontaneous collapse models use non-linear stochastic modifications of the Schro ̈dinger equation to suppress superpositions of eigenstates of the measured observable and drive the state to an eigenstate. It was recently demonstrated that the collapse of the wave function under observation can be modeled by the linear Schr ̈odinger equation with a Hamiltonian represented by a random matrix from the Gaussian unitary ensemble. The matrices representing the Hamiltonian at different time points throughout the observation period are assumed to be independent. Instead of suppressing superpositions, such Schro ̈dinger evolution makes the state perform an isotropic random walk on the projective space of states. The probability of reaching a particular final state is then given by the Born rule. Here, we apply this method to study the dynamics of a two-state system undergoing measurement. It is shown that in this basic case, the state undergoes the gambler’s ruin walk that satisfies the Born rule, providing a suitable representation of the transition from the initial state to an eigenstate of the measured observable.

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Item Type: Preprint
Keywords: measurement problem
Subjects: Specific Sciences > Physics > Quantum Mechanics
Depositing User: Alexey Kryukov
Date Deposited: 15 Feb 2024 02:15
Last Modified: 15 Feb 2024 02:15
Item ID: 23085
Subjects: Specific Sciences > Physics > Quantum Mechanics
Date: 2024

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