37,593 research outputs found
[Colored solutions of Yang-Baxter equation from representations of U_{q}gl(2)]
We study the Hopf algebra structure and the highest weight representation of
a multiparameter version of . The commutation relations as well as
other Hopf algebra maps are explicitly given. We show that the multiparameter
universal matrix can be constructed directly as a quantum double
intertwiner, without using Reshetikhin's transformation. An interesting feature
automatically appears in the representation theory: it can be divided into two
types, one for generic , the other for being a root of unity. When
applying the representation theory to the multiparameter universal
matrix, the so called standard and nonstandard colored solutions of the Yang-Baxter equation is obtained.Comment: [14]pages, latex, no figure
A double bounded key identity for Goellnitz's (big) partition theorem
Given integers i,j,k,L,M, we establish a new double bounded q-series identity
from which the three parameter (i,j,k) key identity of Alladi-Andrews-Gordon
for Goellnitz's (big) theorem follows if L, M tend to infinity. When L = M, the
identity yields a strong refinement of Goellnitz's theorem with a bound on the
parts given by L. This is the first time a bounded version of Goellnitz's (big)
theorem has been proved. This leads to new bounded versions of Jacobi's triple
product identity for theta functions and other fundamental identities.Comment: 17 pages, to appear in Proceedings of Gainesville 1999 Conference on
Symbolic Computation
Violating Bell Inequalities Maximally for Two -Dimensional Systems
We investigate the maximal violation of Bell inequalities for two
-dimensional systems by using the method of Bell operator. The maximal
violation corresponds to the maximal eigenvalue of the Bell operator matrix.
The eigenvectors corresponding to these eigenvalues are described by asymmetric
entangled states. We estimate the maximum value of the eigenvalue for large
dimension. A family of elegant entangled states that violate
Bell inequality more strongly than the maximally entangled state but are
somewhat close to these eigenvectors is presented. These approximate states can
potentially be useful for quantum cryptography as well as many other important
fields of quantum information.Comment: 6 pages, 1 figure. Revised versio
A unified approach for exactly solvable potentials in quantum mechanics using shift operators
We present a unified approach for solving and classifying exactly solvable
potentials. Our unified approach encompasses many well-known exactly solvable
potentials. Moreover, the new approach can be used to search systematically for
a new class of solvable potentials.Comment: RevTex, 8 page
Bogoliubov Hamiltonian as Derivative of Dirac Hamiltonian via Braid Relation
In this paper we discuss a new type of 4-dimensional representation of the
braid group. The matrices of braid operations are constructed by q-deformation
of Hamiltonians. One is the Dirac Hamiltonian for free electron with mass m,
the other, which we find, is related to the Bogoliubov Hamiltonian for
quasiparticles in He-B with the same free energy and mass being m/2. In the
process, we choose the free q-deformation parameter as a special value in order
to be consistent with the anyon description for fractional quantum Hall effect
with .Comment: 3 pages, 5 figure
Relating Quantum Information to Charged Black Holes
Quantum non-cloning theorem and a thought experiment are discussed for
charged black holes whose global structure exhibits an event and a Cauchy
horizon. We take Reissner-Norstr\"{o}m black holes and two-dimensional dilaton
black holes as concrete examples. The results show that the quantum non-cloning
theorem and the black hole complementarity are far from consistent inside the
inner horizon. The relevance of this work to non-local measurements is briefly
discussed.Comment: 14 pages, 2 figure
Stochastic Physics, Complex Systems and Biology
In complex systems, the interplay between nonlinear and stochastic dynamics,
e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in
Darwinian sense, in terms of discrete jumps among attractors, with punctuated
equilibrium, spontaneous random "mutations" and "adaptations". On an
evlutionary time scale it produces sustainable diversity among individuals in a
homogeneous population rather than convergence as usually predicted by a
deterministic dynamics. The emergent discrete states in such a system, i.e.,
attractors, have natural robustness against both internal and external
perturbations. Phenotypic states of a biological cell, a mesoscopic nonlinear
stochastic open biochemical system, could be understood through such a
perspective.Comment: 10 page
Acoustic black holes from supercurrent tunneling
We present a version of acoustic black holes by using the principle of the
Josephson effect. We find that in the case two superconductors and are
separated by an insulating barrier, an acoustic black hole may be created in
the middle region between the two superconductors. We discuss in detail how to
describe an acoustic black hole in the Josephson junction and write the metric
in the langauge of the superconducting electronics. Our final results infer
that for big enough tunneling current and thickness of the junction,
experimental verification of the Hawking temperature could be possible.Comment: 15pages,1 figure, to appear in IJMP
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