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.
arXiv commentAccepted for publication in Physical Review E: https://journals.aps.org/pre/accepted/4f078Y70Cdc1377c77608af6e3ce4da2e4ce56b8d
References in corpus (41)
- On weakly turbulent instability of anti-de Sitter space
- Condensation of classical nonlinear waves
- Holographic Thermalization, stability of AdS, and the Fermi-Pasta-Ulam-Tsingou paradox
- Renormalization group, secular term resummation and AdS (in)stability
- Wave turbulence and vortices in Bose-Einstein condensation
- Renormalization, averaging, conservation laws and AdS (in)stability
- Rayleigh-Jeans condensation of classical light : Observation and thermodynamic characterization
- Resonant dynamics and the instability of anti-de Sitter spacetime
- A simple statistical explanation for the localization of energy in nonlinear lattices with two conserved quantities
- Dramatic acceleration of wave condensation mediated by disorder in multimode fibers
- Self-organization in nonlinear wave turbulence
- Globally regular instability of
- Discrete and mesoscopic regimes of finite-size wave turbulence
- Bose-Einstein condensation and Berezinskii-Kosterlitz-Thouless transition in 2D Nonlinear Schrödinger model
- Exact lowest-Landau-level solutions for vortex precession in Bose-Einstein condensates
- Direct and inverse cascades in turbulent Bose-Einstein condensate
- On the Cubic Lowest Landau Level Equation
- Delayed collapses of BECs in relation to AdS gravity
- AdS (in)stability: an analytic approach
- Conformal flow on and weak field integrability in AdS
- Bounds on quantum evolution complexity via lattice cryptography
- Two infinite families of resonant solutions for the Gross-Pitaevskii equation
- Resonant Hamiltonian systems and weakly nonlinear dynamics in AdS spacetimes
- Numerical analysis of a self-similar turbulent flow in Bose--Einstein condensates
- Solvable cubic resonant systems
- Maximally rotating waves in AdS and on spheres
- A nonrelativistic limit for AdS perturbations
- Large time blow up for a perturbation of the cubic Szegő equation
- Quantum resonant systems, integrable and chaotic
- On the transfer of energy towards infinity in the theory of weak turbulence for the nonlinear Schrödinger equation
- Time-periodic quantum states of weakly interacting bosons in a harmonic trap
- Fermi-Pasta-Ulam phenomena and persistent breathers in the harmonic trap
- Complex plane representations and stationary states in cubic and quintic resonant systems
- Energy level splitting for weakly interacting bosons in a harmonic trap
- Energy returns in global AdS_4
- Turbulent cascades in a truncation of the cubic Szego equation and related systems
- Obstruction to ergodicity in nonlinear Schrödinger equations with resonant potentials
- Breathing modes, quartic nonlinearities and effective resonant systems
- AdS instability: resonant system for gravitational perturbations of AdS in the cohomogeneity-two biaxial Bianchi IX ansatz
- Turbulent cascades for a family of damped Szegö equations
- Resonant Dynamics and the Instability of the Box Minkowski Model