We take a Hamiltonian-based perspective to generalize Nesterov's accelerated gradient descent and Polyak's heavy ball method broad class of momentum methods in the setting (possibly) constrained minimization Euclidean non-Euclidean normed vector spaces. Our leads generic unifying nonasymptotic analysis convergence these both function value (in convex optimization) norm unconstrained, possibly n...

For surface systems, the Rashba effect is studied by using a k·p perturbation method. It is shown that the velocity-operator term in the perturbation gives the generalized Rashba Hamiltonian, of which a group-theoretical analysis is given to explain variations in the spin splitting and spin structure expected for typical surface symmetry. The matrix elements of the velocity and spin-angular-mom...

In this paper we find a explicit moving frame along curves of Lagrangian planes invariant under the action of the symplectic group. We use the moving frame to find a family of independent and generating differential invariants. We then construct geometric Hamiltonian structures in the space of differential invariants and prove that, if we restrict them to a certain Poisson submanifold, they bec...

We examine the mechanical matrix model that can be derived from the SU (2) Yang-Mills light-cone field theory by restricting the gauge fields to depend on the light-cone time alone. We use Dirac's generalized Hamiltonian approach. In contrast to its well-known instant-time counterpart the light-cone version of SU (2) Yang-Mills mechanics has in addition to the constraints, generating the SU (2)...

A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator − d dx2 +Bx+ A x2 + λ x , where α is a real positive parameter. The formalism makes use of a basis provided by exact solutions of Schrödinger’s equation for the Gol’dman and Krivchenkov Hamiltonian, and the corresponding matrix elements that were previously found. For all the discrete eigenva...

We present a new integrable extension of the a = −2, N = 2 SKdV hierarchy, with the ”small” N = 4 superconformal algebra (SCA) as the second hamiltonian structure. As distinct from the previously known N = 4 supersymmetric KdV hierarchy associated with the same N = 4 SCA, the new system respects only N = 2 rigid supersymmetry. We give for it both matrix and scalar Lax formulations and consider ...

A wide class of problems in the study of the spectral and orbital stability of dispersive waves in Hamiltonian systems can be reduced to understanding the so-called “energy spectrum,” that is the spectrum of the second variation of the Hamiltonian evaluated at the wave shape, which is constrained to act on a closed subspace of the underlying Hilbert space. We present a substantially simplified ...

We combine the methods of Hamiltonian Truncation and recently proposed generalisation S-matrix bootstrap that includes local operators to determine two-particle scattering amplitude form factor stress tensor at $s>0$ in 2d $\phi^4$ theory. use $s\le 0$ its spectral density computed using Lightcone Conformal (LCT), inject them into generalized set-up. The obtained results for are fully reliable ...