Related papers: Generalized Hamilton Function in the Phase Space o…

A quantal system in an eigenstate, of operators with a continuous nondegenerate eigenvalue spectrum, slowly transported round a circuit C by varing parameters in its Hamiltonian, will acquire a generalized geometrical phase factor. An…

In the study of Hamiltonian systems on cotangent bundles, it is natural to perturb Hamiltoni-ans by adding potentials (functions depending only on the base point). This led to the definition of Ma{\~n}{\'e} genericity: a property is generic…

The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple…

The noncommutative spectral action extends our familiar notion of commutative spaces, using the data encoded in a spectral triple on an almost commutative space. Varying a rather simple action, one can derive all of the standard model of…

Described is n-level quantum system realized in the n-dimensional ''Hilbert'' space H with the scalar product G taken as a dynamical variable. The most general Lagrangian for the wave function and G is considered. Equations of motion and…

We propose a form for the action of a relativistic particle subject to a positional force that is invariant under time reparametrization and therefore allows for a consistent Hamiltonian formulation of the dynamics. This approach can be…

A large deviation function mathematically characterizes the statistical property of atypical events. Recently, in non-equilibrium statistical mechanics, large deviation functions have been used to describe universal laws such as the…

In most text books of mechanics, Newton's laws or Hamilton's equations of motion are first written down and then solved based on initial conditions to determine the constants of the motions and to describe the trajectories of the particles.…

The Hartle-Hawking wave function is known to be the Fourier dual of the Chern-Simons or Kodama state reduced to mini-superspace, using an integration contour covering the whole real line. But since the Chern-Simons state is a general…

Loop quantum gravity in its Hamiltonian form relies on a connection formulation of the gravitational phase space with three key properties: 1.) a compact gauge group, 2.) real variables, and 3.) canonical Poisson brackets. In conjunction,…

Complex systems consist of many interacting elements which participate in some dynamical process. The activity of various elements is often different and the fluctuation in the activity of an element grows monotonically with the average…

For any given spacetime the choice of time coordinate is undetermined. A particular choice is the absolute time associated with a preferred vector field. Using the absolute time Hamilton's equations are $- (\delta H_{c})/(\delta…

Gravitation is considered to be one of the four fundamental interactions in nature. However, one has so far failed to observe the graviton, the quantum particle that is believed to transmit the gravitational force at a distance - the…

We consider a one-dimensional gas of hard point particles in a finite box that are in thermal equilibrium and evolving under Hamiltonian dynamics. Tagged particle correlation functions of the middle particle are studied. For the special…

A generalized version of the rotating-wave approximation for the single-mode spin-boson Hamiltonian is presented. It is shown that performing a simple change of basis prior to eliminating the off-resonant terms results in a significantly…

A new first-principles statistical mechanics formulation is proposed to describe slow and dilated granular fluids, where prolonged intergranular contacts vitiate collision theory. The contacts, where all the important physics takes place,…

We study three functions which are power series in the variable $z$, Dirichlet series in the variable $s$ and with coefficients given by arithmetical functions. A strong point is to relate these functions to some Hilbert spaces. Three main…

I propose to use Hamiltonians which contain two-dimensional and three-dimensional kinetic terms for the description of two-dimensional systems in physics. As a model system the evolution of three-dimensional wavefunctions in the presence of…

Any constructive continuous function must have a gradually varied approximation in compact space. However, the refinement of domain for $\sigma-$-net might be very small. Keeping the original discretization (square or triangulation), can we…

We formulate a Hamiltonian description of the orbital motion of a point particle in Kerr spacetime for generic (eccentric, inclined) orbits, which accounts for the effects of the conservative part of the gravitational self-force. This…