67,347 research outputs found
Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments
We describe a variety of methods to compute the functions ,
and their derivatives for real and positive . These
functions are numerically satisfactory independent solutions of the
differential equation . In an accompanying paper
(Algorithm xxx: Modified Bessel functions of imaginary order and positive
argument) we describe the implementation of these methods in Fortran 77 codes.Comment: 14 pages, 1 figure. To appear in ACM T. Math. Sof
Two-dimensional Hubbard-Holstein bipolaron
We present a diagrammatic Monte Carlo study of the properties of the
Hubbard-Holstein bipolaron on a two-dimensional square lattice. With a small
Coulomb repulsion, U, and with increasing electron-phonon interaction, and when
reaching a value about two times smaller than the one corresponding to the
transition of light polaron to heavy polaron, the system suffers a sharp
transition from a state formed by two weakly bound light polarons to a heavy,
strongly bound on-site bipolaron. Aside from this rather conventional bipolaron
a new bipolaron state is found for large U at intermediate and large
electron-phonon coupling, corresponding to two polarons bound on
nearest-neighbor sites. We discuss both the properties of the different
bipolaron states and the transition from one state to another. We present a
phase diagram in parameter space defined by the electron-phonon coupling and U.
Our numerical method does not use any artificial approximation and can be
easily modified to other bipolaron models with longer range electron-phonon
and/or electron-electron interaction.Comment: 14 pages, 12 figure
Photonic band mixing in linear chains of optically coupled micro-spheres
The paper deals with optical excitations arising in a one-dimensional chain
of identical spheres due optical coupling of whispering gallery modes (WGM).
The band structure of these excitations depends significantly on the
inter-mixing between WGMs characterized by different values of angular quantum
number, . We develop a general theory of the photonic band structure of
these excitations taking these effects into account and applied it to several
cases of recent experimental interest. In the case of bands originating from
WQMs with the angular quantum number of the same parity, the calculated
dispersion laws are in good qualitative agreement with recent experiment
results. Bands resulting from hybridization of excitations resulting from
whispering gallery modes with different parity of exhibits anomalous
dispersion properties characterized by a gap in the allowed values of
\emph{wave numbers} and divergence of group velocity.Comment: RevTex, 28 pages, 7 Figure
On the construction of pseudo-hermitian quantum system with a pre-determined metric in the Hilbert space
A class of pseudo-hermitian quantum system with an explicit form of the
positive-definite metric in the Hilbert space is presented. The general method
involves a realization of the basic canonical commutation relations defining
the quantum system in terms of operators those are hermitian with respect to a
pre-determined positive definite metric in the Hilbert space. Appropriate
combinations of these operators result in a large number of pseudo-hermitian
quantum systems admitting entirely real spectra and unitary time evolution. The
examples considered include simple harmonic oscillators with complex angular
frequencies, Stark(Zeeman) effect with complex electric(magnetic) field,
non-hermitian general quadratic form of N boson(fermion) operators, symmetric
and asymmetric XXZ spin-chain in complex magnetic field, non-hermitian
Haldane-Shastry spin-chain and Lipkin-Meshkov-Glick model.Comment: 29 pages, revtex, minor changes, version to appear in Journal of
Physics A(v3
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