לוח שנה משולב

Solving the Problem of Anharmonic Densities of States*

Julius Jellinek

Chemical Sciences and Engineering Division
Argonne National Laboratory, Argonne, IL 60439, USA

Density of states (DOS) is a fundamental characteristic of systems that lies in the very foundation of statistical mechanics and all the theoretical constructs that derive from them (e.g., kinetic rate theories, phase diagrams, etc.). Knowledge of DOS is central for calculation of entropy, partition function, free energy, reaction rate constants, and other important characteristics. The accuracy of all these depends on the accuracy with which the DOS is defined. Even though virtually all real systems are anharmonic, the current practice in the computation of vibrational DOSs is largely based on the harmonic approximation. The reason is that despite major efforts over about eight decades a general and exact, yet practical in applications, solution to the problem of anharmonic DOSs stubbornly resisted resolution. The alternatives introduced are mostly limited to cases of weak anharmonicity and/or suffer from other shortcomings.

In a recent development, we formulated a general and exact solution to this long-standing problem, which is applicable to arbitrary degree of anharmonicity (i.e., any system) and that is practical and efficient in applications. The solution and its algorithmic implementations are developed within the frameworks of both classical and quantum mechanics. The quantum implementation involves generalization and significant enhancement in the efficiency of the celebrated Beyer-Swinehart counting scheme, which is the fastest to date algorithm used in the computation of the quantum harmonic DOSs. Our solution is based on simulating the actual dynamical behavior of systems on the time scale of interest, short or long, as defined by the experiment and/or the nature of the process or phenomenon at hand. As a consequence, the resulting anharmonic DOSs are fully dynamically informed and, in general, time-dependent. As such, they lay the foundation for formulation of new statistical mechanical frameworks that incorporate time and reproduce exactly the actual time-averaged dynamical behavior of systems on the temporal scale of interest irrespective of whether this behavior is statistical or not in the traditional sense.

Work has been initiated on extending this development to the general case of rotational(ro)-vibrational DOSs for systems with arbitrary degree of anharmonicity and arbitrarily strong ro-vibrational coupling.
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* This work was supported by the Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences, U.S. Department of Energy under Contract No. DE-AC02-06CH11357.

Within the last two decades it has become clear that cells having the same genetic information can behave very differently, due to inevitable stochastic fluctuations in gene expression, known as noise. How do cells in multicellular organisms achieve high precision in their developmental fate in the presence of noise, in order to reap the benefits of division of labor? We address this fundamental question from Systems Biology and Statistical Physics perspectives, with Anabaena cyanobacterial filaments as a model system, one of the earliest examples of multicellular organisms in nature. These filaments can form one-dimensional, nearly-regular patterns of cells of two types. The developmental program uses tightly regulated, non-linear processes that include activation, inhibition, and transport, in order to create spatial and temporal patterns of gene expression that we can follow in real time, at the level of individual cells. We study cellular decisions, properties of the genetic network behind pattern formation, and establish the spatial extent to which gene expression is correlated along filaments. Motivated by our experimental results, I will show that pattern formation in Anabaena can be described theoretically by a minimal, three-component model that exhibits a deterministic, diffusion-driven Turing instability. Furthermore, I will discuss how noise can enhance considerably the robustness of the developmental program, by promoting the formation of stochastic patterns in regions of parameter space for which deterministic patterns do not form, suggesting a novel mechanism for pattern formation in this and other systems.

Two and three Helium atoms form very unusual and extreme quantum systems. Their typical extend is ten to hundred times bigger than radius of the atoms, the wavefunction lives almost completely in the classically forbidden tunneling region and the binding energy of these systems is about 8 orders of magnitude smaller than that of a normal molecule.
We will show how coincidence detection of charged fragments and super strong laser fields can be used to image the wave functions of these Helium quantum giants and will show the first experimental images of an Efimov state.

Abstract: In my talk I will discuss some new features of conformal anomaly and entanglement entropy in the presence of boundaries. The talk is based on recent papers.This is a project to develop a wide expanse of new quantum field theories in 2n-dimensional space-time manifolds. For each 2d qft, there is to be a qft of extended objects in every 2n-dimensional space-time manifold M. The quantum fields live on ``quasi Riemann surfaces'', which are certain spaces of integral (n-1)-currents in M. The notion of integral current comes from Geometric Measure Theory. The quasi Riemann surfaces are complete metric spaces with analytic properties strictly analogous to Riemann surfaces. The new qfts are to be constructed on the quasi Riemann surfaces just as 2d qfts are constructed on ordinary Riemann surfaces. Local fields in space-time are obtained by restricting to small extended objects.
arXiv:1510.04566, arXiv:1601.06418 and arXiv:1604.07571