Abstract In this work, we study the non-Hermitian Swanson Hamiltonian, particularly non-parity-time symmetry phase. We use formalism of Gel’fand triplet to construct generalized eigenfunctions and corresponding spectrum. Depending on region parameter model space, show that Hamiltonian represents different physical systems, i.e. parabolic barrier, negative mass oscillators. also discussed presen...

The original Calogero model describes N quantum particles on the line interacting pairwise through a inverse square potential. It is well known to be integrable and solvable. Here we extend the Calogero Hamiltonian by means of new interactions which are PT-symmetric but not self adjoint. Some of these new interactions lead to integrable PT-symmetric Hamiltonians; the algebraic properties furthe...

We present an efficient generalization of algebraic dynamic programming (ADP) to unordered data types and a formalism for the automated derivation of outside grammars from their inside progenitors. These theoretical contributions are illustrated by ADP-style algorithms for shortest Hamiltonian path problems. These arise naturally when asking whether the evolutionary history of an ancient gene c...

For a variety of diffeomorphism–invariant field theories describing hypersurface motions (such as relativistic M -branes in space-time dimension M + 2) we perform a Hamiltonian reduction “at level 0”, showing that a simple algebraic function of the normal velocity is canonically conjugate to the shape Σ of the hypersurface. The Hamiltonian dependence on Σ is solely via the domain of integration...

We derive a Weierstrass-type formula for conformal Lagrangian immersions in Euclidean 4-space, and show that the data satisfies an equation similar to Dirac equation with complex potential. Alternatively this representation has a simple formulation using quaternions. We apply it to the Hamiltonian stationary case and construct all possible tori, thus obtaining a first approach to a moduli space...

Abstract. We consider a general class of systems of overdetermined differential-algebraic equations (ODAEs). We are particularly interested in extending the application of the symplectic Gauss methods to Hamiltonian and Lagrangian systems with holonomic constraints. For the numerical approximation to the solution to these ODAEs, we present specialized partitioned additive Runge– Kutta (SPARK) m...

We show that noncommuting electric fields occur naturally in θ-expanded noncommutative gauge theories. Using this noncommutativity, which is field dependent, and a hamiltonian generalisation of the Seiberg-Witten map, the algebraic consistency in the lagrangian and hamiltonain formulations of these theories, is established. A comparison of results in different descriptions shows that this gener...

Free fermions on Hamming graphs H(d,q) are considered and the entanglement entropy for two types of subsystems is computed. For subsets vertices that form subgraphs, an analytical expression obtained. corresponding to a neighborhood, i.e. set sites at fixed distance from reference vertex, decomposition in irreducible submodules Terwilliger algebra also yields closed formula entropy. Finally, ma...

We provide in this paper the discrete equations of motion for the newtonian n-body problem deduced from the quantum calculus of variations (Q.C.V.) developed in [3, 4, 7, 8]. These equations are brought into the usual lagrangian and hamiltonian formulations of the dynamics and yield sampled functional equations involving generalized scale derivatives. We investigate especially homographic solut...