We show that words in a text present long-range frequency fluctuations due to a strong self-attraction, that is directly related to the relevance of the term to the text considered. The standard deviation of the distance between successive occurrences of a word is an excellent parameter to quantify this self-attraction, and provides us with an effective tool for automatic keyword extraction. DNA sequences also present the same features: “words”, for example codons in the coding part of the sequences, attract between themselves.

We studied the efficiency of two different schemes for a quantum heat engine, by considering a single Dirac particle trapped in an infinite one-dimensional potential well as the "working substance." The first scheme is a cycle, composed of two adiabatic and two isoenergetic reversible trajectories in configuration space. The trajectories are driven by a quasistatic deformation of the potential well due to an external applied force. The second scheme is a variant of the former, where isoenergetic trajectories are replaced by isothermal ones, along which the system is in contact with macroscopic thermostats. This second scheme constitutes a quantum analog of the classical Carnot cycle. Our expressions, as obtained from the Dirac single-particle spectrum, converge in the nonrelativistic limit to some of the existing results in the literature for the Schrödinger spectrum.

Until now, design of the annual influenza vaccine has relied on phylogenetic or whole-sequence comparisons of the viral coat proteins hemagglutinin and neuraminidase, with vaccine effectiveness assumed to correlate monotonically to the vaccine-influenza sequence difference. We use a theory from statistical mechanics to quantify the non-monotonic immune response that results from antigenic drift in the epitopes of the hemagglutinin and neuraminidase proteins. The results explain the ineffectiveness of the 2003-2004 influenza vaccine in the United States and provide an accurate measure by which to optimize the effectiveness of future annual influenza vaccines.

We studied the efficiency of two different schemes for a magnetically driven quantum heat engine, by considering as the "working substance" a single non-relativistic particle trapped in a cylindrical potential well, in the presence of an external magnetic field. The first scheme is a cycle, composed of two adiabatic and two iso-energetic reversible trajectories in configuration space. The trajectories are driven by a quasi-static modulation of the external magnetic field intensity. The second scheme is a variant of the former, where the iso-energetic trajectories are replaced by isothermal ones, along which the system is in contact with macroscopic thermostats. This second scheme constitutes a quantum analogue of the classical Carnot cycle.

We propose an alternative conceptual design for a graphene-based quantum engine, driven by a superposition of mechanical strain and an external magnetic field. Engineering of strain in a nanoscale graphene flake creates a gauge field with an associated uniform pseudomagnetic field. The strain-induced pseudomagnetic field can be combined with a real magnetic field, leading to the emergence of discrete relativistic Landau levels within the single-particle picture. The interlevel distance and hence their statistical population can be modulated by quasistatically tuning the magnetic field along a sequence of reversible transformations that constitute a quantum mechanical analog of the classical Otto cycle.

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The nonlinear conductance of semiconductor heterostructures and single molecule devices exhibiting Kondo physics has recently attracted attention. We address the observed sample dependence of the measured steady state transport coefficients by considering additional electronic contributions in the effective low-energy model underlying these experiments that are absent in particle-hole symmetric setups. A novel version of the superperturbation theory of Hafermann et al. in terms of dual fermions is developed, which correctly captures the low-temperature behavior. We compare our results with the measured transport coefficients.

We use a path integral representation to solve the Eigen and Crow-Kimura molecular evolution models for the case of multiple fitness peaks with arbitrary fitness and degradation functions. In the general case, we find that the solution to these molecular evolution models can be written as the optimum of a fitness function, with constraints enforced by Lagrange multipliers and with a term accounting for the entropy of the spreading population in sequence space. The results for the Eigen model are applied to consider virus or cancer proliferation under the control of drugs or the immune system.