Exact solutions for a coherent phenomenon of condensation in conservative Hamiltonian systems
arXiv:2401.15083 · doi:10.1103/PhysRevE.110.034107
Abstract
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 that stands out due to its evolution through highly coherent states. The 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 arbitrarily high modes in finite time, being associated with the formation of a small-scale coherent structure. We provide a fully analytic description of the processes involved.
Accepted for publication in Physical Review E: https://journals.aps.org/pre/accepted/4f078Y70Cdc1377c77608af6e3ce4da2e4ce56b8d
References in corpus (14)
- Renormalization group, secular term resummation and AdS (in)stability
- Renormalization, averaging, conservation laws and AdS (in)stability
- Dramatic acceleration of wave condensation mediated by disorder in multimode fibers
- Direct and inverse cascades in turbulent Bose-Einstein condensate
- Delayed collapses of BECs in relation to AdS gravity
- Bounds on quantum evolution complexity via lattice cryptography
- Resonant Hamiltonian systems and weakly nonlinear dynamics in AdS spacetimes
- Numerical analysis of a self-similar turbulent flow in Bose--Einstein condensates
- Maximally rotating waves in AdS and on spheres
- On the transfer of energy towards infinity in the theory of weak turbulence for the nonlinear Schrödinger equation
- Fermi-Pasta-Ulam phenomena and persistent breathers in the harmonic trap
- Obstruction to ergodicity in nonlinear Schrödinger equations with resonant potentials
- Turbulent cascades for a family of damped Szegö equations
- Resonant Dynamics and the Instability of the Box Minkowski Model