Related papers: Hamiltonians of Spherically Symmetric, Scale-Free …
A family of effective actions in Hamiltonian form is derived for a self-gravitating sphere of isotropic homogeneous dust. Starting from the Einstein-Hilbert action for barotropic perfect fluids and making use of the symmetry and equation of…
We consider one-dimensional classical time-dependent Hamiltonian systems with quasi-periodic orbits. It is well-known that such systems possess an adiabatic invariant which coincides with the action variable of the Hamiltonian formalism. We…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
A group of non-uniform quantum lattice Hamiltonians in one dimension is introduced, which is related to the hyperbolic $1 + 1$-dimensional space. The Hamiltonians contain only nearest neighbor interactions whose strength is proportional to…
In this article, we explore the construction of Hamiltonians with long-range interactions and their corrections using the short-range behavior of the wave function. A key aspect of our investigation is the examination of the one-particle…
We provide a general algorithm to construct a Hamiltonian, such that its dynamical flow covariantly defines any given spherically symmetric and static metric. This Hamiltonian is defined as a linear combination of the standard (general…
A family of classical integrable systems defined on a deformation of the two-dimensional sphere, hyperbolic and (anti-)de Sitter spaces is constructed through Hamiltonians defined on the non-standard quantum deformation of a sl(2) Poisson…
The Hamiltonian formulation of Horava gravity is derived. In a closed universe the Hamiltonian is a sum of generators of gauge symmetries, the foliation-preserving diffeomorphisms, and vanishes on shell. The scalar constraint is second…
We present a gauge fixing of gravity coupled to a scalar field in spherical symmetry such that the Hamiltonian is an integral over space of a local density. Such a formulation had proved elusive over the years. As in any gauge fixing, it…
We introduce a family of Hamiltonian systems for measurement-based quantum computation with continuous variables. The Hamiltonians (i) are quadratic, and therefore two body, (ii) are of short range, (iii) are frustration-free, and (iv)…
An infinite family of quasi-maximally superintegrable Hamiltonians with a common set of (2N-3) integrals of the motion is introduced. The integrability properties of all these Hamiltonians are shown to be a consequence of a hidden…
Nonlocal terms in the Einstein Hilbert(EH) action appears as IR corrections in effective theory of quantum gravity. Here we have considered such an action keeping the terms which are quadratic in Ricci Scalar. We obtain the solution for a…
We provide a quantum algorithm for simulating the dynamics of sparse Hamiltonians with complexity sublogarithmic in the inverse error, an exponential improvement over previous methods. Specifically, we show that a $d$-sparse Hamiltonian $H$…
We investigate properties of the most general PT-symmetric non-Hermitian Hamiltonian of cubic order in the annihilation and creation operators as a ten parameter family. For various choices of the parameters we systematically construct an…
Galaxies and the dark matter halos that host them are not spherically symmetric, yet spherical symmetry is a helpful simplifying approximation for idealised calculations and analysis of observational data. The assumption leads to an exact…
We derive an effective Hamiltonian for the nonlinear process of parametric down conversion in the presence of absorption. Based upon the Green function method for quantizing the electromagnetic field, we first set up Heisenberg's equations…
We consider 4-dimensional space-times which are asymptotically flat at spatial infinity and show that, in the first order framework, action principle for general relativity is well-defined \emph{without the need of infinite counter terms.}…
We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this…
We present a general analytical formalism to determine the energy spectrum of a quantum particle in a cubic lattice subject to translationally invariant commensurate magnetic fluxes and in the presence of a general space-independent…
In a vast class of systems, which includes members as diverse as sedimenting particles and bird flocks, interactions do not stem from a potential, and are in general nonreciprocal. Thus, it is not possible to define a conventional energy…