2,376 research outputs found
Non-positivity of the Wigner function and bounds on associated integrals
The Wigner function shares several properties with classical distribution
functions on phase space, but is not positive-definite. The integral of the
Wigner function over a given region of phase space can therefore lie outside
the interval [0,1]. The problem of finding best-possible upper and lower bounds
for a given region is the problem of finding the greatest and least eigenvalues
of an associated Hermitian operator. Exactly solvable examples are described,
and possible extensions are indicated.Comment: 5 pages, Latex2e fil
Torture Is Not Protected Speech: Free Speech Analysis of Bans on Gay Conversion Therapy
As state and municipal bans on conversion therapy sweep the nation, questions are mounting over whether sexual orientation change efforts (SOCE) are protected speech under the First Amendment. The Supreme Court in National Institute of Family and Life Advocates v. Becerra in 2018 injected tremendous uncertainty into this area when it abrogated the reasoning of both Circuit Court of Appeals decisions that had upheld the validity of state SOCE bans against free speech challenges. Most courts and scholars in this area fall into the trap of the speech-and-action distinction, failing to ask the important threshold question: is this kind of communication covered by the First Amendment? This paper argues for a paradigm shift: conversion therapy is not covered by the Free Speech Clause, and thus, legislation banning it is valid. Analysis of this issue reinforces the argument that courts and scholars should take more seriously the distinctions between free speech coverage and free speech protection
Non-positivity of Groenewold operators
A central feature in the Hilbert space formulation of classical mechanics is
the quantisation of classical Liouville densities, leading to what may be
termed term Groenewold operators. We investigate the spectra of the Groenewold
operators that correspond to Gaussian and to certain uniform Liouville
densities. We show that when the classical coordinate-momentum uncertainty
product falls below Heisenberg's limit, the Groenewold operators in the
Gaussian case develop negative eigenvalues and eigenvalues larger than 1.
However, in the uniform case, negative eigenvalues are shown to persist for
arbitrarily large values of the classical uncertainty product.Comment: 9 pages, 1 figures, submitted to Europhysics Letter
Integrable Electron Model with Correlated Hopping and Quantum Supersymmetry
We give the quantum analogue of a recently introduced electron model which
generalizes the Hubbard model with additional correlated hopping terms and
electron pair hopping. The model contains two independent parameters and is
invariant with respect to the quantum superalgebra . It is
integrable in one dimension by means of the quantum inverse scattering method.Comment: 7 pages, AmsTex fil
A New Supersymmetric and Exactly Solvable Model of Correlated Electrons
A new lattice model is presented for correlated electrons on the unrestricted
-dimensional electronic Hilbert space (where
is the lattice length). It is a supersymmetric generalization of the
Hubbard model, but differs from the extended Hubbard model proposed by Essler,
Korepin and Schoutens. The supersymmetry algebra of the new model is
superalgebra . The model contains one symmetry-preserving free real
parameter which is the Hubbard interaction parameter , and has its origin
here in the one-parameter family of inequivalent typical 4-dimensional irreps
of . On a one-dimensional lattice, the model is exactly solvable by
the Bethe ansatz.Comment: 10 pages, LaTex. (final version to appear in Phys.Rev.Lett.
Infinite Families of Gauge-Equivalent -Matrices and Gradations of Quantized Affine Algebras
Associated with the fundamental representation of a quantum algebra such as
or , there exist infinitely many gauge-equivalent
-matrices with different spectral-parameter dependences. It is shown how
these can be obtained by examining the infinitely many possible gradations of
the corresponding quantum affine algebras, such as and
, and explicit formulae are obtained for those two cases.
Spectral-dependent similarity (gauge) transformations relate the -matrices
in different gradations. Nevertheless, the choice of gradation can be
physically significant, as is illustrated in the case of quantum affine Toda
field theories.Comment: 14 pages, Latex, UQMATH-93-10 (final version for publication
The quantum state vector in phase space and Gabor's windowed Fourier transform
Representations of quantum state vectors by complex phase space amplitudes,
complementing the description of the density operator by the Wigner function,
have been defined by applying the Weyl-Wigner transform to dyadic operators,
linear in the state vector and anti-linear in a fixed `window state vector'.
Here aspects of this construction are explored, with emphasis on the connection
with Gabor's `windowed Fourier transform'. The amplitudes that arise for simple
quantum states from various choices of window are presented as illustrations.
Generalized Bargmann representations of the state vector appear as special
cases, associated with Gaussian windows. For every choice of window, amplitudes
lie in a corresponding linear subspace of square-integrable functions on phase
space. A generalized Born interpretation of amplitudes is described, with both
the Wigner function and a generalized Husimi function appearing as quantities
linear in an amplitude and anti-linear in its complex conjugate.
Schr\"odinger's time-dependent and time-independent equations are represented
on phase space amplitudes, and their solutions described in simple cases.Comment: 36 pages, 6 figures. Revised in light of referees' comments, and
further references adde
Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters
We present a systematic technique to construct solutions to the Yang-Baxter
equation which depend not only on a spectral parameter but in addition on
further continuous parameters. These extra parameters enter the Yang-Baxter
equation in a similar way to the spectral parameter but in a non-additive form.
We exploit the fact that quantum non-compact algebras such as
and type-I quantum superalgebras such as and are
known to admit non-trivial one-parameter families of infinite-dimensional and
finite dimensional irreps, respectively, even for generic . We develop a
technique for constructing the corresponding spectral-dependent R-matrices. As
examples we work out the the -matrices for the three quantum algebras
mentioned above in certain representations.Comment: 13 page
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