Temps multi-dimensionnel

Résumé

La possibilité qu'il pourrait y avoir plus d'une dimension de temps est parfois discutée dans la physique et la philosophie. Physique thumb|La structure causale d'un espace-temps à deux dimensions de temps et une dimension d'espace. La relativité restreinte décrit l'espace-temps comme une variété pseudo-riemannienne dont le tenseur métrique a une valeur propre négative. Ceci correspond à l'existence d'une direction . Une métrique avec plusieurs valeurs propres négatives impliquerait en conséquence plusieurs directions de type temps, à savoir de multiples dimensions de temps, mais il n'y aucun consensus au sujet de la relation de ces supplémentaires avec le temps tel que classiquement compris. Si la théorie de la relativité restreinte peut être généralisée pour le cas du temps de k-dimensionnelle (t_1, t_2..., t_k) et espace à n dimensions (x_k + 1, x_k + 2..., x_k + n) , alors l'intervalle de dimension-(k + n) étant invariant, est donné par

Source officielle

https://fr.wikipedia.org/wiki/Temps_multi-dimensionnel

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The S-matrix Bootstrap Reloaded

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Quantum field theories (QFTs) are the backbone upon which the edifice of modern physics is built. In this thesis we explore the S-matrix bootstrap which is a non-perturbative method that constrains the vast space of QFTs by using consistency conditions that they must satisfy. The thesis is divided into two parts.In part I of the thesis we study the S-matrix bootstrap for particles with spin in 4 spacetime dimensions and apply the formalism to scattering of identical Majorana fermions to estimate bounds on their quartic couplings and their cubic (Yukawa) coupling to scalar particles. In part II of the thesis, we consider the scattering of massless (Goldstone) excitations on a long flux tube. We use the S-matrix bootstrap to constrain Wilson coefficients of higher dimension operators in the low energy flux tube effective field theory. These constraints naturally translate to bounds on the ground state and excited state energy levels of long flux tubes. The techniques used in this thesis should be extendable to many other systems, both massive and massless. We conclude by discussing some of these possibilities.

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Work fluctuations in the active Ornstein-Uhlenbeck particle model

Francesco Cagnetta

We study the large deviations of the power injected by the active force for an active Ornstein-Uhlenbeck particle (AOUP), free or in a confining potential. For the free-particle case, we compute the rate function analytically in d-dimensions from a saddle-point expansion, and numerically in two dimensions by (a) direct sampling of the active work in numerical solutions of the AOUP equations and (b) Legendre-Fenchel transform of the scaled cumulant generating function obtained via a cloning algorithm. The rate function presents asymptotically linear branches on both sides and it is independent of the system's dimensionality, apart from a multiplicative factor. For the confining potential case, we focus on two-dimensional systems and obtain the rate function numerically using both methods (a) and (b). We find a different scenario for harmonic and anharmonic potentials: in the former case, the phenomenology of fluctuations is analogous to that of a free particle, but the rate function might be non-analytic; in the latter case the rate functions are analytic, but fluctuations are realised by entirely different means, which rely strongly on the particle-potential interaction. Finally, we check the validity of a fluctuation relation for the active work distribution. In the free-particle case, the relation is satisfied with a slope proportional to the bath temperature. The same slope is found for the harmonic potential, regardless of activity, and for an anharmonic potential with low activity. In the anharmonic case with high activity, instead, we find a different slope which is equal to an effective temperature obtained from the fluctuation-dissipation theorem.

IOP Publishing Ltd2021

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