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DY: Fachverband Dynamik und Statistische Physik
DY 32: Nonlinear Stochastic Systems
DY 32.6: Vortrag
Donnerstag, 20. März 2025, 11:00–11:15, H43
The effect of noise on the breather solutions of the discrete nonlinear schrödinger equation — •Mahdieh Ebrahimi1, Barbara Drossel1, and Wolfram Just2 — 1Institute of Condensed Matter Physics, Technical University of Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany — 2Institute of Mathematics, University of Rostock, D-18057 Rostock Germany
The Discrete Nonlinear Schrödinger Equation (DNSE) finds applications across diverse scientific fields, including physics, chemistry, and biology. This dynamical equation is characterized by localized solutions known as breathers. Gaining insights into the processes governing discrete systems is crucial for understanding phenomena such as excitations in crystal lattices and molecular chains, light propagation in waveguide arrays, and the dynamics of Bose-condensate droplets. In this study, we treat the DNSE as an effective macroscopic equation for a quantum many-particle system and investigate the impact of two types of noise (additive and multiplicative noise) on its Hamiltonian equations of motion using symplectic integration. Our findings reveal that the system's normalization increases linearly with time under additive noise, leading to unbounded energy. Conversely, multiplicative noise preserves normalization but causes the system to heat up, ultimately destabilizing the breather in the presence of noise. Our results vividly illustrate the relevance of conserved quantities for the stochastic dynamics in Hamiltonian systems.
Keywords: Nonlinear Schroedinger equation; stochastic Hamiltonian dynamics; Breather; Symplectic integration; multiplicative noise