On the Role of Constraints and Degrees of Freedom in the Hamiltonian Formalism by Alexey Golovnev

“…In this article, I give a pedagogical introduction to the degenerate Hamiltonian systems, showing both very simple mechanical examples and general arguments about how it works. …”
Get full text

Separation of variables for the classical elliptic reflection equation algebra by T. Skrypnyk

“…We consider two examples of such the integrable hamiltonian systems governed by the simplest Poisson brackets connected with classical reflection equation algebra with the elliptic r−s matrices. …”
Get full text

Projection of the Russian economic development in the framework of the optimal control model by investments in fixed assets by Alexander Mikhajlovich Tarasyev, Anastasy Aleksandrovna Usova, Yulia Valer’evna Shmotina

“…We study the qualitative properties of optimal trajectories as solutions of the Hamiltonian systems arising in Pontryagin’s maximum principle. …”
Get full text

Subharmonic solutions for a class of predator-prey models with degenerate weights in periodic environments by López-Gómez Julián, Muñoz-Hernández Eduardo, Zanolin Fabio

“…This article deals with the existence, multiplicity, minimal complexity, and global structure of the subharmonic solutions to a class of planar Hamiltonian systems with periodic coefficients, being the classical predator-prey model of V. …”
Get full text

One-particle and few-particle billiards. by Lansel, S, Porter, M, Bunimovich, L

“…In the one-particle case, we investigate the formation and destruction of resonance islands in (generalized) mushroom billiards, which are a recently discovered class of Hamiltonian systems with mixed regular-chaotic dynamics. …”

Local characterization of one-dimensional topologically ordered states by Cui, J, Amico, L, Fan, H, Gu, M, Hamma, A, Vedral, V

“…We consider one-dimensional Hamiltonian systems whose ground states display symmetry-protected topological order. …”

A New Thermodynamics from Nuclei to Stars by Dieter H.E. Gross

“…Abstract: Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. …”
Get full text

Analysis of Novel Oscillations of Quantized Mechanical Energy in Mass-Accreting Nano-Oscillator Systems by Jeong Ryeol Choi

“…Quantum characteristics of a mass-accreting oscillator are investigated using the invariant operator theory, which is a rigorous mathematical tool for unfolding quantum theory for time-dependent Hamiltonian systems. In particular, the quantum energy of the system is analyzed in detail and compared to the classical one. …”
Get full text

Chemical ordering induced elastic hardening and thermoelastic properties of β phase Mg1-xScx lightweight shape memory alloys by Narisu Bao, You Zhou, Lin-ping Sun, Xibin Li, Xiaoxia Wu, B. Narsu

Get full text

Symmetries and Geometrical Properties of Dynamical Fluctuations in Molecular Dynamics by Robert L. Jack, Marcus Kaiser, Johannes Zimmer

“…That is, we consider Hamiltonian systems, coupled to external heat baths, and driven out of equilibrium by non-conservative forces. …”
Get full text

Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries by Sahand Seifnashri

“…We study 't Hooft anomalies of global symmetries in 1+1d lattice Hamiltonian systems. We consider anomalies in internal and lattice translation symmetries. …”
Get full text

Matter-wave solitons with a periodic, piecewise-constant scattering length by Rodrigues, A, Kevrekidis, P, Porter, M, Frantzeskakis, D, Schmelcher, P, Bishop, A

“…To accurately quantify the stability of bright and dark solitons, we adapt general tools from the theory of perturbed Hamiltonian systems. We show that stationary solitons must be centered in one of the constant regions of the piecewise-constant nonlinearity. …”

Lagrangian structures in time-periodic vortical flows by S. V. Kostrykin, A. A. Khapaev, V. M. Ponomarev, I. G. Yakushkin

“…A qualitative interpretation of phenomena observed on the basis of the theory of adiabatic chaos in the Hamiltonian systems is given. <br><br> The Lagrangian trajectories are numerically simulated under varying flow parameters. …”
Get full text

Quasi-stationary-state duration in d-dimensional long-range model by Antonio Rodríguez, Fernando D. Nobre, Constantino Tsallis

“…This paves the way for other long-range Hamiltonian systems, such as gravitation, the α-XY, and Coulombian models, among others.…”
Get full text

Instability dynamics of nonlinear normal modes in the Fermi–Pasta–Ulam–Tsingou chains by Liangtao Peng, Weicheng Fu, Yong Zhang, Hong Zhao

“…Nonlinear normal modes are periodic orbits that survive in nonlinear chains, whose instability plays a crucial role in the dynamics of many-body Hamiltonian systems toward thermalization. Here we focus on how the stability of nonlinear modes depends on the perturbation strength and the system size to observe whether they have the same behavior in different models. …”
Get full text

Dimension reduction in recurrent networks by canonicalization by Grigoryeva, Lyudmila, Ortega, Juan-Pablo

“…Additionally, the notion of optimal reduction coming from the theory of symmetric Hamiltonian systems is implemented in our setup to construct canonical realizations out of input forgetting but not necessarily canonical ones. …”
Get full text

Necessary and Sufficient Conditions for Time Reversal Symmetry in Presence of Magnetic Fields by Davide Carbone, Lamberto Rondoni

“…In this paper we advance this investigation for classical Hamiltonian systems, substantially increasing the number of symmetries that yield TRI in presence of a magnetic field. …”
Get full text

A Proof of Chaos for a Seasonally Perturbed Version of Goodwin Growth Cycle Model: Linear and Nonlinear Formulations by Marina Pireddu

“…Namely, the original and the modified formulations of Goodwin model are described by Hamiltonian systems, characterized by the presence of a nonisochronous center, and the seasonal variation of the parameter, representing the ratio between capital and output, which is common to both frameworks, is empirically grounded. …”
Get full text

Multivariate fluctuation relations for currents by Pierre Gaspard

“…In this way, multivariate fluctuation relations are obtained for energy or particle transport in the effusion of an ideal gas, heat transport in Hamiltonian systems coupled by Langevin stochastic forces to heat reservoirs, driven Brownian motion of an electrically charged particle subjected to an external magnetic field, and quantum electron transport in multi-terminal mesoscopic circuits where the link to the scattering approach is established.…”
Get full text

A Quantum Formalism for Abstract Dynamical Systems by Joan C. Micó

“…A classical linear Hamiltonian can be derived for ADS by using Dirac’s dynamics for singular Hamiltonian systems. Also, a corresponding first-order Schrödinger equation (which involves the existence of a system Planck constant particular of each system) can be derived from this Hamiltonian. …”
Get full text