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We extract all the invariants (i.e. all the functions which do not depend on the choice of phase-space coordinates) of the dynamics of two point-masses, at the third post-Newtonian (3PN) approximation of general relativity. We start by…
We study the evolution of angular variable (phase) for general (not necessarily Hamiltonian) perturbations of Hamiltonian systems with one degree of freedom near separatrices of the unperturbed system. To this end, we use averaged system of…
We formulate a complex action theory which includes operators of coordinate and momentum $\hat{q}$ and $\hat{p}$ being replaced with non-hermitian operators $\hat{q}_{new}$ and $\hat{p}_{new}$, and their eigenstates ${}_m <_{new} q |$ and…
We investigate the dynamical properties of one-dimensional dissipative Fermi-Hubbard models, which are described by the Lindblad master equations with site-dependent jump operators. The corresponding non-Hermitian effective Hamiltonians…
We present an approach for eliminating the gauge freedom for derivative couplings in nonadiabatic dynamics in the presence of geometric phase effects. This approach relies on a bottom-up construction of a parametric quantum Hamiltonian in…
A description of the space of G-connections using the tangent groupoid is given. As the tangent groupoid parameter is away from zero, the G-connections act as convolution operators on a Hilbert space. The gauge action is examined in the…
Within the framework of weighted integrable Hamiltonian systems, we study the long-time behavior of the associated statistical ensembles. We construct an action-dependent angular conjugacy that rectifies the nonuniform angular flow into a…
In this paper, we systematically study the effective action for non-commutative QED in the static limit at high temperature. When $\theta p^{2}\ll 1$, where $\theta$ represents the magnitude of the parameter for non-commutativity and $p$…
Angular momentum dependences of the parity splitting and electric dipole transitions in the alternating parity bands of heavy nuclei have been analyzed. It is shown that these dependences can be treated in a universal way with a single…
We study a system of electrons on a one-dimensional lattice, interacting through the long range Coulomb forces, by means of a variational technique which is the strong coupling analog of the Gutzwiller approach. The problem is thus the…
The stationary points of the Hamiltonian H of the classical XY chain with power-law pair interactions (i.e., decaying like r^{-{\alpha}} with the distance) are analyzed. For a class of "spinwave-type" stationary points, the asymptotic…
Straight-field-line coordinates are very useful for representing magnetic fields in toroidally confined plasmas, but fundamental problems arise regarding their definition in 3-D geometries because of the formation of islands and chaotic…
Cyclic algebraic Z^d-actions are defined by ideals of Laurent polynomials in d commuting variables. Such an action is expansive precisely when the complex variety of the ideal is disjoint from the multiplicative d-torus. For such expansive…
A novel Dirac Hamiltonian formulation of the first order Einstein-Hilbert (EH) action, in which algebraic constraints are not solved to eliminate fields from the action at the Lagrangian level, has been shown to lead to an action and a…
In this paper, we give an update on divergent problems concerning the radiative corrections of quantum electrodynamics in $(3+1)$ dimensions. In doing so, we introduce a geometric adaptation for the covariant photon propagator by including…
Many practical reinforcement learning environments have a discrete factored action space that induces a large combinatorial set of actions, thereby posing significant challenges. Existing approaches leverage the regular structure of the…
Gravitational and electromagnetic interactions are Hamiltonian systems with forces between pairs of particles. We propose an alternative: Hamiltonian dynamics with triplet interactions between point particles. Our system has a potential…
We present a simple formula for the Hamiltonian in terms of the actions for spherically symmetric, scale-free potentials. The Hamiltonian is a power-law or logarithmic function of a linear combination of the actions. Our expression reduces…
Schroedinger equation on a Hilbert space ${\cal H}$, represents a linear Hamiltonian dynamical system on the space of quantum pure states, the projective Hilbert space $P {\cal H}$. Separable states of a bipartite quantum system form a…
An additive action on an algebraic variety is an effective action of the vector group with an open orbit. We describe projective surfaces with du Val singularities that admit an additive action with a finite number of orbits. In particular,…