The idea of this contribution is to suggest a way to get rid of gravity as a dynamical space time approximately in cosmology and thus be able to use Hamiltonian formulation ignoring the gravitational degrees of freedom, treating them just as backgrou...
This supplement to the article "Approximating multi-dimensional Hamiltonian flows by billiards" contains the proofs of C$^{0}$ and C$^{r}$ - closeness theorems stated in the article....
Enthusiast's perspective: We analyze the effectiveness of AQC for a small rank problem Hamiltonian $H_F$ with the arbitrary initial Hamiltonian $H_I$. We prove that for the generic $H_I$ the running time cannot be smaller than $O(\sqrt N)$, where $N$...
The recent work of Delabaere and Trinh (2000 J. Phys. A 33 8771) discovered the existence of ${\cal P}{\cal T}$-symmetry breaking, complex energy, $L^2$ solutions for the one dimensional Hamiltonian, $P^2+iX^3+iαX$, in the asymptotic limit, $α\to...
The Eigenvalue Moment Method (EMM), Handy (2001), Handy and Wang (2001)) is applied to the $H_α\equiv P^2 + iX^3 + iαX$ Hamiltonian, enabling the algebraic/numerical generation of converging bounds to the complex energies of the $L^2$ states, as...
A conceptually simple physical interpretation of a conserved Hamiltonian $\mathcal{H}$ for a mechanical system with a time-dependent constraint is given. For the case of a bead on a vertical hoop forced to rotate with constant angular velocity $ω$,...
Kinetics of metastable systems modeled by Hamiltonians containing nonlocal and nonconservative terms is reproduced by the Fokker-Planck and imaginary time Schrodinger equation scheme with subsequent symplectic integration. Example solutions for erg...
For a Hamilton cycle in a rectangular $m \times n$ grid, what is the greatest number of turns that can occur? We give the exact answer in several cases and an answer up to an additive error of $2$ in all other cases. In particular, we give a new proo...
The article reviews the general version of the Bohr collective model for the description of quadrupole collective states, including a detailed study the model's kinematics. The general form of the classical and quantum Bohr Hamiltonian is presented...
Hamiltonian formalisms provide powerful tools for the computation of approximate analytic solutions of the Einstein field equations. The post-Newtonian computations of the explicit analytic dynamics and motion of compact binaries are discussed within...
Welcome the Official /r/CFL Game Thread for the 102nd Grey Cup, this match will feature a tilt between the Eastern Division Champions the Hamilton Tiger-Catss and the Western Division Champions the Ca...
We determine the form of the unitary transformation that diagonalizes the Jaynes-Cummings Hamiltonian. This leads to operators the action of which has a simple interpretation in terms of the dressed states, the energy eigenstates. This suggests a set...
In this short note, we make an observation relating symplectic packings of the standard symplectic ball by two sets and Hamiltonian linking....
they're not getting the info they need". CBC News. January 22, 2023. Mann, Ken (September 15, 2021). "Key LRT decision ratified by Hamilton city council"
We prove a $C^\infty$ closing lemma for Hamiltonian diffeomorphisms of closed surfaces. This is a consequence of a $C^\infty$ closing lemma for Reeb flows on closed contact three-manifolds, which was recently proved as an application of spectral inva...
This paper studies a quantum simulation technique for solving the Fokker-Planck equation. Traditional semi-discretization methods often fail to preserve the underlying Hamiltonian dynamics and may even modify the Hamiltonian structure, particularly w...
The Jupiter-Saturn 2:5 near-commensurability is analyzed in a fully analytic Hamiltonian planetary theory. Computations for the Sun-Jupiter-Saturn system, extending to the third order of the masses and to the 8th degree in the eccentricities and in...
An algorithm to create difficult Sudoku puzzles is proposed. An Ising spin-glass like Hamiltonian describing difficulty of puzzles is defined, and difficult puzzles are created by minimizing the energy of the Hamiltonian. We adopt the replica exchang...
Wave turbulence formalism for long internal waves in a stratified fluid is developed, based on a natural Hamiltonian description. A kinetic equation appropriate for the description of spectral energy transfer is derived, and its self-similar statio...
We analyse computational efficiency of Metropolis-Hastings algorithms with AR(1) process proposals. These proposals include, as a subclass, discretized Langevin diffusion (e.g. MALA) and discretized Hamiltonian dynamics (e.g. HMC). By including the...