Remarks on the Extended Characteristic Uncertainty Relations

Three remarks concerning the form and the range of validity of the state-extended characteristic uncertainty relations (URs) are presented. A more general definition of the uncertainty matrix for pure and mixed states is suggested. Some new URs are provided.Comment: LaTex, 4 pages, no figure

Comment on "On the uncertainty relations and squeezed states for the quantum mechanics on a circle"

It is shown by examples that the position uncertainty on a circle, proposed recently by Kowalski and Rembieli\'nski [J. Phys. A 35 (2002) 1405] is not consistent with the state localization. We argue that the relevant uncertainties and uncertainty relations (UR's) on a circle are that based on the Gram-Robertson matrix. Several of these generalized UR's are displayed and related criterions for squeezed states are discussed.Comment: 5 pages, LaTex2e, 3 figures.ep

Photon recoil momentum in a Bose-Einstein condensate of a dilute gas

We develop a "minimal" microscopic model to describe a two-pulse-Ramsay-interferometer-based scheme of measurement of the photon recoil momentum in a Bose-Einstein condensate of a dilute gas [Campbell et al., Phys. Rev. Lett. 94, 170403 (2005)]. We exploit the truncated coupled Maxwell-Schroedinger equations to elaborate the problem. Our approach provides a theoretical tool to reproduce essential features of the experimental results. Additionally, we enable to calculate the quantum-mechanical mean value of the recoil momentum and its statistical distribution that provides a detailed information about the recoil event.Comment: 6 pages, 4 figure

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

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

Stretching semiflexible filaments with quenched disorder

We study the effect of quenched randomness in the arc-length dependent spontaneous curvature of a wormlike chain under tension. In the weakly bending approximation in two dimensions, we obtain analytic results for the force-elongation curve and the width of transverse fluctuations. We compare quenched and annealed disorder and conclude that the former cannot always be reduced to a simple change in the stiffness of the pure system. We also discuss the effect of a random transverse force on the stretching response of a wormlike chain without spontaneous curvature.Comment: 5 pages, minor changes, added references, final version as published in PR

Uncertainty Relations in Deformation Quantization

Robertson and Hadamard-Robertson theorems on non-negative definite hermitian forms are generalized to an arbitrary ordered field. These results are then applied to the case of formal power series fields, and the Heisenberg-Robertson, Robertson-Schr\"odinger and trace uncertainty relations in deformation quantization are found. Some conditions under which the uncertainty relations are minimized are also given.Comment: 28+1 pages, harvmac file, no figures, typos correcte

Nucleation at the DNA supercoiling transition

Twisting DNA under a constant applied force reveals a thermally activated transition into a state with a supercoiled structure known as a plectoneme. Using transition state theory, we predict the rate of this plectoneme nucleation to be of order 10^4 Hz. We reconcile this with experiments that have measured hopping rates of order 10 Hz by noting that the viscosity of the bead used to manipulate the DNA limits the measured rate. We find that the intrinsic bending caused by disorder in the base-pair sequence is important for understanding the free energy barrier that governs the transition. Both analytic and numerical methods are used in the calculations. We provide extensive details on the numerical methods for simulating the elastic rod model with and without disorder.Comment: 18 pages, 15 figure

Stretching an heteropolymer

We study the influence of some quenched disorder in the sequence of monomers on the entropic elasticity of long polymeric chains. Starting from the Kratky-Porod model, we show numerically that some randomness in the favoured angles between successive segments induces a change in the elongation versus force characteristics, and this change can be well described by a simple renormalisation of the elastic constant. The effective coupling constant is computed by an analytic study of the low force regime.Comment: Latex, 7 pages, 3 postscript figur