70 research outputs found
Generalized Supersymmetric Perturbation Theory
Using the basic ingredient of supersymmetry, we develop a simple alternative
approach to perturbation theory in one-dimensional non-relativistic quantum
mechanics. The formulae for the energy shifts and wave functions do not involve
tedious calculations which appear in the available perturbation theories. The
model applicable in the same form to both the ground state and excited bound
states, unlike the recently introduced supersymmetric perturbation technique
which, together with other approaches based on logarithmic perturbation theory,
are involved within the more general framework of the present formalism.Comment: 13 pages article in LaTEX (uses standard article.sty). No Figures.
Sent to Ann. Physics (2004
Wilson loops in the adjoint representation and multiple vacua in two-dimensional Yang-Mills theory
with fermions in the adjoint representation is invariant under
and thereby is endowed with a non-trivial vacuum structure
(k-sectors). The static potential between adjoint charges, in the limit of
infinite mass, can be therefore obtained by computing Wilson loops in the pure
Yang-Mills theory with the same non-trivial structure. When the (Euclidean)
space-time is compactified on a sphere , Wilson loops can be exactly
expressed in terms of an infinite series of topological excitations
(instantons). The presence of k-sectors modifies the energy spectrum of the
theory and its instanton content. For the exact solution, in the limit in which
the sphere is decompactified, a k-sector can be mimicked by the presence of
k-fundamental charges at , according to a Witten's suggestion. However
this property neither holds before decompactification nor for the genuine
perturbative solution which corresponds to the zero-instanton contribution on
.Comment: RevTeX, 46 pages, 1 eps-figur
Phase Space Reduction and Vortex Statistics: An Anyon Quantization Ambiguity
We examine the quantization of the motion of two charged vortices in a
Ginzburg--Landau theory for the fractional quantum Hall effect recently
proposed by the first two authors. The system has two second-class constraints
which can be implemented either in the reduced phase space or
Dirac-Gupta-Bleuler formalism. Using the intrinsic formulation of statistics,
we show that these two ways of implementing the constraints are inequivalent
unless the vortices are quantized with conventional statistics; either
fermionic or bosonic.Comment: 14 pages, PHYZZ
The stability of vacua in two-dimensional gauge theory
We discuss the stability of vacua in two-dimensional gauge theory for any
simple, simply connected gauge group. Making use of the representation of a
vacuum in terms of a Wilson line at infinity, we determine which vacua are
stable against pair production of heavy matter in the adjoint of the gauge
group. By calculating correlators of Wilson loops, we reduce the problem to a
problem in representation theory of Lie groups, that we solve in full
generality.Comment: 12 pages, 1 figur
Bound - states for truncated Coulomb potentials
The pseudoperturbative shifted - expansion technique PSLET is generalized
for states with arbitrary number of nodal zeros. Bound- states energy
eigenvalues for two truncated coulombic potentials are calculated using PSLET.
In contrast with shifted large-N expansion technique, PSLET results compare
excellently with those from direct numerical integration.Comment: TEX file, 22 pages. To appear in J. Phys. A: Math. & Ge
Operator Algebra in Chern-Simons Theory on a Torus
We consider Chern-Simons gauge theory on a torus with both nonrelativistic
and relativistic matter. It is shown that the Hamiltonian and two total momenta
commute among themselves only in the physical Hilbert space. We also discuss
relations among degenerate physical states, degenerate vacua, and the existence
of multicomponent Schrodinger wavefunctions.Comment: 12 pages, TPI-Minn-92/41-T, UMN-TH-1105/9
Ordered spectral statistics in 1D disordered supersymmetric quantum mechanics and Sinai diffusion with dilute absorbers
Some results on the ordered statistics of eigenvalues for one-dimensional
random Schr\"odinger Hamiltonians are reviewed. In the case of supersymmetric
quantum mechanics with disorder, the existence of low energy delocalized states
induces eigenvalue correlations and makes the ordered statistics problem
nontrivial. The resulting distributions are used to analyze the problem of
classical diffusion in a random force field (Sinai problem) in the presence of
weakly concentrated absorbers. It is shown that the slowly decaying averaged
return probability of the Sinai problem, \mean{P(x,t|x,0)}\sim \ln^{-2}t, is
converted into a power law decay, \mean{P(x,t|x,0)}\sim t^{-\sqrt{2\rho/g}},
where is the strength of the random force field and the density of
absorbers.Comment: 10 pages ; LaTeX ; 4 pdf figures ; Proceedings of the meeting
"Fundations and Applications of non-equilibrium statistical mechanics",
Nordita, Stockholm, october 2011 ; v2: appendix added ; v3: figure 2.left
adde
When is working memory important for arithmetic?: the impact of strategy and age
Our ability to perform arithmetic relies heavily on working memory, the manipulation and maintenance of information in mind. Previous research has found that in adults, procedural strategies, particularly counting, rely on working memory to a greater extent than retrieval strategies. During childhood there are changes in the types of strategies employed, as well as an increase in the accuracy and efficiency of strategy execution. As such it seems likely that the role of working memory in arithmetic may also change, however children and adults have never been directly compared. This study used traditional dual-task methodology, with the addition of a control load condition, to investigate the extent to which working memory requirements for different arithmetic strategies change with age between 9-11 years, 12-14 years and young adulthood. We showed that both children and adults employ working memory when solving arithmetic problems, no matter what strategy they choose. This study highlights the importance of considering working memory in understanding the difficulties that some children and adults have with mathematics, as well as the need to include working memory in theoretical models of mathematical cognition
Semiclassical treatment of logarithmic perturbation theory
The explicit semiclassical treatment of logarithmic perturbation theory for
the nonrelativistic bound states problem is developed. Based upon
-expansions and suitable quantization conditions a new procedure for
deriving perturbation expansions for the one-dimensional anharmonic oscillator
is offered. Avoiding disadvantages of the standard approach, new handy
recursion formulae with the same simple form both for ground and exited states
have been obtained. As an example, the perturbation expansions for the energy
eigenvalues of the harmonic oscillator perturbed by are
considered.Comment: 6 pages, LATEX 2.09 using IOP style
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