2,122 research outputs found
Congruence modularity implies cyclic terms for finite algebras
An n-ary operation f : A(n) -> A is called cyclic if it is idempotent and f(a(1), a(2), a(3), ... , a(n)) = f(a(2), a(3), ... , a(n), a(1)) for every a(1), ... , a(n) is an element of A. We prove that every finite algebra A in a congruence modular variety has a p-ary cyclic term operation for any prime p greater than vertical bar A vertical bar
Relativistic calculations of charge transfer probabilities in U92+ - U91+(1s) collisions using the basis set of cubic Hermite splines
A new approach for solving the time-dependent two-center Dirac equation is
presented. The method is based on using the finite basis set of cubic Hermite
splines on a two-dimensional lattice. The Dirac equation is treated in rotating
reference frame. The collision of U92+ (as a projectile) and U91+ (as a target)
is considered at energy E_lab=6 MeV/u. The charge transfer probabilities are
calculated for different values of the impact parameter. The obtained results
are compared with the previous calculations [I. I. Tupitsyn et al., Phys. Rev.
A 82, 042701 (2010)], where a method based on atomic-like Dirac-Sturm orbitals
was employed. This work can provide a new tool for investigation of quantum
electrodynamics effects in heavy-ion collisions near the supercritical regime
Weakly-nonlocal Symplectic Structures, Whitham method, and weakly-nonlocal Symplectic Structures of Hydrodynamic Type
We consider the special type of the field-theoretical Symplectic structures
called weakly nonlocal. The structures of this type are in particular very
common for the integrable systems like KdV or NLS. We introduce here the
special class of the weakly nonlocal Symplectic structures which we call the
weakly nonlocal Symplectic structures of Hydrodynamic Type. We investigate then
the connection of such structures with the Whitham averaging method and propose
the procedure of "averaging" of the weakly nonlocal Symplectic structures. The
averaging procedure gives the weakly nonlocal Symplectic Structure of
Hydrodynamic Type for the corresponding Whitham system. The procedure gives
also the "action variables" corresponding to the wave numbers of -phase
solutions of initial system which give the additional conservation laws for the
Whitham system.Comment: 64 pages, Late
Relativistic calculations of the U91+(1s)-U92+ collision using the finite basis set of cubic Hermite splines on a lattice in coordinate space
A new method for solving the time-dependent two-center Dirac equation is
developed. The approach is based on the using of the finite basis of cubic
Hermite splines on a three-dimensional lattice in the coordinate space. The
relativistic calculations of the excitation and charge-transfer probabilities
in the U91+(1s)-U92+ collisions in two and three dimensional approaches are
performed. The obtained results are compared with our previous calculations
employing the Dirac-Sturm basis sets [I.I. Tupitsyn et al., Phys. Rev. A 82,
042701 (2010)]. The role of the negative-energy Dirac spectrum is investigated
within the monopole approximation
Why nonlocal recursion operators produce local symmetries: new results and applications
It is well known that integrable hierarchies in (1+1) dimensions are local
while the recursion operators that generate them usually contain nonlocal
terms. We resolve this apparent discrepancy by providing simple and universal
sufficient conditions for a (nonlocal) recursion operator in (1+1) dimensions
to generate a hierarchy of local symmetries. These conditions are satisfied by
virtually all known today recursion operators and are much easier to verify
than those found in earlier work.
We also give explicit formulas for the nonlocal parts of higher recursion
operators, Poisson and symplectic structures of integrable systems in (1+1)
dimensions.
Using these two results we prove, under some natural assumptions, the
Maltsev--Novikov conjecture stating that higher Hamiltonian, symplectic and
recursion operators of integrable systems in (1+1) dimensions are weakly
nonlocal, i.e., the coefficients of these operators are local and these
operators contain at most one integration operator in each term.Comment: 10 pages, LaTeX 2e, final versio
Calculation of the moscovium ground-state energy by quantum algorithms
We investigate the possibility to calculate the ground-state energy of the
atomic systems on a quantum computer. For this purpose we evaluate the lowest
binding energy of the moscovium atom with the use of the iterative phase
estimation and variational quantum eigensolver. The calculations by the
variational quantum eigensolver are performed with a disentangled unitary
coupled cluster ansatz and with various types of hardware-efficient ansatze.
The optimization is performed with the use of the Adam and Quantum Natural
Gradients procedures. The scalability of the ansatze and optimizers is tested
by increasing the size of the basis set and the number of active electrons. The
number of gates required for the iterative phase estimation and variational
quantum eigensolver is also estimated.Comment: 29 pages, 5 figure
Quasiperiodic functions theory and the superlattice potentials for a two-dimensional electron gas
We consider Novikov problem of the classification of level curves of
quasiperiodic functions on the plane and its connection with the conductivity
of two-dimensional electron gas in the presence of both orthogonal magnetic
field and the superlattice potentials of special type. We show that the
modulation techniques used in the recent papers on the 2D heterostructures
permit to obtain the general quasiperiodic potentials for 2D electron gas and
consider the asymptotic limit of conductivity when . Using the
theory of quasiperiodic functions we introduce here the topological
characteristics of such potentials observable in the conductivity. The
corresponding characteristics are the direct analog of the "topological
numbers" introduced previously in the conductivity of normal metals.Comment: Revtex, 16 pages, 12 figure
Relativistic Stark energies of hydrogen-like ions
The relativistic energies and widths of hydrogen-like ions exposed to the
uniform electric field are calculated. The calculations are performed for the
ground and lowest excited states using the complex scaling technique in
combination with a finite-basis method. The obtained results are compared with
the non-relativistic values. The role of relativistic effects is investigated.Comment: 21 pages, 5 figure
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