Density-matrix functionals for pairing in mesoscopic superconductors

A functional theory based on single-particle occupation numbers is developed for pairing. This functional, that generalizes the BCS approach, directly incorporates corrections due to particle number conservation. The functional is benchmarked with the pairing Hamiltonian and reproduces perfectly the energy for any particle number and coupling.Comment: 4 pages, 4 figures, revised versio

The Glass Transition and the Jarzynski Equality

A simple model featuring a double well potential is used to represent a liquid that is quenched from an ergodic state into a history dependent glassy state. Issues surrounding the application of the Jarzynski Equality to glass formation are investigated. We demonstrate that the Jarzynski Equality gives the free energy difference between the initial state and the state we would obtain if the glass relaxed to true thermodynamic equilibrium. We derive new variations of the Jarzynski Equality which are relevant to the history dependent glassy state rather than the underlying equilibrium state. It is shown how to compute the free energy differences for the nonequilibrium history dependent glassy state such that it remains consistent with the standard expression for the entropy and with the second law inequality.Comment: 16 pages, 5 figure

Properties of iterative Monte Carlo single histogram reweighting

We present iterative Monte Carlo algorithm for which the temperature variable is attracted by a critical point. The algorithm combines techniques of single histogram reweighting and linear filtering. The 2d Ising model of ferromagnet is studied numerically as an illustration. In that case, the iterations uncovered stationary regime with invariant probability distribution function of temperature which is peaked nearly the pseudocritical temperature of specific heat. The sequence of generated temperatures is analyzed in terms of stochastic autoregressive model. The error of histogram reweighting can be better understood within the suggested model. The presented model yields a simple relation, connecting variance of pseudocritical temperature and parameter of linear filtering.Comment: 3 figure

Period Doubling Renormalization for Area-Preserving Maps and Mild Computer Assistance in Contraction Mapping Principle

It has been observed that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of {\fR}^2. A renormalization approach has been used in a "hard" computer-assisted proof of existence of an area-preserving map with orbits of all binary periods in Eckmann et al (1984). As it is the case with all non-trivial universality problems in non-dissipative systems in dimensions more than one, no analytic proof of this period doubling universality exists to date. In this paper we attempt to reduce computer assistance in the argument, and present a mild computer aided proof of the analyticity and compactness of the renormalization operator in a neighborhood of a renormalization fixed point: that is a proof that does not use generalizations of interval arithmetics to functional spaces - but rather relies on interval arithmetics on real numbers only to estimate otherwise explicit expressions. The proof relies on several instance of the Contraction Mapping Principle, which is, again, verified via mild computer assistance

Stochastic mean-field dynamics for fermions in the weak coupling limit

Assuming that the effect of the residual interaction beyond mean-field is weak and has a short memory time, two approximate treatments of correlation in fermionic systems by means of Markovian quantum jump are presented. A simplified scenario for the introduction of fluctuations beyond mean-field is first presented. In this theory, part of the quantum correlations between the residual interaction and the one-body density matrix are neglected and jumps occur between many-body densities formed of pairs of states $D=| \Phi_a > < \Phi_b |/$ where $| \Phi_a >$ and $| \Phi_b >$ are antisymmetrized products of single-particle states. The underlying Stochastic Mean-Field (SMF) theory is discussed and applied to the monopole vibration of a spherical $^{40}$Ca nucleus under the influence of a statistical ensemble of two-body contact interaction. This framework is however too simplistic to account for both fluctuation and dissipation. In the second part of this work, an alternative quantum jump method is obtained without making the approximation on quantum correlations. Restricting to two particles-two holes residual interaction, the evolution of the one-body density matrix of a correlated system is transformed into a Lindblad equation. The associated dissipative dynamics can be simulated by quantum jumps between densities written as $D = | \Phi >$ is a normalized Slater determinant. The associated stochastic Schroedinger equation for single-particle wave-functions is given.Comment: Enlarged version, 10 pages, 2 figure

Pairing dynamics in particle transport

We analyze the effect of pairing on particle transport in time-dependent theories based on the Hartree-Fock-Bogoliubov (HFB) or BCS approximations. The equations of motion for the HFB density matrices are unique and the theory respects the usual conservation laws defined by commutators of the conserved quantity with the Hamiltonian. In contrast, the theories based on the BCS approximation are more problematic. In the usual formulation of TDHF+BCS, the equation of continuity is violated and one sees unphysical oscillations in particle densities. This can be ameliorated by freezing the occupation numbers during the evolution in TDHF+BCS, but there are other problems with the BCS that make it doubtful for reaction dynamics. We also compare different numerical implementations of the time-dependent HFB equations. The equations of motion for the $U$ and $V$ Bogoliubov transformations are not unique, but it appears that the usual formulation is also the most efficient. Finally, we compare the time-dependent HFB solutions with numerically exact solutions of the two-particle Schrodinger equation. Depending on the treatment of the initial state, the HFB dynamics produces a particle emission rate at short times similar to that of the Schrodinger equation. At long times, the total particle emission can be quite different, due to inherent mean-field approximation of the HFB theory.Comment: 11 pages, 9 figure

STM Studies of Synthetic Peptide Monolayers

We have used scanning probe microscopy to investigate self-assembled monolayers of chemically synthesized peptides. We find that the peptides form a dense uniform monolayer, above which is found a sparse additional layer. Using scanning tunneling microscopy, submolecular resolution can be obtained, revealing the alpha helices which constitute the peptide. The nature of the images is not significantly affected by the incorporation of redox cofactors (hemes) in the peptides.Comment: 4 pages, 3 figures (4 gifs); to appear in the Proceedings of the XIIth Int. Winterschool on Electronic Properties of Novel Materials "Molecular Nanostructures", Kirchberg/Tyrol, Febr. 199

Squid stock fluctuations and water temperature: temporal analysis of English Channel Loliginidae

1. Monthly series of abundance indexes for the English Channel squid stock, based on fishery statistics of the United Kingdom (1980–93) and France (1986–96), were compared with water temperature data. The two objectives of the study were to test empirical predictive models and to analyse the stock–environment relationship at various time scales; both correlation and time-series statistical techniques were applied. Sea surface temperature (SST) showed inter-annual fluctuations and month-to-month auto-correlation in addition to the annual cycle. 2. Trends in squid landings and temperature at the annual scale were found to be related, whatever the statistical method used (moving averages, cumulative functions or regression using averaged data). 3. Variable selection applied in a ‘multi-month’ model suggested that fishing season indexes could be predicted from temperatures observed in the previous winter. The link between mild winter conditions and cohort success in winter/spring spawning species suggested that early life survival (and/or growth) was involved. This empirical model is a first step in the development of environment-predicted recruitment indexes useful for management advice. 4. Seasonal decomposition was performed on both the squid resource data and SST data in search of short-term relationships. In spite of the flexibility of the loliginid life-cycle, no significant relationship was found between squid seasonally adjusted indexes and temperature anomalies in the previous months. This underlined the conclusion that temperature effect on cohort success was not constant throughout the year

Nonlinear Transport Near a Quantum Phase Transition in Two Dimensions

The problem of non-linear transport near a quantum phase transition is solved within the Landau theory for the dissipative insulator-superconductor phase transition in two dimensions. Using the non-equilibrium Schwinger round-trip Green function formalism, we obtain the scaling function for the non-linear conductivity in the quantum disordered regime. We find that the conductivity scales as $E^2$ at low field but crosses over at large fields to a universal constant on the order of $e^2/h$. The crossover between these two regimes obtains when the length scale for the quantum fluctuations becomes comparable to that of the electric field within logarithmic accuracy.Comment: 4.15 pages, no figure

Traffic jams and intermittent flows in microfluidic networks

We investigate both experimentally and theoretically the traffic of particles flowing in microfluidic obstacle networks. We show that the traffic dynamics is a non-linear process: the particle current does not scale with the particle density even in the dilute limit where no particle collision occurs. We demonstrate that this non-linear behavior stems from long range hydrodynamic interactions. Importantly, we also establish that there exists a maximal current above which no stationary particle flow can be sustained. For higher current values, intermittent traffic jams form thereby inducing the ejection of the particles from the initial path and the subsequent invasion of the network. Eventually, we put our findings in the broader context of the transport proccesses of driven particles in low dimension