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It is sometimes speculated that the sign problem that afflicts many quantum field theories might be reduced or even eliminated by choosing an alternative domain of integration within a complexified extension of the path integral (in the spirit of the stationary phase integration method). In this paper we start to explore this possibility somewhat systematically. A first inspection reveals the presence of many difficulties but-quite surprisingly-most of them have an interesting solution. In particular, it is possible to regularize the lattice theory on a Lefschetz thimble, where the imaginary part of the action is constant and disappears from all observables. This regularization can be justified in terms of symmetries and perturbation theory. Moreover, it is possible to design a Monte Carlo algorithm that samples the configurations in the thimble. This is done by simulating, effectively, a five dimensional system. We describe the algorithm in detail and analyze its expected cost and stability. Unfortunately, the measure term also produces a phase which is not constant and it is currently very expensive to compute. This residual sign problem is expected to be much milder, as the dominant part of the integral is not affected, but we have still no convincing evidence of this. However, the main goal of this paper is to introduce a new approach to the sign problem, that seems to offer much room for improvements. An appealing feature of this approach is its generality. It is illustrated first in the simple case of a scalar field theory with chemical potential, and then extended to the more challenging case of QCD at finite baryonic density.

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We present the first practical Monte Carlo calculations of the recently proposed Lefschetz thimble formulation of quantum field theories. Our results provide strong evidence that the numerical sign problem that afflicts Monte Carlo calculations of models with complex actions can be softened significantly by changing the domain of integration to the Lefschetz thimble or approximations thereof. We study the interacting complex scalar field theory (relativistic Bose gas) in lattices of size up to 8 4 using a computationally inexpensive approximation of the Lefschetz thimble. Our results are in excellent agreement with known results. We show that-at least in the case of the relativistic Bose gas-the thimble can be systematically approached and the remaining residual phase leads to a much more tractable sign problem (if at all) than the original formulation. This is especially encouraging in view of the wide applicability-in principle-of our method to quantum field theories with a sign problem. We believe that this opens up new possibilities for accurate Monte Carlo calculations in strongly interacting systems of sizes much larger that previously possible.

The development of micelle-templated silicas (MTS) has represented one of the most original fields of materials research since the seminal papers from the Kresge and Beck groups on MCM-41 and MCM-48. [1,2] The self-assembly of surfactant aggregates and mineral species can be controlled to provide stable mesoporous materials with extremely narrow pore-size distributions. Several recent reviews show the advances in the preparation of ordered porous oxides, [3±5] as well as their applications in catalysis. [6±8] Adsorbents with narrow pore-size distribution at the nanometer scale allow new applications to be devised for the separation of large organic molecules. MCM-41 silicas have been proposed as possible stationary phases for size-exclusion chromatography, [9] normal-phase HPLC, [10] capillary gas chromatography, [11] and enantioselective HPLC. [12,13] The control of the size and shape of the adsorbent particles is an essential condition for any chromatographic application: particle-size scattering affects separation and plate height. Indeed, the preparation of spheres of MTS with predetermined monodispersed size has been the target of several research groups. Positive results have been obtained by introducing surfactant templates in classical preparations of silica gel with controlled grain size. In this way, spheres of MTS have been prepared from water ± alcohol systems, [14,15] by controlled hydrolysis, [16,17] or by spray-drying techniques. [18] A frequent drawback of these methods is the need to simultaneously optimize the conditions for the synthesis of the desired silica ± surfactant mesophase and for the successful formation of monodispersed spheres. This situation restrains the experimental conditions and makes a fine tuning of the properties of MTS, such as, pore size and topology, wall thickness, and aluminum content, difficult. It would be expedient to independently optimize the properties of the particles and the properties of the micelle-templated phase. Herein, a method to achieve this result by transformation of preformed spheres of silica gel into MTS is proposed.The synthesis procedure is directly adapted from the synthesis of MCM-41, [1,2] by using commercial spheres of silica gel as the source of silica. Lichrosphere 100 (Merck) was stirred in an alkaline solution of cetyltrimethylammonium bromide (CTAB), the molar composition of the system being 1 SiO 2 /0.25 NaOH/0.1 CTAB/20 H 2 O. After 30 min stirring at room temperature, the system was put in an autoclave at 388 K for 24 h. The parent silica (Lichrosphere 100) and the recovered solid share the same spherical morphology and granulometric distribution (Figure 1). However, while the parent silica is amorphous, the CTAB-treated solid presents the characteristic X-ray powder diffraction pattern of MCM-41. Figure 1. Pseudomorphic transformation of silica gel to MCM-41. Micrographs (a, b), granulometric distributions; the distribution is given in volume V as a function of particle diameter D p (c, d), and powder diffraction patterns (e, f) fo...

A thermoresponsive hydrogel, poly(N‐isopropylacrylamide) (poly(NIPAM)), is synthesized in situ within an oxidized porous Si template, and the nanocomposite material is characterized. Infiltration of the hydrogel into the interconnecting nanoscale pores of the porous SiO2 host is confirmed by scanning electron microscopy. The optical reflectivity spectrum of the nanocomposite hybrid displays Fabry–Pérot fringes characteristic of thin film interference, enabling direct, real‐time observation of the volume phase transition of the confined poly(NIPAM) hydrogel. Reversible optical reflectivity changes are observed to correlate with the temperature‐dependent volume phase transition of the hydrogel, providing a new means of studying nanoscale confinement of responsive hydrogels. The confined hydrogel displays a swelling and shrinking response to changes in temperature that is significantly faster than that of the bulk hydrogel. The porosity and pore size of the SiO2 template, which are precisely controlled by the electrochemical synthesis parameters, strongly influence the extent and rate of changes in the reflectivity spectrum of the nanocomposite. The observed optical response is ascribed to changes in both the mechanical and the dielectric properties of the nanocomposite.

Surprisingly, SBA-15 mesoporous silicas are not as stable as expected in water, even at room temperature, despite their thick walls. The microporosity of SBA-15, synthesized at a temperature below 110 °C, is lost during water treatment, leading to a strong decrease in specific surface area and an increase in mesopore size. Only SBA-15s without microporosity, such as the ones synthesized at 130 °C, are stable under water treatment. Investigations by nitrogen adsorption isotherms and hyperpolarized 129 Xe NMR spectroscopy have been performed in an effort to understand the silica dissolution/redeposition processes occurring during water treatment at room temperature and at the boiling point for three SBA-15s synthesized at different temperature levels: 60, 100, and 130 °C. The differences between the local curvatures of silica in the different structures explain the difference of behavior in water with respect to silica dissolution/redeposition. Similar experiments on MCM-41 lead to a totally different dissolution/redeposition process because of its thinner walls: decrease of pore size, surface area and pore volume.