Related papers: Invariant Manifolds and Collective Coordinates
We propose a new quantum approach for describing a system of $n$ interacting particles with variable mass connected by an unknown field with variable form ($n$-VMVF systems). Instead of assuming any particular nature for variation of the…
In this paper we construct integrable three-dimensional quantum-mechanical systems with magnetic fields, admitting pairs of commuting second-order integrals of motion. The case of Cartesian coordinates is considered. Most of the systems…
We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies obtained for linear systems without zero order term in bounded domains and…
This paper employs the post-Newtonian approximations of scalar-tensor theory of gravity along with the Cartesian STF tensors and the Blanchet-Damour multipole formalism to derive translational and rotational equations of motion of N…
Multibody dynamics simulators are an important tool in many fields, including learning and control for robotics. However, many existing dynamics simulators suffer from inaccuracies when dealing with constrained mechanical systems due to…
Many-body systems undergoing quantum phase transitions reveal substantial growth of non-classical correlations between different parties of the system. This behavior is manifested by characteristic divergences of the von Neumann entropy.…
Under ceratin conditions, generalized action-angle coordinates can be introduced near non-compact invariant manifolds of completely and partially integrable Hamiltonian systems.
Quantum systems of indistinguishable particles are commonly described using the formalism of second quantisation, which relies on the assumption that any admissible quantum state must be either symmetric or anti-symmetric under particle…
We present a set of global invariants, called "mass integrals", which can be defined for a large class of asymptotically hyperbolic Riemannian manifolds. When the "boundary at infinity" has spherical topology one single invariant is…
The description of invariants of surfaces with respect to the motion groups is reduced to the description of invariants of parameterized surfaces with respect to the motion groups. Existence of a commuting system of invariant partial…
A study of the integrability of one-dimensional quantum mechanical many-body systems with general point interactions and boundary conditions describing the interactions which can be independent or dependent on the spin states of the…
We consider a physical system comprising discrete massive particles on the real line whose trajectories interact via perfectly inelastic collision, also known as sticky particles. It turns out that polygons formed in a convex "cumulative…
Galilei-invariant equations for massless fields are obtained via contractions of relativistic wave equations. It is shown that the collection of non-equivalent Galilei-invariant wave equations for massless fields with spin equal 1 and 0 is…
To describe the ``slow'' motions of n interacting mass points, we give the most general 4-d non-instantaneous, non-particle symmetric Galilei-invariant variational principle. It involves two-body invariants constructed from particle…
Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type ("acceleration equals forces") which determine the motion of points in the complex plane. These…
The complete invariant for gradient like Morse-Smale dynamical systems (vector fields and diffeomorphisms) on closed 4-manifolds are constructed. It is same as Kirby diagram in a case of polar vector field without fixed points of index 3.
Collective coordinates provide a powerful tool for separating collective and elementary excitations, allowing both to be treated in the full quantum theory. The price is a canonical transformation which leads to a complicated starting point…
Quantum many-body systems exhibit an extremely diverse range of phases and physical phenomena. Here, we prove that the entire physics of any other quantum many-body system is replicated in certain simple, "universal" spin-lattice models. We…
We consider few-body systems in which only a certain subset of the particle-particle interactions is resonant. We characterize each subset by a {\it unitary graph} in which the vertices represent distinguishable particles and the edges…
We study the interplay between collective and incoherent single-particle motion in a model of two chains of particles whose interaction comprises a non-integrable part. In the perturbative regime, but for a general form of the interaction,…