Single-molecule pump-probe detection resolves ultrafast pathways in individual and coupled quantum systems

We report the first experimental study of individual molecules with femtosecond time resolution using a novel ultrafast single-molecule pump-probe method. A wide range of relaxation times from below 100 up to 400 fs is found, revealing energy redistribution over different vibrational modes and phonon coupling to the nanoenvironment. Addressing quantum-coupled molecules we find longer decay times, pointing towards inhibited intramolecular decay due to delocalized excitation. Interestingly, each individual system shows discrete jumps in femtosecond response, reflecting sudden breakup of the coupled superradiant state.     

Sukzessive Minima mit und ohne Nebenbedingungen

Given semi-normsf andg on ⁿ and a real number >0. Then the successive minima off under the constraintg are defined by _j : = inf {: there existj linear independent vectors inZ ⁿ withf andg}. The main theorem of this paper (Lagrange multiplier theorem) states that the successive minima of a certainnorm h on ⁿ (without constraints) coincide with the _j 's up to bounded factors. Moreover, this norm is constructed explicitly. Using Minkowski's wellknown theorem on successive minima and our result certain inequalities on simultaneous Diophantine approximations are derived.     

Ein LIFO Branch and Bound Verfahren zur optimalen Altstoffbehälterallokation

Zusammenfassung In diesem Artikel wird auf ein Problem eingegangen, das sich im Rahmen einer abfallwirtschaftlichen Studie ergab, in der die Durchführbarkeit von Altstoffsammlungen im dichtverbauten Siedlungsgebiet untersucht wurde. Als wichtige Teilaufgabe war dabei eine platzminimale Altstoffbehälterkombination für jede Altstoffart und für jedes Haus des untersuchten Sammelgebietes zu ermitteln, wobei unter anderem die Zugänglichkeit des Behälterraumes für die Sammelmannschaft und dessen topographische Gegebenheiten zu beachten waren. Zur Lösung dieser Aufgabe, deren Formalisierung auf ein ganzzahliges LP führte, wurde ein LIFO Branch and Bound Verfahren entwickelt. Dieses wird an Hand der wesentlichen Bestandteile eines jeden Algorithmus vom Branch and Bound Typ: der Branching Strategie, der Bounding Strategie und der Search Strategie dargestellt. Der Algorithmus wurde in PL/I programmiert und hat seine Leistungsfähigkeit in zahlreichen Programmläufen unter Beweis gestellt.

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Summary In this article a problem is treated which rose in the course of a research into the suitability for reconditioning used materials. This study analyzes the feasibility of scrap collection in densily populated, urban areas. One major aspect was to provide for a space saving combination of containers for every kind of scrap and for each house of the test area, bearing in mind the constraints given by the topographical conditions of the container room and its accessibility to the collection personnel. The formulation of this problem led to an all integer program. To solve this program a LIFO branch and bound algorithm was developed. The algorithm is presented by discussing its branching strategy, its bounding strategy and its search strategy, which constitute the essential parts of each procedure of the branch and bound type. The algorithm was programmed in PL/I and proved its efficiency in numerous runs.

     

A sufficient condition for a graph to be hamiltonian

Those non-hamiltonian graphsG withn vertices are characterized, which satisfy the Ore-type degree-conditiond(x)+d(y)n–2 for each pairx,yM of different nonadjacent vertices whereM consists of two vertices ofG. As an application a theorem on hamiltonian connectivity of graphs is given. Furthermore, a condition is presented which is sufficient for the existence of a covering of a graph by two disjoint paths with prescribed set of startpoints and prescribed set of endpoints. A class of graphs is described which have no covering of this kind.     

Über Mittelwerte multiplikativer zahlentheoretischer Funktionen mehrerer Variablen

In [8] the author extended the concept of neighbouring functions (cp. [9]) to the case of several variables. Using these results it is shown that under some weak conditions a multiplicative functionf in two variables has a mean-value different from zero if and only if the two multiplicative functionsf ₁(n)=f(n, 1) andf ₂(n)=f(1,n) have mean-values different from zero. Applications to theorems ofDelange [3],Elliott [6] andDaboussi [1] are given.     

Generalized localization and convergence tests for double trigonometric Fourier series of functions fromL p,p>1

. E , f(x)L _p (T ^N ),P1,f(x)=0 E (E— ^N =[-, ]^N) E , . , .

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In closing the author thanks V. A. Il'in and . A. Alimov for their constant attention paid to the present work.     

Solvent Relaxation in Phospholipid Bilayers: Principles and Recent Applications

Although there exist a number of methods, such as NMR, X-ray, e.g., which explore the hydration of phospholipid bilayers, the solvent relaxation (SR) method has the advantage of simple instrumentation, easy data treatment and possibility of measuring fully hydrated samples. The main information gained from SR by the analysis of recorded “time-resolved emission spectra” (TRES) is micro-viscosity and micro-polarity of the dye microenvironment. Based on these parameters, one can draw conclusions about water structure in the bilayer. In this review, we focus on physical background of this method, on all the procedures that are needed in order to obtain relevant parameters, and on the requirements on the fluorescence dyes. Furthermore, a few recent applications (the effect of curvature, binding of antibacterial peptides and phase transition) illustrating the versatility of this method are mentioned. Moreover, limitations and potential problems are discussed.     

Mach–Zehnder interferometers in photonic crystals

Photonic crystal technology allows the creation of optical waveguides with low sharp-bending losses as well as ultra-low group velocity. This last property is particularly interesting to develop highly-compact optical devices based on the controlled modification of the optical phase of the signals traveling through the waveguides. Among these devices, the Mach–Zehnder interferometer acquires fundamental importance because it can be used as a building block of more complex optical devices and functionalities such as optical filters, wavelength demultiplexers, channels interleavers, intensity modulators, switches and optical gates. In this paper, the performance of a Mach–Zehnder interferometer consisting of two coupled-cavity waveguides with different lengths created in a two-dimensional photonic crystal is theoretically analyzed. We also provide simulation results using a finite-difference time-domain code that confirm the theoretical analysis. The main limitations in the performance of the structure are addressed and discussed.     

Asymptotic violation of Bell inequalities and distillability

A multipartite quantum state violates a Bell inequality asymptotically if, after jointly processing by general local operations an arbitrarily large number of copies of it, the result violates the inequality. In the bipartite case we show that asymptotic violation of the Clauser-Horne-Shimony-Holt inequality is equivalent to distillability. Hence, bound entangled states do not violate it. In the multipartite case we consider the complete set of full-correlation Bell inequalities with two dichotomic observables per site. We show that asymptotic violation of any of these inequalities by a multipartite state implies that pure-state entanglement can be distilled from it, although the corresponding distillation protocol may require that some of the parties join into several groups. We also obtain the extreme points of the set of distributions generated by measuring N quantum systems with two dichotomic observables per site.