429 research outputs found
Entanglement Generation in the Scattering of One-Dimensional Particles
This article provides a convenient framework for quantitative evaluation of
the entanglement generated when two structureless, distinguishable particles
scatter non-relativistically in one dimension. It explores how three factors
determine the amount of entanglement generated: the momentum distributions of
the incoming particles, their masses, and the interaction potential. Two
important scales emerge, one set by the kinematics and one set by the dynamics.
This method also provides two approximate analytic formulas useful for
numerical evaluation of entanglement and reveals an interesting connection
between purity, linear coordinate transformations, and momentum uncertainties.Comment: 11 pages, submitted to PR
Five is More: Comments on Symmetry, Integrability, and Solvability for a Few Particles in a One-Dimensional Trap
This contributed conference proceeding reviews some results about a system of
a few identical particles with spin trapped in one-dimensional potentials and
experiencing two-body interactions. The focus is on how symmetry,
integrability, and solvability depend on the trap shape, two-body interaction,
the number of particles, and the number of spin components. A series of
comments are presented that characterize the minimal symmetries possible for a
composite system constructed from interacting single particles, with special
focus on the contact interaction. For five and more particles with internal
components like spin, a kind of universality called algebraically solvability
is lost.Comment: 8 pages in preprint format, short conference proceeding, submitted to
FB21; v2 references added and title changed. Comments welcome
Symmetries of Three Harmonically-Trapped Particles in One Dimension
We present a method for solving trapped few-body problems and apply it to
three equal-mass particles in a one-dimensional harmonic trap, interacting via
a contact potential. By expressing the relative Hamiltonian in Jacobi
cylindrical coordinates, i.e. the two-dimensional version of three-body
hyperspherical coordinates, we discover an underlying symmetry.
This symmetry simplifies the calculation of energy eigenstates of the full
Hamiltonian in a truncated Hilbert space constructed from the trap Hamiltonian
eigenstates. Particle superselection rules are implemented by choosing the
relevant representations of . We find that the one-dimensional
system shows nearly the full richness of the three-dimensional system, and can
be used to understand separability and reducibility in this system and in
standard few-body approximation techniques.Comment: 27 pages, 5 figures, 6 tables, 37 references, 4 footnotes, 1 article;
v2 has revised introduction and results sections as well as typos correcte
Observables and Entanglement in the Two-Body System
Using the quantum two-body system as a familiar model, this talk will
describe how entanglement can be used to select preferred observables for
interrogating a physical system. The symmetries and dynamics of the quantum
two-body system provide a backdrop for testing the relativity of entanglement
with respect to observable-induced tensor product structures. We believe this
exploration leads us to a general statement: the physically-meaningful
observable subalgebras are the ones that minimize entanglement in typical
states.Comment: 5 pages, no figs. Contributed to conference proceedings for Quantum
Theory: Reconsideration of Foundations 6 at Linnaeus University, June 11-14,
201
Tensor Product Structures, Entanglement, and Particle Scattering
Particle systems admit a variety of tensor product structures (TPSs)
depending on the complete system of commuting observables chosen for the
analysis. Different notions of entanglement are associated with these different
TPSs. Global symmetry transformations and dynamical transformations factor into
products of local unitary operators with respect to certain TPSs and not with
respect to others. Symmetry-invariant and dynamical-invariant TPSs and
corresponding measures of entanglement are defined for particle scattering
systems.Comment: 7 pages, no figures; v.2 typo in references corrected, submitted to
OSID as part of SMP3
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