Related papers: Notes On The Born-Oppenheimer Approach In A Closed…
We investigate the dynamics of a family of functional extensions of the (Eddington-inspired) Born-Infeld gravity theory, constructed with the inverse of the metric and the Ricci tensor. We provide a generic formal solution for the…
Using the Teleparallel Equivalent of General Relativity formulated in Weitzenb\"{o}ck spacetime, we thoroughly explore a kind of Born-Infeld regular gravity leading to second order field equations for the vielbein components. We explicitly…
The paradigm of considering open quantum systems -- i.e. focusing only on the system of interest, and treating the rest of the world as an effective environment -- has proven to be a highly effective way to understand a range of quantum…
We introduce a new approach to modified gravity which generalizes the recently proposed hybrid metric-Palatini gravity. The gravitational action is taken to depend on a general function of both the metric and Palatini curvature scalars. The…
Semi-classical gravity is an approximation to quantum gravity where gravity is treated classically and matter quantum mechanically. Matter is described by quantum field theory on curved space-time, whereas gravity is described by a…
A new method of post-Newtonian approximation (PNA) for weak gravitational fields is presented together with its application to test an alternative, scalar theory of gravitation. The new method consists in defining a one-parameter family of…
Recent theoretical works on alternative metric theories of gravity give greater significance to solar-system tests of General Relativity. In particular, it is suggested that the post-Newtonian parameter $\gamma$ ought to be determined with…
The field equations associated with the Born-Infeld-Einstein action including matter are derived using a Palatini variational principle. Scalar, electromagnetic, and Dirac fields are considered. It is shown that an action can be chosen for…
Contrary to general relativity, quantum theory treats space and time in fundamentally different ways. In particular, while joint probabilities associated with spacelike separated measurements are defined in terms of the Born rule, joint…
The conditions are found that all solutions of a systems dynamic equations on time scales tends to finite limits as $t\to\infty$.
Linear-time invariant (LTI) oscillation systems such as forced mechanical vibration, series RLC and parallel RLC circuits can be solved by using simplest initial conditions or employing of Green's function of which knowledge of initial…
Geometric confinement and topological constraints present promising means of controlling active materials. By combining analytical arguments derived from the Born-Oppenheimer approximation with numerical simulations, we investigate the…
The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are…
There is a distinct possibility that current and future cosmological data can be used to constrain Einstein's theory of gravity on the very largest scales. To be able to do this in a model-independent way, it makes sense to work with a…
A modified theory of gravity with the function $F(R) = (1-\sqrt{1-2\lambda R})/\lambda$ is suggested and analyzed. At small value of the parameter $\lambda$ introduced the action is converted into Einstein$-$Hilbert action. The theory is…
I review recent results obtained for extensions of general relativity formulated within the Palatini formalism, an approach in which metric and connection are treated as independent geometrical entities. The peculiar dynamics of these…
We show that a recent proposal for the quantization of gravity based on discrete space-time implies a modification of standard quantum mechanics that naturally leads to a loss of coherence in quantum states of the type discussed by Milburn.…
We study the center-of-mass motion in systems of trapped interacting particles with space- and velocity-dependent friction and anharmonic traps. Our approach, based on a dynamical ansatz assuming a fixed density profile, allows us to obtain…
Nick Huggett, James Ladyman, and Karim Thebault (HLT) have presented a comprehensive article examining the Born-Oppenheimer Approximation (BOA). Their central objective is to challenge our position on the matter-namely, that the BOA…
Validity of the mean-field approach to open system dynamics in the optical cavity system is examined. It is rigorously shown that the mean-field approach is justified in the thermodynamic limit. The result is applicable to nonequilibrium…