Nonlinear lattice dynamics of Bose-Einstein condensates. by Porter, M, Carretero-González, R, Kevrekidis, P, Malomed, B

“…The Fermi-Pasta-Ulam (FPU) model, which was proposed 50 years ago to examine thermalization in nonmetallic solids and develop "experimental" techniques for studying nonlinear problems, continues to yield a wealth of results in the theory and applications of nonlinear Hamiltonian systems with many degrees of freedom. Inspired by the studies of this seminal model, solitary-wave dynamics in lattice dynamical systems have proven vitally important in a diverse range of physical problems-including energy relaxation in solids, denaturation of the DNA double strand, self-trapping of light in arrays of optical waveguides, and Bose-Einstein condensates (BECs) in optical lattices. …”

Duality, hidden symmetry, and dynamic isomerism in 2D hinge structures by Lei, Qun-Li, Tang, Feng, Hu, Ji-Dong, Ma, Yu-Qiang, Ni, Ran

“…At last, by further studying a 2D nonmechanical magnonic system, we show that the duality and the associated hidden symmetry should exist in a broad range of Hamiltonian systems.…”
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A new canonical affine bracket formulation of Hamiltonian classical field theories of first order by Gay-Balmaz, François, Marrero, Juan C., Alba, Nicolás Martínez

“…The construction is analogous to the canonical Poisson formulation of Hamiltonian systems although the nature of our formulation is linear-affine and not bilinear as the standard Poisson bracket. …”
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Lieb-Schultz-Mattis, Luttinger, and 't Hooft - anomaly matching in lattice systems by Meng Cheng, Nathan Seiberg

“…We analyze lattice Hamiltonian systems whose global symmetries have 't Hooft anomalies. …”
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Integrable Systems: In the Footprints of the Greats by Velimir Jurdjevic

“…We then show that the classical integrals of motion associated, with the Kowalewski top, the two-body problem of Kepler, and Jacobi’s geodesic problem on the ellipsoid can be all derived from the aforementioned Hamiltonian systems. We also introduce a rolling geodesic problem that admits a spectral representation on symmetric Riemannian spaces and we then show the relevance of the corresponding integrals on the nature of the curves whose elastic energy is minimal.…”
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Chaotic Dynamics of the Interface between Dielectric Liquids at the Regime of Stabilized Kelvin-Helmholtz Instability by a Tangential Electric Field by Evgeny A. Kochurin, Nikolay M. Zubarev

“…Such a behaviour is consistent with the Kolmogorov-Arnold-Moser theory describing quasi-periodic chaotic motion in Hamiltonian systems. At the developed chaotic state, the system fast loses the information on its initial state; the corresponding estimate for Lyapunov exponent is obtained. …”
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Mathematical Tools for Discontinuous Dynamical Systems by Billingsley, Matthew Ryan

“…Next, a new nonsmooth formulation of Hamiltonian dynamics for Hamiltonian systems with nonsmooth potential energy is developed, using lexicographic differentiation to derive a system of discontinuous differential equations, and theoretical results are developed. …”
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Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrodinger equation by Colliander, J., Keel, M., Staffilani, Gigliola, Takaoka, H., Tao, T.

“…The techniques used here are related to but are distinct from those traditionally used to prove Arnold Diffusion in perturbations of Hamiltonian systems.…”
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Entropy as a Metric Generator of Dissipation in Complete Metriplectic Systems by Massimo Materassi

“…The motivation of expressing through a bracket algebra and a motion-generating function F is to endow the theory of the system at hand with all the powerful machinery of Hamiltonian systems in terms of symmetries that become evident and readable. …”
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Lyapunov spectra of chaotic recurrent neural networks by Rainer Engelken, Fred Wolf, L. F. Abbott

“…We show that a generalized time-reversal symmetry of the network dynamics induces a point symmetry of the Lyapunov spectrum reminiscent of the symplectic structure of chaotic Hamiltonian systems. Temporally fluctuating input can drastically reduce both the entropy rate and the attractor dimension. …”
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Reduced Models of Point Vortex Systems by Jonathan Maack, Bruce Turkington

“…Optimal closure refers to a general method of reduction for Hamiltonian systems, in which macroscopic states are required to belong to a parametric family of distributions on phase space. …”
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Solutions of a Two-Particle Interacting Quantum Walk by Alessandro Bisio, Giacomo Mauro D’Ariano, Nicola Mosco, Paolo Perinotti, Alessandro Tosini

“…The present automaton exhibits scattering solutions with nontrivial momentum transfer, jumping between different regions of the Brillouin zone that can be interpreted as Fermion-doubled particles, in stark contrast with the customary momentum-exchange of the one-dimensional Hamiltonian systems. A further difference compared to the Hamiltonian model is that there exist bound states for every value of the total momentum and of the coupling constant. …”
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Meaning of temperature in different thermostatistical ensembles by Hänggi, Peter, Hilbert, Stefan, Dunkel, Joern

“…It can be proved, however, that only the volume entropy satisfies exactly the traditional form of the laws of thermodynamics for a broad class of physical systems, including all standard classical Hamiltonian systems, regardless of their size. This mathematically rigorous fact implies that negative ‘absolute’ temperatures and Carnot efficiencies more than 1 are not achievable within a standard thermodynamical framework. …”
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Quantum Current Algebra Symmetry and Description of Boltzmann Type Kinetic Equations in Statistical Physics by Lev I. Ivankiv, Yarema A. Prykarpatsky, Valeriy H. Samoilenko, Anatolij K. Prykarpatski

“…We review a non-relativistic current algebra symmetry approach to constructing the Bogolubov generating functional of many-particle distribution functions and apply it to description of invariantly reduced Hamiltonian systems of the Boltzmann type kinetic equations, related to naturally imposed constraints on many-particle correlation functions. …”
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Generalization of the Schrödinger Equation for Open Systems Based on the Quantum-Statistical Approach by Konstantin G. Zloshchastiev

“…This uncovers a large class of quantum-mechanical non-Hamiltonian systems whose dynamics are not determined by conventional mechanics’ potentials and forces, but rather come about through quantum statistical effects caused by the system’s environment.…”
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Universal state conversion in discrete and slowly varying non-Hermitian cyclic systems: An analytic proof and exactly solvable examples by Nicholas S. Nye

“…Overall, our results provide a deeper theoretical insight on slowly varying discrete non-Hermitian Hamiltonian systems, and pave the way towards exploring the dynamics underpinning the traversal of higher-dimensional cyclic parametric trajectories in the vicinity (or not) of higher-order spectral singularities for both continuous and discrete settings under linear or nonlinear conditions.…”
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Implicit Regularization and Momentum Algorithms in Nonlinearly Parameterized Adaptive Control and Prediction by Boffi, Nicholas M, Slotine, Jean-Jacques E

“…We apply this result to regularized dynamics predictor and observer design, and as concrete examples, we consider Hamiltonian systems, Lagrangian systems, and recurrent neural networks. …”
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Quantum entanglement growth under random unitary dynamics by Nahum, A, Ruhman, J, Vijay, S, Haah, J

“…Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the “entanglement tsunami” in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ) equation. …”

A Poisson map from kinetic theory to hydrodnamics with non-constant entropy by Chong, CL

“…Both systems can be formulated as noncanonical Hamiltonian systems. Each configuration space is an infinite-dimensional Poisson manifold, and the dynamics is the flow generated by a Hamiltonian functional via a Poisson bracket. …”

Classical and Quantum Spherical Pendulum by Richard Cushman, Jędrzej Śniatycki

“…In particular, we want to extend Bohr–Sommerfeld theory to a full quantum theory of completely integrable Hamiltonian systems, which is compatible with geometric quantization. …”
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