Exact solutions for a coherent phenomenon of condensation in conservative Hamiltonian systems - Archive ouverte HAL
Article Dans Une Revue Physical Review E Année : 2024

Exact solutions for a coherent phenomenon of condensation in conservative Hamiltonian systems

Résumé

While it is known that Hamiltonian systems may undergo a phenomenon of condensation akin to Bose-Einstein condensation, not all the manifestations of this phenomenon have been uncovered yet. In this work, we present a novel form of condensation in conservative Hamiltonian systems, which happens through coherent states and exploits the discreteness of our system. Both features markedly differ from well-known condensation processes in the literature. Our result is based on a deterministic approach to obtain exact explicit solutions representing the dynamical formation of condensates in finite time. We reveal a dual-cascade behavior during the process, featuring inverse and direct transfer of conserved quantities across the spectrum. The direct cascade yields the excitation of high modes in finite time, a phenomenon quantified through the blow-up of Sobolev norms. We provide a fully analytic description of all the processes involved.

Dates et versions

hal-04446208 , version 1 (08-02-2024)

Identifiants

Citer

Anxo Biasi. Exact solutions for a coherent phenomenon of condensation in conservative Hamiltonian systems. Physical Review E , 2024, 110 (3), pp.034107. ⟨10.1103/PhysRevE.110.034107⟩. ⟨hal-04446208⟩
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