16,623 research outputs found
Infinitely many shape invariant potentials and cubic identities of the Laguerre and Jacobi polynomials
We provide analytic proofs for the shape invariance of the recently
discovered (Odake and Sasaki, Phys. Lett. B679 (2009) 414-417) two families of
infinitely many exactly solvable one-dimensional quantum mechanical potentials.
These potentials are obtained by deforming the well-known radial oscillator
potential or the Darboux-P\"oschl-Teller potential by a degree \ell
(\ell=1,2,...) eigenpolynomial. The shape invariance conditions are attributed
to new polynomial identities of degree 3\ell involving cubic products of the
Laguerre or Jacobi polynomials. These identities are proved elementarily by
combining simple identities.Comment: 13 page
Unified Theory of Annihilation-Creation Operators for Solvable (`Discrete') Quantum Mechanics
The annihilation-creation operators are defined as the
positive/negative frequency parts of the exact Heisenberg operator solution for
the `sinusoidal coordinate'. Thus are hermitian conjugate to each
other and the relative weights of various terms in them are solely determined
by the energy spectrum. This unified method applies to most of the solvable
quantum mechanics of single degree of freedom including those belonging to the
`discrete' quantum mechanics.Comment: 43 pages, no figures, LaTeX2e, with amsmath, amssym
Comment on "Memory Effects in an Interacting Magnetic Nanoparticle System"
In Phys. Rev. Lett. 91 167206 (2003), Sun et al. study memory effects in an
interacting nanoparticle system with specific temperature and field protocols.
The authors claim that the observed memory effects originate from spin-glass
dynamics and that the results are consistent with the hierarchical picture of
the spin-glass phase. In this comment, we argue their claims premature by
demonstrating that all their experimental curves can be reproduced
qualitatively using only a simplified model of isolated nanoparticles with a
temperature dependent distribution of relaxation times.Comment: 1 page, 2 figures, slightly changed content, the parameters involved
in Figs. 1 and 2 are changed a little for a semi-quantitative comparision
with experimental result
A new family of shape invariantly deformed Darboux-P\"oschl-Teller potentials with continuous \ell
We present a new family of shape invariant potentials which could be called a
``continuous \ell version" of the potentials corresponding to the exceptional
(X_{\ell}) J1 Jacobi polynomials constructed recently by the present authors.
In a certain limit, it reduces to a continuous \ell family of shape invariant
potentials related to the exceptional (X_{\ell}) L1 Laguerre polynomials. The
latter was known as one example of the `conditionally exactly solvable
potentials' on a half line.Comment: 19 pages. Sec.5(Summary and Comments): one sentence added in the
first paragraph, several sentences modified in the last paragraph.
References: one reference ([25]) adde
Experimental demonstration of entanglement assisted coding using a two-mode squeezed vacuum state
We have experimentally realized the scheme initially proposed as quantum
dense coding with continuous variables [Ban, J. Opt. B \textbf{1}, L9 (1999),
and Braunstein and Kimble, \pra\textbf{61}, 042302 (2000)]. In our experiment,
a pair of EPR (Einstein-Podolski-Rosen) beams is generated from two independent
squeezed vacua. After adding two-quadrature signal to one of the EPR beams, two
squeezed beams that contain the signal were recovered. Although our squeezing
level is not sufficient to demonstrate the channel capacity gain over the
Holevo limit of a single-mode channel without entanglement, our channel is
superior to conventional channels such as coherent and squeezing channels. In
addition, optical addition and subtraction processes demonstrated are
elementary operations of universal quantum information processing on continuous
variables.Comment: 4 pages, 4 figures, submitted to Phys. Rev.
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