Related papers: A standard Hamiltonian formulation for the dynamic…

This paper builds on our earlier proposal for construction of a positive inner product for pseudo-Hermitian Hamiltonians and we give several examples to clarify our method. We show through the example of the harmonic oscillator how our…

Here it is shown that the unitary dynamics of a quantum object may be obtained as the conditional expectation of a counting process of object-clock interactions. Such a stochastic process arises from the quantization of the clock, and this…

We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…

We consider the problem of motion-induced photon creation from quantum vacuum inside closed, perfectly conducting cavities with time-dependent geometries. These include one dimensional Fabry-Perrot resonators with Dirichlet or Neumann…

In this work we consider the dynamical Casimir effect for a massless scalar field -- under Dirichlet boundary conditions -- between two concentric spherical shells. We obtain a general expression for the average number of particle creation,…

The concept of parity-time (PT) symmetry originates from the framework of quantum mechanics, where if the Hamiltonian operator satisfies the commutation relation with the parity and time operators, it shows all real eigen-energy spectrum.…

We present a numerical analysis of the particle creation for a quantum field in the presence of time dependent boundary conditions. Having in mind recent experiments involving superconducting circuits, we consider their description in terms…

For ultrashort VUV pulses with a pulse length comparable to the orbital time of the bound electrons they couple to we propose a simplified envelope Hamiltonian. It is based on the Kramers-Henneberger representation in connection with a…

We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…

The Hamiltonian approach to the General Relativity is formulated as a joint nonlinear realization of conformal and affine symmetries by means of the Dirac scalar dilaton and the Maurer-Cartan forms. The dominance of the Casimir vacuum…

We propose the use of quantum optical systems to perform universal simulation of quantum dynamics. Two specific implementations that require present technology are put forward for illustrative purposes. The first scheme consists of neutral…

We consider a real massless scalar field in 3+1 dimensions satisfying a Robin boundary condition at a nonrelativistic moving mirror. Considering vacuum as the initial field state, we compute explicitly the number of particles created per…

We calculate the Casimir energy for scalar and gauge fields in interaction with zero-width mirrors, including quantum effects due to the matter fields inside the mirrors. We consider models where those fields are either scalar or fermionic,…

We analyze the high temperature (or classical) limit of the Casimir effect. A useful quantity which arises naturally in our discussion is the ``relative Casimir energy", which we define for a configuration of disjoint conducting boundaries…

We propose an optomechanical structure consisting of a photonic-crystal (holey) membrane suspended above a layered silicon-on-insulator substrate in which resonant bonding/antibonding optical forces created by externally incident light from…

We present a formalism for light optics starting with the Maxwell equations and casting them into an exact matrix form taking into account the spatial and temporal variations of the permittivity and permeability. This $8 \times 8$ matrix…

We apply the background field method and the effective action formalism to describe the four-dimensional dynamical Casimir effect. Our picture corresponds to the consideration of quantum cosmology for an expanding FRW universe (the boundary…

A general procedure for constructing action principles for continuum models via a generalization of Hamilton's principle of mechanics is described. Through the procedure, an action principle for a gyroviscous magnetohydrodynamics (MHD)…

The Casimir effect is a quantum phenomenon induced by the zero-point energy of relativistic fields confined in a finite-size system. This effect for photon fields has been studied for a long time, while the realization of counterparts for…

Using the modified Prelle- Singer approach, we point out that explicit time independent first integrals can be identified for the damped linear harmonic oscillator in different parameter regimes. Using these constants of motion, an…