Graphs can be used to model various problems and relations in diverse domains eg. Computer Science, Biological, Chemical and many other. There exist various hard problems in communication networks, which are practically hard but can be shaped in the form of graphs. A Hamiltonian Path is a spanning trail in a network graph i.e. a path through every network node and a spanning cycle in a network ...

We study the off-equilibrium dynamics of the Edwards–Anderson spin glass in four dimensions under the influence of a non-Hamiltonian perturbation (i.e. with asymmetric couplings). We find that for small asymmetry the model behaves like the Hamiltonian model, while for large asymmetry the behaviour of the model can be well described by an interrupted ageing scenario. The autocorrelation function...

We give a Hamiltonian analysis of the asymptotically flat spherically symmetric system of gravity coupled to a scalar field. This 1+1 dimensional field theory may be viewed as the ”standard model” for studying black hole physics. Our analysis is adapted to the flat slice Painleve-Gullstrand coordinates. We give a Hamiltonian action principle for this system, which yields an asymptotic mass form...

We formulate the quark meson coupling model as a many-body effective Hamiltonian. This leads naturally to the appearance of many-body forces. We investigate the zero range limit of the model and compare its Hartree-Fock Hamiltonian to that corresponding to the Skyrme effective force. By fixing the three parameters of the model to reproduce the binding and symmetry energy of nuclear matter, we f...

We construct a two dimensional nonlinear σ-model that describes the Hamiltonian flow in the loop space of a classical dynamical system. This model is obtained by equivariantizing the standard N=1 supersymmetric nonlinear σ-model by the Hamiltonian flow. We use localization methods to evaluate the corresponding partition function for a general class of integrable systems, and find relations that...

Fluid reductions of the Vlasov–Ampère equations that preserve the Hamiltonian structure of the parent kinetic model are investigated. Hamiltonian closures using the first four moments of the Vlasov distribution are obtained, and all closures provided by a dimensional analysis procedure for satisfying the Jacobi identity are found. Two Hamiltonian models emerge, for which the explicit closures a...

We present a method of localised control of chaos in Hamiltonian systems. The aim is to modify the perturbation locally by a small control term which makes the controlled Hamiltonian more regular. We provide an explicit expression for the control term which is able to recreate invariant (KAM) tori without modifying other parts of phase space. We apply this method of localised control to a force...

In this paper, we consider the Hamiltonian alternating path problem for graphs, multigraphs, and digraphs. We describe an approach to solve the problem. This approach is based on constructing logical models for the problem. We use logical models for the Hamiltonian alternating path problem to solve the Hamiltonian path problem and the planning a typical working day for indoor service robots pro...

An exact boson mapping of the reduced BCS (equal strength) pairing Hamiltonian is considered. In the mapping, fermion pair operators are mapped exactly to the corresponding bosons. The image of the mapping results in a Bose-Hubbard model with level dependent hopping. Though the resultant Bose-Hubbard Hamiltonian is non-Hermitian, all eigenvalues are real when Uk/t < 1, where k is the total numb...