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Beyond pilot wave dynamics : non-linearity and non-equilibrium in quantum mechanics

Abstract : The quantum theory has modified the way we interpret what in the past was commonly called "physical reality". As an example, according to the standard interpretation of quantum mechanics (the so-called probabilistic interpretation of Copenhagen), the properties of a quantum object have no physical reality, at least not before the observer measures them. Moreover, everything seems to happen as if there was an intrinsic indeterminism in the quantum dynamics that forbids to predict with certainty the result of a measurement. From then, several physical and philosophical interpretations were born to describe (our knowledge of) this reality.It is in 1927, during the Solvay conference, that Louis de Broglie, an opponent of the probabilistic interpretation, proposed an alternative solution to that problem. He proposed on the one hand to restore determinism (as well as realism) and on the other hand to bring back the notion of trajectory to the foreground. Subsequently this theory was rediscovered and supplemented by David Bohm to give birth to the theory known today as pilot wave theory. John Bell said about this interpretation: " In 1952, I saw the impossible done. It was in papers by David Bohm. Bohm showed explicitly how .... the indeterministic description could be transformed into a deterministic one."The works carried out in this manuscript are in continuity with de Broglie’s view and can be summed up in two main parts, each of them having the aim of answering a particular problem. In the first part, we consider two versions of the pilot wave theory: a deterministic version (de Broglie-Bohm dynamics in chapter 2) as well as one of its stochastic extensions (Bohm-Hiley-Nelson dynamics in chapter 3). In the framework of what is called the "Quantum non-equilibrium" approach we shall see how the quantum probability emerges from those dynamics. This approach makes it possible to get rid of the axiomatic status of the probability distribution but also to justify it by arguments similar to those found in statistical mechanics. Among these arguments we shall for instance find ergodicity, chaos, mixing and other properties that will be studied in depth (chapter 4). In particular, the emergence of the quantum probability is accompanied by a relaxation process that will be characterized for both dynamics (in chapter 3 we derive a strong H-theorem for the stochastic dynamics which quantitatively describes how this process occurs). In addition, we will try in a phenomenological approach to apply these quantum pilot wave theories to the macroscopic dynamics of bouncing oil droplets (chapter 5).The second problem is linked to a hypothetical nonlinear generalization of the quantum theory. In particular, we considered the Schrodinger Newton equation as a first proposal to this generalization. In a nutshell, this non-linear equation derives from a semi-classical approximation of gravity and has been proposed by Roger Penrose among others to explain the collapse of the wave function. We shall first show how it is related to the double solution program of Louis de Broglie (chapter 6). Subsequently we will see how to test this nonlinear generalization by considering two experimental proposals (chapter 7). In particular, one of these proposals will lead us to study the interplay between decoherence and Doppler cooling (chapter 8). To do this we shall use the model of Ghirardi-Rimini and Weber (GRW) as a decoherence model, which will allow us to generalize their original results.
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Mohamed Hatifi. Beyond pilot wave dynamics : non-linearity and non-equilibrium in quantum mechanics. Quantum Physics [quant-ph]. Ecole Centrale Marseille, 2019. English. ⟨NNT : 2019ECDM0006⟩. ⟨tel-02869778⟩

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