Description du projet
Le théorème de Lee-Yang s’étend au domaine quantique pour décrire les systèmes quantiques à plusieurs corps
La théorie Lee-Yang fournit une description des transitions de phase et des propriétés analytiques des fonctions thermodynamiques basées sur la distribution des zéros des fonctions de partition. Les zéros de Lee-Yang ne sont plus seulement un concept théorique; ils ont récemment été déterminés à partir de mesures d’objets observables fluctuants, offrant une perspective entièrement nouvelle sur les transitions de phase dans les systèmes à plusieurs corps en interaction. Le projet QuLeeYang, financé par l’UE, permettra d’étendre la théorie de Lee-Yang au-delà des systèmes d’équilibre classiques. Il formulera une théorie unifiée des transitions de phase dans les systèmes quantiques à plusieurs corps en interaction, du point de vue des zéros de Lee-Yang, et utilisera des dispositifs quantiques conçus pour tester les prédictions sur les transitions de phase. Les résultats du projet auront des implications importantes pour le traitement de l’information quantique et la thermodynamique quantique.
Objectif
Over the last years, investigations of Lee-Yang zeros – complex zeros of the partition function for systems of finite size – have become an indispensable theoretical tool in equilibrium statistical physics with diverse applications, ranging from protein folding and percolation to complex networks and magnetism. In the thermodynamic limit, the Lee-Yang zeros approach the real value of the control parameter for which a phase transition occurs. Despite these developments, surprisingly little attention has so far been devoted to applications of Lee-Yang theory beyond classical equilibrium systems. One reason may be that Lee-Yang zeros (being complex values of physical quantities) for years were seen as a purely theoretical concept with little relevance to experiments. However, this view has recently been contested by several experiments, in which Lee-Yang zeros have been determined. A novel cumulant method allows for the determination of Lee-Yang zeros from measurements of fluctuating observables, thus offering a completely new perspective on phase transitions in interacting many-body systems. Here, building on this cumulant method, I propose to formulate a unifying theory of phase transitions in interacting quantum many-body systems, including space-time, dynamical, and quantum phase transitions, from the perspective of Lee-Yang zeros. I will connect this theoretical framework to large-deviation statistics, fluctuation relations, and many-body entanglement in non-classical systems. Furthermore, I will devise experimental schemes to test my predictions and, in particular, investigate quantum phase transitions in engineered quantum devices. Fulfilling these objectives will expand the field far beyond its current state-of-the-art and potentially result in major scientific breakthroughs with important implications for other research fields, such as quantum information processing and quantum thermodynamics.
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MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)Coordinateur
02150 Espoo
Finlande