66 research outputs found
Dimensional perturbation theory for vibration-rotation spectra of linear triatomic molecules
A very efficient large-order perturbation theory is formulated for the
nuclear motion of a linear triatomic molecule. To demonstrate the method, all
of the experimentally observed rotational energies, with values of almost
up to 100, for the ground and first excited vibrational states of CO and
for the ground vibrational states of NO and of OCS are calculated. All
coupling between vibration and rotation is included. The perturbation
expansions reported here are rapidly convergent. The perturbation parameter is
, where is the dimensionality of space. Increasing is
qualitatively similar to increasing the angular momentum quantum number .
Therefore, this approach is especially suited for states with high rotational
excitation. The computational cost of the method scales only as ,
where is the size of the vibrational basis set.Comment: submitted to Journal of Chemical Physics, 23 pages, REVTeX, no
figure
On the concepts of radial and angular kinetic energies
We consider a general central-field system in D dimensions and show that the
division of the kinetic energy into radial and angular parts proceeds
differently in the wavefunction picture and the Weyl-Wigner phase-space
picture. Thus, the radial and angular kinetic energies are different quantities
in the two pictures, containing different physical information, but the
relation between them is well defined. We discuss this relation and illustrate
its nature by examples referring to a free particle and to a ground-state
hydrogen atom.Comment: 10 pages, 2 figures, accepted by Phys. Rev.
The Heine-Stieltjes correspondence and the polynomial approach to the standard pairing problem
A new approach for solving the Bethe ansatz (Gaudin-Richardson) equations of
the standard pairing problem is established based on the Heine-Stieltjes
correspondence. For pairs of valence nucleons on different
single-particle levels, it is found that solutions of the Bethe ansatz
equations can be obtained from one (k+1)x(k+1) and one (n-1)x(k+1) matrices,
which are associated with the extended Heine-Stieltjes and Van Vleck
polynomials, respectively. Since the coefficients in these polynomials are free
from divergence with variations in contrast to the original Bethe ansatz
equations, the approach thus provides with a new efficient and systematic way
to solve the problem, which, by extension, can also be used to solve a large
class of Gaudin-type quantum many-body problems and to establish a new
efficient angular momentum projection method for multi-particle systems.Comment: ReVTeX, 4 pages, no figur
Renormalization of the Inverse Square Potential
The quantum-mechanical D-dimensional inverse square potential is analyzed
using field-theoretic renormalization techniques. A solution is presented for
both the bound-state and scattering sectors of the theory using cutoff and
dimensional regularization. In the renormalized version of the theory, there is
a strong-coupling regime where quantum-mechanical breaking of scale symmetry
takes place through dimensional transmutation, with the creation of a single
bound state and of an energy-dependent s-wave scattering matrix element.Comment: 5 page
Quantum mechanics in multiply connected spaces
This paper analyses quantum mechanics in multiply connected spaces. It is
shown that the multiple connectedness of the configuration space of a physical
system can determine the quantum nature of physical observables, such as the
angular momentum. In particular, quantum mechanics in compactified Kaluza-Klein
spaces is examined. These compactified spaces give rise to an additional
angular momentum which can adopt half-integer values and, therefore, may be
identified with the intrinsic spin of a quantum particle.Comment: Latex 15 page
Fokker-Planck description of the transfer matrix limiting distribution in the scattering approach to quantum transport
The scattering approach to quantum transport through a disordered
quasi-one-dimensional conductor in the insulating regime is discussed in terms
of its transfer matrix \bbox{T}. A model of one-dimensional wires which
are coupled by random hopping matrix elements is compared with the transfer
matrix model of Mello and Tomsovic. We derive and discuss the complete
Fokker-Planck equation which describes the evolution of the probability
distribution of \bbox{TT}^{\dagger} with system length in the insulating
regime. It is demonstrated that the eigenvalues of \ln\bbox{TT}^{\dagger}
have a multivariate Gaussian limiting probability distribution. The parameters
of the distribution are expressed in terms of averages over the stationary
distribution of the eigenvectors of \bbox{TT}^{\dagger}. We compare the
general form of the limiting distribution with results of random matrix theory
and the Dorokhov-Mello-Pereyra-Kumar equation.Comment: 25 pages, revtex, no figure
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Development of the applied mathematics originating from the group theory of physical and mathematical problems
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). Group theoretical methods are a powerful tool both in their applications to mathematics and to physics. The broad goal of this project was to use such methods to develop the implications of group (symmetry) structures underlying models of physical systems, as well as to broaden the understanding of simple models of chaotic systems. The main thrust was to develop further the complex mathematics that enters into many-particle quantum systems with special emphasis on the new directions in applied mathematics that have emerged and continue to surface in these studies. In this area, significant advances in understanding the role of SU(2) 3nj-coefficients in SU(3) theory have been made and in using combinatoric techniques in the study of generalized Schur functions, discovered during this project. In the context of chaos, the study of maps of the interval and the associated theory of words has led to significant discoveries in Galois group theory, to the classification of fixed points, and to the solution of a problem in the classification of DNA sequences
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