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Kondrat S.,Imperial College London | Georgi N.,Max Planck Institute For Mathematik In Den Naturwissenschaften | Fedorov M.V.,Max Planck Institute For Mathematik In Den Naturwissenschaften | Kornyshev A.A.,Imperial College London
Physical Chemistry Chemical Physics | Year: 2011

Recently observed anomalous properties of ionic-liquid-based nanoporous supercapacitors [C. Largot et al., J. Am. Chem. Soc., 2008, 130, 2730-2731] have attracted much attention. Here we present Monte Carlo simulations of a model ionic liquid in slit-like metallic nanopores. We show that exponential screening of the electrostatic interactions of ions inside a pore, as well as the image-charge attraction of ions to the pore surface, lead to the 'anomalous' increase of the capacitance with decreasing the pore width. The simulation results are in good agreement with the experimental data. The capacitance as a function of voltage is almost constant for low voltages and vanishes above a certain threshold voltage. For very narrow pores, these two regions are separated by a peak. With increase of the pore size the peak turns into a bump and disappears for wide pores. This effect, related to a specific character of the voltage-induced filling of nanopores with counterions at high densities, is yet to be verified experimentally. © the Owner Societies.


Luo H.,Max Planck Institute For Mathematik In Den Naturwissenschaften
Journal of Chemical Physics | Year: 2011

We investigate the performance of the newly developed variational transcorrelated (VTC) method (H. Luo, J. Chem. Phys. 133, 154109 (2010)10.1063/1.3505037) on the overall optimisation of the multi-configuration Jastrow wave function. Similar to the standard multi-configuration self consistent field methods, optimisations of orbitals are realized by iterative unitary transformations, where the skew-symmetric matrix elements are determined by using Newton-Raphson scheme. Third order density matrices are introduced to deal with the three-body VTC potential. Test calculations are performed for the C2 molecule on several small complete active spaces, and the results are compared with those of variational quantum Monte Carlo calculations. The results demonstrate that with the VTC method one can practically recover the results of highly non-linear variational calculations. © 2011 American Institute of Physics.


Kondrat S.,Imperial College London | Kondrat S.,Max Planck Institute For Mathematik In Den Naturwissenschaften | Kornyshev A.,Imperial College London
Journal of Physics Condensed Matter | Year: 2011

In recent experiments (Chmiola et al 2006 Science 313 1760; Largeot et al 2008 J. Am. Chem. Soc. 130 2730) an anomalous increase of the capacitance with a decrease of the pore size of a carbon-based porous electric double-layer capacitor has been observed. We explain this effect by image forces which exponentially screen out the electrostatic interactions of ions in the interior of a pore. Packing of ions of the same sign becomes easier and is mainly limited by steric interactions. We call this state 'superionic' and suggest a simple model to describe it. The model reveals the possibility of a voltage-induced first order transition between a cation(anion)-deficient phase and a cation(anion)-rich phase which manifests itself in a jump of capacitance as a function of voltage. © 2011 IOP Publishing Ltd.


Zocher B.,University of Leipzig | Zocher B.,Max Planck Institute For Mathematik In Den Naturwissenschaften | Rosenow B.,University of Leipzig
Physical Review Letters | Year: 2013

We study charge transport through a topological superconductor with a pair of Majorana end states coupled to leads via quantum dots with resonant levels. The nonlocality of the Majorana bound states opens the possibility of crossed Andreev reflection with nonlocal shot noise due to the injection of an electron into one end of the superconductor followed by the emission of a hole at the other end. In the space of energies of the two resonant quantum dot levels, we find a four peaked cloverlike pattern for the strength of noise due to crossed Andreev reflection, distinct from the single ellipsoidal peak found in the absence of Majorana bound states. © 2013 American Physical Society.


Zocher B.,University of Leipzig | Zocher B.,Max Planck Institute For Mathematik In Den Naturwissenschaften | Rosenow B.,University of Leipzig
Physical Review B - Condensed Matter and Materials Physics | Year: 2013

We investigate characteristic features in the spin response of doped three-dimensional topological insulators with odd-parity unequal-spin superconducting pairing, which are predicted to have gapless Majorana surface modes. These Majorana modes contribute to the local spin susceptibility, giving rise to a characteristic temperature behavior of the Knight shift and the spin-lattice relaxation time in magnetic resonance experiments. Because of their different decay lengths, the Majorana modes can be observed and clearly distinguished from the Dirac modes of the topological insulator by local probes, which allow for a depth-controlled study of the electron spins on the nanometer length scale. © 2013 American Physical Society.


Hackbusch W.,Max Planck Institute For Mathematik In Den Naturwissenschaften
Computing and Visualization in Science | Year: 2015

We give an overview of various methods based on tensor structured techniques for the solution of linear systems in high spatial dimensions. In particular, we discuss the role of multi-grid variants. © 2016, The Author(s).


Luo H.,Max Planck Institute For Mathematik In Den Naturwissenschaften
Journal of Chemical Physics | Year: 2010

We propose a new approach to the use of Jastrow ansatz in the calculation of electron correlations, based on a modification of the transcorrelated method of Boys and Handy [Proc. R. Soc. London, Ser. A 309, 209 (1969)]. In this new method, the original transcorrelated orbital equation is replaced with a general variational equation for the reference wave function, whereas the equation for the correlation factor remains the same. The method can be applied to a single determinant Jastrow ansatz as well as to a multideterminant one. For the single determinant ansatz, we obtain a Hartree-Fock type self-consistent equation for the optimization of orbitals, and for the multideterminant ansatz we have tested a CI type equation. We apply the new method in calculations of the C 2 molecule and compare the results with those of variational quantum Monte Carlo calculations. © 2010 American Institute of Physics.


Luo H.,Max Planck Institute For Mathematik In Den Naturwissenschaften
Journal of Chemical Physics | Year: 2012

We have constructed the complete transcorrelated equation for homogeneous electron gases and investigated this equation on two- and three-dimensional systems. Correct asymptotic behaviours of the correlation factors can be easily obtained from the transcorrelated equation, both the long-range RPA type decay and the short-range spin dependent cusp conditions. The complete transcorrelated equation is solved numerically and the outcome correlation energies agree very well with variational quantum Monte Carlo results. Possible simplifications of the transcorrelated calculations are discussed, where we find that the RPA equation for the correlation factor can be considerably improved by adding one more term in the equation. © 2012 American Institute of Physics.


Maes C.,Catholic University of Leuven | Steffenoni S.,Max Planck Institute For Mathematik In Den Naturwissenschaften
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2015

We investigate the fluctuation dynamics of a probe around a deterministic motion induced by interactions with driven particles. The latter constitute the nonequilibrium medium in which the probe is immersed and is modeled as overdamped Langevin particle dynamics driven by nonconservative forces. The expansion that yields the friction and noise expressions for the reduced probe dynamics is based on linear response around a time-dependent nonequilibrium condition of the medium. The result contains an extension of the second fluctuation-dissipation relation between friction and noise for probe motion in a nonequilibrium fluid. © 2015 American Physical Society.


Otto F.,Max Planck Institute For Mathematik In Den Naturwissenschaften | Seis C.,Max Planck Institute For Mathematik In Den Naturwissenschaften
Journal of Mathematical Physics | Year: 2011

We consider Rayleigh-Bénard convection as modelled by the Boussinesq equations in the infinite-Prandtl-number limit. We are interested in the scaling of the average upward heat transport, the Nusselt number Nu, in terms of the non-dimensionalized temperature forcing, the Rayleigh number Ra. Experiments, asymptotics and heuristics suggest that Nu ~ Ra 1/3. This work is mostly inspired by two earlier rigorous work on upper bounds of Nu in terms of Ra. (1) The work of Constantin and Doering establishing Nu ≲ Ra 1/3ln 21/3Ra with help of a (logarithmically failing) maximal regularity estimate in L∞ on the level of the Stokes equation. (2) The work of Doering, Reznikoff and the first author establishing Nu ≲ Ra 1/3ln 1/3 Ra with help of the background field method. The paper contains two results. (1) The background field method can be slightly modified to yield Nu ≲ Ra 1/3ln 1/15Ra. (2) The estimates behind the background field method can be combined with the maximal regularity in L∞ to yield Nu ≲ Ra 1/3ln 1/3ln Ra - an estimate that is only a double logarithm away from the supposedly optimal scaling. © 2011 American Institute of Physics.

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