820 research outputs found
Hidden Algebras of the (super) Calogero and Sutherland models
We propose to parametrize the configuration space of one-dimensional quantum
systems of N identical particles by the elementary symmetric polynomials of
bosonic and fermionic coordinates. It is shown that in this parametrization the
Hamiltonians of the A_N, BC_N, B_N, C_N and D_N Calogero and Sutherland models,
as well as their supersymmetric generalizations, can be expressed -- for
arbitrary values of the coupling constants -- as quadratic polynomials in the
generators of a Borel subalgebra of the Lie algebra gl(N+1) or the Lie
superalgebra gl(N+1|N) for the supersymmetric case. These algebras are realized
by first order differential operators. This fact establishes the exact
solvability of the models according to the general definition given by one of
the authors in 1994, and implies that the Calogero and Jack-Sutherland
polynomials, as well as their supersymmetric generalizations, are related to
finite-dimensional irreducible representations of the Lie algebra gl(N+1) and
the Lie superalgebra gl(N+1|N).Comment: 35 pages, plain LaTeX. Paper expanded, some formulas for SUSY
hamiltonians corrected. Appendix with clarifying technical details adde
Topological Edge States with Zero Hall Conductivity in a Dimerized Hofstadter Model
The Hofstadter model is a simple yet powerful Hamiltonian to study quantum
Hall physics in a lattice system, manifesting its essential topological states.
Lattice dimerization in the Hofstadter model opens an energy gap at half
filling. Here we show that even if the ensuing insulator has a Chern number
equal to zero, concomitantly a doublet of edge states appear that are pinned at
specific momenta. We demonstrate that these states are topologically protected
by inversion symmetry in specific one-dimensional cuts in momentum space,
define and calculate the corresponding invariants and identify a platform for
the experimental detection of these novel topological states.Comment: 5 pages, 3 figures + Supplemental Material (6 pages
On Time-Bandwidth Product of Multi-Soliton Pulses
Multi-soliton pulses are potential candidates for fiber optical transmission
where the information is modulated and recovered in the so-called nonlinear
Fourier domain. While this is an elegant technique to account for the channel
nonlinearity, the obtained spectral efficiency, so far, is not competitive with
the classic Nyquist-based schemes. In this paper, we study the evolution of the
time-bandwidth product of multi-solitons as they propagate along the optical
fiber. For second and third order soliton pulses, we numerically optimize the
pulse shapes to achieve the smallest time-bandwidth product when the phase of
the spectral amplitudes is used for modulation. Moreover, we analytically
estimate the pulse-duration and bandwidth of multi-solitons in some practically
important cases. Those estimations enable us to approximate the time-bandwidth
product for higher order solitons.Comment: Accepted for ISIT 201
Interface-controlled creep in metallic glass composites
In this work we present molecular dynamics simulations on the creep behavior
of metallic glass composites. Surprisingly, all composites
exhibit much higher creep rates than the homogeneous glass. The glass-crystal
interface can be viewed as a weak interphase, where the activation barrier of
shear transformation zones is lower than in the surrounding glass. We observe
that the creep behavior of the composites does not only depend on the interface
area but also on the orientation of the interface with respect to the loading
axis. We propose an explanation in terms of different mean Schmid factors of
the interfaces, with the amorphous interface regions acting as preferential
slip sites.Comment: 11 pages, 13 figure
Tunable coupling of qubits: nonadiabatic corrections
We analyze the coupling of qubits mediated by a tunable and fast element
beyond the adiabatic approximation. The nonadiabatic corrections are important
and even dominant in parts of the relevant parameter range. As an example, we
consider the tunable capacitive coupling between two charge qubits mediated by
a gated Josephson junction, as suggested by Averin and Bruder. The
nonadiabatic, inductive contribution persists when the capacitive coupling is
tuned to zero. On the other hand, the total coupling can be turned off (in the
rotating wave approximation) if the qubits are operated at symmetry points.Comment: 7 pages, 2 figures, accepted in Europhysics Letter
Hidden algebra of the -body Calogero problem
A certain generalization of the algebra of first-order
differential operators acting on a space of inhomogeneous polynomials in is constructed. The generators of this (non)Lie algebra depend on
permutation operators. It is shown that the Hamiltonian of the -body
Calogero model can be represented as a second-order polynomial in the
generators of this algebra. Given representation implies that the Calogero
Hamiltonian possesses infinitely-many, finite-dimensional invariant subspaces
with explicit bases, which are closely related to the finite-dimensional
representations of above algebra. This representation is an alternative to the
standard representation of the Bargmann-Fock type in terms of creation and
annihilation operators.Comment: 10pp., CWRU-Math, October 199
Publishing (mal)practices and their (re)colonising effects: Double affiliations in academic publishing
The present article discusses one of the lesser researched flaws in the South African Subsidy System (SASS) which was created to enhance research (output) done by and at South African academic institutions. By making use of decolonial theories and reviewing the research output generated by an organizational entity at a South African tertiary educational institution over the last six years (i.e., from 2016 to 2021), the authors propose the following: the recruitment of doubly affiliated appointees (specifically, extraordinary professors and research fellows) to boost the research output of tertiary educational centres constitutes a practice that violates the principles of SASS and consequently contributes to the epistemic recolonization of academy
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