相关论文: Hamiltonian monodromy as lattice defect
The phenomenon of a topological monodromy in integrable Hamiltonian and nonholonomic systems is discussed. An efficient method for computing and visualizing the monodromy is developed. The comparative analysis of the topological monodromy…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
Recent work has demonstrated the existence of universal Hamiltonians - simple spin lattice models that can simulate any other quantum many body system to any desired level of accuracy. Until now proofs of universality have relied on…
A summary of a recently proposed description of quantum-classical hybrids is presented, which concerns quantum and classical degrees of freedom of a composite object that interact directly with each other. This is based on notions of…
The aim of this work is to show that particle mechanics, both classical and quantum, Hamiltonian and Lagrangian, can be derived from few simple physical assumptions. Assuming deterministic and reversible time evolution will give us a…
We consider the classical and quantum dynamics in M(atrix) theory. Using a simple ansatz we show that a classical trajectory exhibits a chaotic motion. We argue that the holographic feature of M(atrix) theory is related with the repulsive…
The appearance of Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen…
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation…
The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the underlying hidden symmetry algebra. (In typical applications the latter is either the…
We show that the main difference between classical and quantum systems can be understood in terms of information entropy. Classical systems can be considered the ones where the internal dynamics can be known with arbitrary precision while…
The classical invariants of a Hamiltonian system are expected to be derivable from the respective quantum spectrum. In fact, semiclassical expressions relate periodic orbits with eigenfunctions and eigenenergies of classical chaotic…
The Hamiltonian theory of isomonodromy equations for meromorphic connections with irregular singularities on algebraic curves is constructed. An explicit formula for the symplectic structure on the space of monodromy and Stokes matrices is…
Classical Hamiltonian systems with conserved charges and those with constraints often describe dynamics on a pre-symplectic manifold. Here we show that a pre-symplectic manifold is also the proper stage to describe autonomous energy…
The analysis of the Helmholtz equation is shown to lead to an exact Hamiltonian system of equations describing in terms of ray trajectories a very wide family of wave-like phenomena (including diffraction and interference) going much beyond…
The strict connection between Lie point-symmetries of a dynamical system and its constants of motion is discussed and emphasized, through old and new results. It is shown in particular how the knowledge of a symmetry of a dynamical system…
The interaction of an atom with an electromagnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electromagnetic fields helps to design the quantum analog of…
We describe our recent proposal of a path integral formulation of classical Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics, which concerns the direct coupling of classical and quantum mechanical degrees of…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
A class of one dimensional classical systems is characterized from an algebraic point of view. The Hamiltonians of these systems are factorized in terms of two functions that together with the Hamiltonian itself close a Poisson algebra.…