587 research outputs found
Effects of Sequence Disorder on DNA Looping and Cyclization
Effects of sequence disorder on looping and cyclization of the
double-stranded DNA are studied theoretically. Both random intrinsic curvature
and inhomogeneous bending rigidity are found to result in a remarkably wide
distribution of cyclization probabilities. For short DNA segments, the range of
the distribution reaches several orders of magnitude for even completely random
sequences. The ensemble averaged values of the cyclization probability are also
calculated, and the connection to the recent experiments is discussed.Comment: 8 pages, 4 figures, LaTeX; accepted to Physical Review E; v2: a
substantially revised version; v3: references added, conclusions expanded,
minor editorial corrections to the text; v4: a substantially revised and
expanded version (total number of pages doubled); v5: new Figure 4, captions
expanded, minor editorial improvements to the tex
Barut-Girardello coherent states for u(p,q) and sp(N,R) and their macroscopic superpositions
The Barut-Girardello coherent states (BG CS) representation is extended to
the noncompact algebras u(p,q) and sp(N,R) in (reducible) quadratic boson
realizations. The sp(N,R) BG CS take the form of multimode ordinary
Schr\"odinger cat states. Macroscopic superpositions of 2^{n-1} sp(N,R) CS (2^n
canonical CS, n=1,2,...) are pointed out which are overcomplete in the N-mode
Hilbert space and the relation between the canonical CS and the u(p,q) BG-type
CS representations is established. The sets of u(p,q) and sp(N,R) BG CS and
their discrete superpositions contain many states studied in quantum optics
(even and odd N-mode CS, pair CS) and provide an approach to quadrature
squeezing, alternative to that of intelligent states. New subsets of weakly and
strongly nonclassical states are pointed out and their statistical properties
(first- and second-order squeezing, photon number distributions) are discussed.
For specific values of the angle parameters and small amplitude of the
canonical CS components these states approaches multimode Fock states with one,
two or three bosons/photons. It is shown that eigenstates of a squared
non-Hermitian operator A^2 (generalized cat states) can exhibit squeezing of
the quadratures of A.Comment: 29 pages, LaTex, 5 figures. Improvements in text, corrections in some
formulas. To appear in J. Phys. A, v. 3
Robertson Intelligent States
Diagonalization of uncertainty matrix and minimization of Robertson
inequality for n observables are considered. It is proved that for even n this
relation is minimized in states which are eigenstates of n/2 independent
complex linear combinations of the observables. In case of canonical
observables this eigenvalue condition is also necessary. Such minimizing states
are called Robertson intelligent states (RIS).
The group related coherent states (CS) with maximal symmetry (for semisimple
Lie groups) are particular case of RIS for the quadratures of Weyl generators.
Explicit constructions of RIS are considered for operators of su(1,1), su(2),
h_N and sp(N,R) algebras. Unlike the group related CS, RIS can exhibit strong
squeezing of group generators. Multimode squared amplitude squeezed states are
naturally introduced as sp(N,R) RIS. It is shown that the uncertainty matrices
for quadratures of q-deformed boson operators a_{q,j} (q > 0) and of any k
power of a_j = a_{1,j} are positive definite and can be diagonalized by
symplectic linear transformations. PACS numbers: 03.65.Fd, 42.50.DvComment: 23 pages, LaTex. Minor changes in text and references. Accepted in J.
Phys.
Generation of single-mode SU(1,1) intelligent states and an analytic approach to their quantum statistical properties
We discuss a scheme for generation of single-mode photon states associated
with the two-photon realization of the SU(1,1) algebra. This scheme is based on
the process of non-degenerate down-conversion with the signal prepared
initially in the squeezed vacuum state and with a measurement of the photon
number in one of the output modes. We focus on the generation and properties of
single-mode SU(1,1) intelligent states which minimize the uncertainty relations
for Hermitian generators of the group. Properties of the intelligent states are
studied by using a ``weak'' extension of the analytic representation in the
unit disk. Then we are able to obtain exact analytical expressions for
expectation values describing quantum statistical properties of the SU(1,1)
intelligent states. Attention is mainly devoted to the study of photon
statistics and linear and quadratic squeezing.Comment: to appear in Quantum Semiclass. Opt., LaTeX, epsf style, 21 pages
including 5 Postscript figures. More information on
http://www.technion.ac.il/~brif/science.htm
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