A statistical model for antibody-antigen binding

We discuss a statistical model for antibody-antigen binding. The two macromolecules are assumed to be linked by a number of relatively weak bonds (or groups of correlated bonds) that are assumed to open and close statistically. We use the model for a preliminary analysis of experiments performed in the Institute of Biophysics at the Johannes Kepler University. In these experiments the two molecules are brought into contact using an atomic force microscope; then a prescribed time dependent force is applied to the bond and the distribution of times needed to pull the molecules completely apart is measured. This quantity is calculated with our model; its dependence on the model parameters (binding free energies, number of groups of correlated elementary bonds, force dependence of the binding free energy) is determined.Обговорюється статистична модель, яка описує зв’язування антитіло-антиген. При цьому вважається, що дві макромолекули можуть поєднуватись через набір відносно слабих зв’язків (чи груп скорельованих зв’язків), що відкриваються і закриваються статистично. Ця модель використовується для попереднього аналізу експериментів, виконаних в Інституті біофізики Університету Йогана Кеплера. У цих експериментах дві молекули приводились у контакт, використовуючи атомної сили мікроскоп, а потім прикладалася певна залежна від часу сила до зв’язку і вимірювався розподіл часів, необхідних для повного розділення молекул. Ця характеристика розраховується з використанням запропонованої моделі; знайдена її залежність від модельних параметрів (вільних енергій зв’язування, числа груп скорельованих елементарних зв’язків, залежності вільної енергії зв’язування від сили)

Mode structure and photon number correlations in squeezed quantum pulses

The question of efficient multimode description of optical pulses is studied. We show that a relatively very small number of nonmonochromatic modes can be sufficient for a complete quantum description of pulses with Gaussian quadrature statistics. For example, a three-mode description was enough to reproduce the experimental data of photon number correlations in optical solitons [S. Spalter et al., Phys. Rev. Lett. 81, 786 (1998)]. This approach is very useful for a detailed understanding of squeezing properties of soliton pulses with the main potential for quantum communication with continuous variables. We show how homodyne detection and/or measurements of photon number correlations can be used to determine the quantum state of the multi-mode field. We also discuss a possible way of physical separation of the nonmonochromatic modes.Comment: 14 pages, 4 figures; minor revisions of the text, new references; to appear in the Phys. Rev.

Corrections to Einstein's relation for Brownian motion in a tilted periodic potential

In this paper we revisit the problem of Brownian motion in a tilted periodic potential. We use homogenization theory to derive general formulas for the effective velocity and the effective diffusion tensor that are valid for arbitrary tilts. Furthermore, we obtain power series expansions for the velocity and the diffusion coefficient as functions of the external forcing. Thus, we provide systematic corrections to Einstein's formula and to linear response theory. Our theoretical results are supported by extensive numerical simulations. For our numerical experiments we use a novel spectral numerical method that leads to a very efficient and accurate calculation of the effective velocity and the effective diffusion tensor.Comment: 29 pages, 7 figures, submitted to the Journal of Statistical Physic

Homodyne detection for measuring internal quantum correlations of optical pulses

A new method is described for determining the quantum correlations at different times in optical pulses by using balanced homodyne detection. The signal pulse and sequences of ultrashort test pulses are superimposed, where for chosen distances between the test pulses their relative phases and intensities are varied from measurement to measurement. The correlation statistics of the signal pulse is obtained from the time-integrated difference photocurrents measured.Comment: 7 pages, A4.sty include

Generation of atom-photon entangled states in atomic Bose-Einstein condensate via electromagnetically induced transparency

In this paper, we present a method to generate continuous-variable-type entangled states between photons and atoms in atomic Bose-Einstein condensate (BEC). The proposed method involves an atomic BEC with three internal states, a weak quantized probe laser and a strong classical coupling laser, which form a three-level Lambda-shaped BEC system. We consider a situation where the BEC is in electromagnetically induced transparency (EIT) with the coupling laser being much stronger than the probe laser. In this case, the upper and intermediate levels are unpopulated, so that their adiabatic elimination enables an effective two-mode model involving only the atomic field at the lowest internal level and the quantized probe laser field. Atom-photon quantum entanglement is created through laser-atom and inter-atomic interactions, and two-photon detuning. We show how to generate atom-photon entangled coherent states and entangled states between photon (atom) coherent states and atom-(photon-) macroscopic quantum superposition (MQS) states, and between photon-MQS and atom-MQS states.Comment: 9 pages, 1 figur

A Quantum-mechanical Approach for Constrained Macromolecular Chains

Many approaches to three-dimensional constrained macromolecular chains at thermal equilibrium, at about room temperatures, are based upon constrained Classical Hamiltonian Dynamics (cCHDa). Quantum-mechanical approaches (QMa) have also been treated by different researchers for decades. QMa address a fundamental issue (constraints versus the uncertainty principle) and are versatile: they also yield classical descriptions (which may not coincide with those from cCHDa, although they may agree for certain relevant quantities). Open issues include whether QMa have enough practical consequences which differ from and/or improve those from cCHDa. We shall treat cCHDa briefly and deal with QMa, by outlining old approaches and focusing on recent ones.Comment: Expands review published in The European Physical Journal (Special Topics) Vol. 200, pp. 225-258 (2011

Quantum statistics can suppress classical interference

Original article can be found at: http://prola.aps.org/--Copyright American Physical SocietyClassical optical interference experiments correspond to a measurement of the first-order correlation function of the electromagnetic field. The converse of this statement: exper- iments that measure the first order correlation functions do not distinguish between the quantum and classical theories of light, does not always hold. A counter example is given.Peer reviewe

Boundary layer effects on the rate of diffusion-controlled reactions

International audienceThe description using the Smoluchowski equation, on which the traditional theory of diffusion-controlled reactions is based, presupposes local equilibrium. Hence it must break down in the vicinity of an absorbing wall, where a kinetic boundary layer is formed. We explore in this paper the effects of this boundary layer on the reaction rate. We start from a description using the Klein-Kramers equation and use two approximate treatments of the boundary layer that gave satisfactory results for the analogous one-dimensional problem. The simplest one leads to a simple analytic correction factor in the Smoluchowski-Debye reaction rate that becomes appreciable for particle radii not very large compared to a typical length, the velocity persistence length. The correction factor always decreases the reaction rate. For constant of piecewise constant potentials between the reacting particles we also work out a somewhat more elaborate approximation, based on Grad's thirteen-moment equations. It yields effects of the same order of magnitude as the simple theory; the differences between the two approximate treatments should give an indication of the errors still contained in each of them

The covariant form of the Klein-Kramers equation and the associated moment equations

International audienceWe provide a covariant, coordinate-free formulation of the many-dimensional Klein-Kramers equation for the phase space distribution of a Brownian particle. We construct a complete set of eigenfunctions of the collision operator adapted to the coordinate system, which involve covariant tensorial Hermite polynomials. The Klein-Kramers equation can then be reformulated as a system of coupled equations for the expansion coefficients with respect to this system. Truncation of this system of moment equations and application of a subsidiary condition yields a covariant generalization of Grad's thirteen-moment equations. As an application we give the explicit form of these equations for spherically symmetric, stationary solutions in spherical coordinates. We briefly comment on possible extensions of our treatment to slightly more complicated cases

On the deduction of Carathéodory's axiom from Kelvin's principle

Landsberg recently proved that Carathéodory's axiom is a logical consequence of Kelvin's principle. His proof is here modified, so that the consequences of an implicit assumption become apparent. The result may be summarised as follows: Purely mechanical systems are the only systems that obey Kelvin's principle but not Carathéodory's axiom