Related papers: Bali's ancient rice terraces: A Hamiltonian approa…
We construct so-called Darboux transformations and solutions of the dynamical Hamiltonian systems with several space variables $\frac{\partial \psi}{\partial t}=\sum_{k=1}^r H_k(t)\frac{\partial \psi}{\partial \zeta_k}\,$ $( H_k(t)=…
For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.
A stationary physical system satisfies peculiar balance conditions involving mean values of appropriate observables. In this paper we show how to deduce such quantitative links, named balance equations, demonstrating as well their…
The dynamics of the spin-boson Hamiltonian is considered in the stochastic approximation. The Hamiltonian describes a two-level system coupled to an environment and is widely used in physics, chemistry and the theory of quantum measurement.…
We study the phase diagram of two different Hamiltonians with competiting local, nearest-neighbour, and mean-field couplings. The first example corresponds to the HMF Hamiltonian with an additional short-range interaction. The second…
We propose and solve a Hamiltonian model for multidimensional epistastatic interactions between beneficial mutations. The model is able to give rise either to a phase transition between two equilibrium states, without any coexistence, or…
Gravitational and electromagnetic interactions are Hamiltonian systems with forces between pairs of particles. We propose an alternative: Hamiltonian dynamics with triplet interactions between point particles. Our system has a potential…
We introduce an extension of the lattice model of melting of semiflexible polymers originally proposed by Flory. Along with a bending penalty, present in the original model and involving three sites of the lattice, we introduce an…
We will discuss various aspects of thermalization, chaos and hydrodynamics in one dimensional classical Hamiltonian systems. We study two problems. First, we will revisit the Fermi-Pasta-Ulam-Tsingou (FPUT) problem in order to understand…
We consider a Hamiltonian system made of $N$ classical particles moving in two dimensions, coupled via an {\it infinite-range interaction} gauged by a parameter $A$. This system shows a low energy phase with most of the particles trapped in…
Hamiltonian mechanics can be used to constrain temperature simultaneously with energy. We illustrate the interesting situations that develop when two different temperatures are imposed within a composite Hamiltonian system. The model…
In the present work we analyse the structure of the Hamiltonian field theory in the neighbourhood of the wave equation $q_{tt}=q_{xx}$. We show that, restricting to ``graded'' polynomial perturbations in $q_x$, $p$ and their space…
The Husimi distribution provides for a coarse grained representation of the phase space distribution of a quantum system, which may be used to track the growth of entropy of the system. We present a general and systematic method of solving…
The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential energy. However, in the nonlinear context, there may be other…
An analytical solution for the out-of-equilibrium quasi-stationary states of the paradigmatic Hamiltonian Mean Field (HMF) model can be obtained from a maximum entropy principle. The theory has been so far tested with reference to a…
Couplings of a system to other degrees of freedom (that is, environmental degrees of freedom) lead to energy dissipation when the number of environmental degrees of freedom is large enough. Here we discuss quantal treatments for such energy…
We consider an ensemble of three-level particles in lambda-configuration interacting with two bosonic modes. The Hamiltonian has the form of a generalized Dicke-model. We show that in the thermodynamic limit this model supports a…
A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward…
Port-Hamiltonian (pH) systems offer a highly structured and energy-based modular framework for control systems. Many pH systems exhibit non-polynomial non-linearities. We consider the problem of immersing such systems into a…
Port-Hamiltonian systems theory provides a structured approach to modelling, optimization and control of multiphysical systems. Yet, its relationship to thermodynamics seems to be unclear. The Hamiltonian is traditionally thought of as…