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Even within a closed (or reversible) quantum system, where unitary time evolution retains all information about its initial state, subsystems can still thermalize using the rest of the system as an effective heat bath.
Motivated by this argument, we develop a practical framework for describing black hole evaporation via unitary time evolution, based on a holographic perspective in which all black hole degrees of freedom live on the stretched horizon.
Thus there is a sense in which the completeness of the state is maintained by unitary time evolution.
In contrast to the unitary time evolution of quantum processes, Penrose suggests that a valid formulation of quantum state reduction replacing von Neumann's projection postulate must faithfully describe an objective physical process that he calls objective reduction.
Only for this appendix, we denote with λ ¯ the fraction of the total unitary time when no relay is transmitting, λ when all relays are transmitting, λ i when only relay i is transmitting and λ ¯ i when only relay i is not transmitting.
We have tested whether the subjective duration increase of a frightening event is due to increased temporal resolution (as from the speeding of a camera) or instead whether duration distortions do not necessarily entail the expected consequences of a unitary time slowing down.
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We propose a Lyapunov control design to achieve specific (or a family of) unitary time-evolution operators, i.e., quantum gates in the Schrödinger picture by tracking control.
Thus, we consider a unitary time-evolution of an initial state (4).
The argument is based on the construction of μ-packings for manifolds of observables with identical spectra and a comparison of their cardinalities to those of μ-coverings for quantum circuits and unitary time-evolution operators.
The question whether unitary time-dynamics leads to thermalization or not can be re-phrased in terms of the "eigenstate thermalization" [1 3], which we will briefly review here.
In the remainder of this paper we will simplify the question of thermalization to the coherent dynamics after a single spontaneous emission event, i.e. we ask whether expectation values of observables relax to thermal values in a unitary time-dynamics after we apply a single quantum jump.
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