34,205 research outputs found
On the Integrability of Classical Ruijsenaars-Schneider Model of Type
The problem of finding most general form of the classical integrable
relativistic models of many-body interaction of the type is
considered. In the simplest nontrivial case of ,the extra integral of
motion is presented in explicit form within the ansatz similar to the
nonrelativistic Calogero-Moser models. The resulting Hamiltonian has been found
by solving the set of two functional equations.Comment: 10 pages, LaTeX2e, no figure
Tree tensor network state with variable tensor order: an efficient multireference method for strongly correlated systems
We study the tree-tensor-network-state (TTNS) method with variable tensor orders for quantum chemistry. TTNS is a variational method to efficiently approximate complete active space (CAS) configuration interaction (CI) wave functions in a tensor product form. TTNS can be considered as a higher order generalization of the matrix product state (MPS) method. The MPS wave function is formulated as products of matrices in a multiparticle basis spanning a truncated Hilbert space of the original CAS-CI problem. These matrices belong to active orbitals organized in a one-dimensional array, while tensors in TTNS are defined upon a tree-like arrangement of the same orbitals. The tree-structure is advantageous since the distance between two arbitrary orbitals in the tree scales only logarithmically with the number of orbitals N, whereas the scaling is linear in the MPS array. It is found to be beneficial from the computational costs point of view to keep strongly correlated orbitals in close vicinity in both arrangements; therefore, the TTNS ansatz is better suited for multireference problems with numerous highly correlated orbitals. To exploit the advantages of TTNS a novel algorithm is designed to optimize the tree tensor network topology based on quantum information theory and entanglement. The superior performance of the TTNS method is illustrated on the ionic-neutral avoided crossing of LiF. It is also shown that the avoided crossing of LiF can be localized using only ground state properties, namely one-orbital entanglement
A rigorous analysis using optimal transport theory for a two-reflector design problem with a point source
We consider the following geometric optics problem: Construct a system of two
reflectors which transforms a spherical wavefront generated by a point source
into a beam of parallel rays. This beam has a prescribed intensity
distribution. We give a rigorous analysis of this problem. The reflectors we
construct are (parts of) the boundaries of convex sets. We prove existence of
solutions for a large class of input data and give a uniqueness result. To the
author's knowledge, this is the first time that a rigorous mathematical
analysis of this problem is given. The approach is based on optimal
transportation theory. It yields a practical algorithm for finding the
reflectors. Namely, the problem is equivalent to a constrained linear
optimization problem.Comment: 5 Figures - pdf files attached to submission, but not shown in
manuscrip
Microlensing Detections of Moons of Exoplanets
We investigate the characteristic of microlensing signals of Earth-like moons
orbiting ice-giant planets. From this, we find that non-negligible satellite
signals occur when the planet-moon separation is similar to or greater than the
Einstein radius of the planet. We find that the satellite signal does not
diminish with the increase of the planet-moon separation beyond the Einstein
radius of the planet unlike the planetary signal which vanishes when the planet
is located well beyond the Einstein radius of the star. We also find that the
satellite signal tends to have the same sign as that of the planetary signal.
These tendencies are caused by the lensing effect of the star on the moon in
addition to the effect of the planet. We determine the range of satellite
separations where the microlensing technique is optimized for the detections of
moons. By setting an upper limit as the angle-average of the projected Hill
radius and a lower limit as the half of the Einstein radius of the planet, we
find that the microlensing method would be sensitive to moons with projected
separations from the planet of for a Jupiter-mass planet, for a Saturn-mass planet, and for a Uranus-mass planet. We compare the
characteristics of the moons to be detected by the microlensing and transit
techniquesComment: 6pages, 6 figure
Broadband dielectric response of glycerol and propylene carbonate: a comparison
Dielectric data on glycerol and propylene carbonate covering 18 decades of
frequency are presented and compared to each other. Both materials exhibit
qualitatively similar behavior except for marked differences in the
high-frequency region just below the boson peak. The results on both materials
are consistent with the mode coupling theory of the glass transition.Comment: 8 pages including 4 figure
- …