相关论文: Nonholonomic Constraints in Time-Dependent Mechani…

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…

We formulate a set of conditions under which dynamics of a time-dependent quantum Hamiltonian are integrable. The main requirement is the existence of a nonabelian gauge field with zero curvature in the space of system parameters. Known…

The main goal of these lectures is to introduce and review the Hamiltonian formalism for classical constrained systems and in particular gauge theories. Emphasis is put on the relation between local symmetries and constraints and on the…

In this note we address the exact solutions of a time-dependent Hamiltonian composed by an oscillator-like interaction with both a frequency and a mass term that depend on time. The latter is achieved by constructing the appropriate point…

In the quadri-dimensional space-time, the variation of Hamilton's action is a powerful tool to study the process equations for conservative fluid media. In this framework, Hamilton's principle allows to obtain equation of motions, equation…

We derive the effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) in the asymptotic limit where the restoring forces tend to infinity. In contrast to…

A relativistic quantum mechanics is studied for bound hadronic systems in the framework of the Point Form Relativistic Hamiltonian Dynamics. Negative energy states are introduced taking into account the restrictions imposed by a correct…

We develop a formalism for the robust dynamical decoupling and Hamiltonian engineering of strongly interacting qudit systems. Specifically, we present a geometric formalism that significantly simplifies qudit pulse sequence design, while…

We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar…

The constraint distribution in non-holonomic mechanics has a double role. On one hand, it is a kinematic constraint, that is, it is a restriction on the motion itself. On the other hand, it is also a restriction on the allowed variations…

In this study, firstly, the k-th order extension of complex product manifold is consid- ered. Then the higher order vertical, complete lifts of geometric structures on product manifold to its extended spaces are given. Also higher order…

In this paper, by arising condition in variation, from equal time to non-equal time, I reconsider how geometrodynamics equations allow to be derived from variational principle in general relativity and then find the variation of extrinsic…

We consider solutions of Lagrangian variational problems with linear constraints on the derivative. These solutions are given by curves $\gamma$ in a differentiable manifold $M$ that are everywhere tangent to a smooth distribution $\mathcal…

We apply the method of transitionless quantum driving for time-dependent quantum systems to spin systems. For a given Hamiltonian, the driving Hamiltonian is constructed so that the adiabatic states of the original system obey the…

We implement the Hamiltonian treatment of a nonAbelian noncommutative gauge theory, considering with some detail the algebraic structure of the noncommutative symmetry group. The first class constraints and Hamiltonian are obtained and…

Many chemical processes exhibit diverse timescale dynamics with a strong coupling between timescale sensitive variables. Model predictive control with a non-uniformly spaced optimisation horizon is an effective approach to multi-timescale…

The short-time behavior of the survival probability of a system governed by a time-dependent non-Hermitian Hamiltonian is derived using to the second order perturbative approach. The resulting expression allows for the analysis of some…

The problem of constant-speed ballistics is studied under the umbrella of non-linear non-holonomic constrained systems. The Newtonian approach is shown to be equivalent to the use of Chetaev's rule to incorporate the constraint within the…

In recent works we have used quantum tools in the analysis of the time evolution of several macroscopic systems. The main ingredient in our approach is the self-adjoint Hamiltonian $H$ of the system $\Sc$. This Hamiltonian quite often, and…

We study mechanical systems subject to constraint functions that can be dependent at some points and independent at the rest. Such systems are modelled by means of generalized codistributions. We discuss how the constraint force can…