Related papers: Hamilton's equations for relaxation function
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
A holonomic constraint is used to enforce a constant instantaneous configurational temperature on an equilibrium system. Three sets of equations of motion are obtained, differing according to the way in which the holonomic constraint is…
It is most common to construct the Hamiltonian function and Hamilton's canonical equations through a Legendre transformation of the Lagrangean function or through the central equation. These common perspectives, however, seem abstract and…
Hamilton's equations with noise and friction possess a hidden supersymmetry, valid for time-independent as well as periodically time-dependent systems. It is used to derive topological properties of critical points and periodic trajectories…
We present the basic formulation of Hamilton dynamics in complex phase space. We extend the Hamilton's function by including the imaginary part and find out the corresponding Hamilton's canonical equation of motion. Example of simple…
In order to solve quantum field theory in a non-perturbative way, Lagrangian lattice simulations have been very successful. Here we discuss a recently proposed alternative Hamiltonian lattice formulation - the Monte Carlo Hamiltonian. In…
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…
Sampling the stationary points of a complicated potential energy landscape is a challenging problem. Here we introduce a sampling method based on relaxation from stationary points of the highest index of the Hessian matrix. We illustrate…
The traditional method of teaching canonical transformations involves the introduction of generating functions of various types. This method obscures the underlying structure of the Hamiltonian least-action principle, and can make a…
We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in…
We evaluate the relaxation time to equilibrium, and especially show that it is almost independent from the system size for macroscopic isolated quantum systems. It at most polynomially depends on the system size. This estimation holds when…
The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…
Hamilton's principle is extended to have compatible initial conditions to the strong form. To use a number of computational and theoretical benefits for dynamical systems, the mixed variational formulation is preferred in the systems other…
A variational formulation for nonequilibrium thermodynamics was recently proposed in \cite{GBYo2017a,GBYo2017b} for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include…
We consider two high-frequency thermal processes in uniformly heated harmonic crystals relaxing towards equilibrium: (i) equilibration of kinetic and potential energies and (ii) redistribution of energy among spatial directions. Equation…
We derive the Hamilton equations of motion for a constrained system in the form given by Dirac, by a limiting procedure, starting from the Lagrangean for an unconstrained system. We thereby ellucidate the role played by the primary…
Consider a homogenous fluid membrane described by the Helfrich-Canham energy, quadratic in the mean curvature of the membrane surface. The shape equation that determines equilibrium configurations is fourth order in derivatives and cubic in…
A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. As in standard projection operator methods, a set of resolved variables is…
Based on two dissipative models, universal asymptotic behavior of flow equations for Hamiltonians is found and discussed. Universal asymptotic behavior only depends on fundamental bath properties but not on initial system parameters, and…
Using Hamilton-Jacobi formalism, The scenario of warm inflation with viscous pressure is considered. The formalism gives a way of computing the slow-rolling parameters without extra approximation, and it is well-known as a powerful method…