Density functional theory in the canonical ensemble I General formalism

Density functional theory stems from the Hohenberg-Kohn-Sham-Mermin (HKSM) theorem in the grand canonical ensemble (GCE). However, as recent work shows, although its extension to the canonical ensemble (CE) is not straightforward, work in nanopore systems could certainly benefit from a mesoscopic DFT in the CE. The stumbling block is the fixed $N$ constraint which is responsible for the failure in proving the interchangeability of density profiles and external potentials as independent variables. Here we prove that, if in the CE the correlation functions are stripped off of their asymptotic behaviour (which is not in the form of a properly irreducible $n$-body function), the HKSM theorem can be extended to the CE. In proving that, we generate a new {\it hierarchy} of $N$-modified distribution and correlation functions which have the same formal structure that the more conventional ones have (but with the proper irreducible $n$-body behaviour) and show that, if they are employed, either a modified external field or the density profiles can indistinctly be used as independent variables. We also write down the $N$-modified free energy functional and prove that the thermodynamic potential is minimized by the equilibrium values of the new hierarchy.Comment: 17 pages, IOP style, submitted to J. Phys. Condens. Matte

Price setting behaviour in Spain: stylised facts using consumer price micro data

This paper identifies the basic features of the price setting mechanism in the Spanish economy, using a large dataset that contains over 1.1 million price records and covers around 70% of the expenditure on the CPI basket. In particular, the paper identifies differences in the frequency and size of price adjustments across types of products and explores how these general features are affected by certain specific factors: seasonality, the level of inflation, changes in indirect taxation and the practice of using psychological and round prices. We find that prices do not change often but do so by a large amount, although there is a marked heterogeneity across products. Moreover, the high frequency of price reductions suggests that there is no strong downward rigidity. Our evidence also supports the use of time and state-dependent pricing strategies. JEL Classification: E31, D40, C25consumer prices, frequency of price changes, price setting

The price setting behaviour of Spanish firms: evidence from survey data

This paper reports the results of a survey carried out by the Banco de España on a sample of around 2000 spanish firms to deepen the understanding of firms’ price setting behaviour. The main findings may be summarised as follows. Most Spanish firms are price setters that use predominantly state-dependent rules or a combination of time- and statedependent rules when reviewing their prices. Changes in costs are the main factor underlying price increases, whereas changes in market conditions (demand and competitors’ prices) are the main driving forces of price decreases. The degree of price flexibility is directly related to the share of energy inputs over total costs and to the intensity of competition, whereas it is inversely linked to the labour share. The three theories of price stickiness that receive the highest empirical support are implicit contracts, coordination failure and explicit contracts. JEL Classification: D40, E31price setting, Price stickiness, survey data

Spin transport in proximity induced ferromagnetic graphene

Magnetic gates in close proximity to graphene can induce ferromagnetic correlations. We study the effect of such induced magnetization dependent Zeeman splittings on the graphene transport properties. We estimate that induced spin splittings of the order of \Delta ~ 5 meV could be achieved with the use of magnetic insulator gates, e.g. EuO-gates, deposited on top of graphene. We demonstrate that such splittings in proximity induced ferromagnetic graphene could be determined directly from the tunneling resonances in the linear response conductance, as the top gate creates also a tunable barrier in the graphene layer. We show how such splittings could also be determined independently by magnetoresistance measurements in a spin-valve geometry. Because the spin polarization of the current near the Dirac point increases with the length of the barrier, long magnetic gates are desirable for determining \Delta experimentally.Comment: 9 pages, 11 figure

A compound figure of merit for photonic applications of metal nanocomposites

Selecting nanocomposites for photonic switching applications requires optimizing their thermal, nonlinear and two-photon absorption characteristics. We simplify this step by defining a compound figure of merit (FOM_{C}) for nanocomposites of noble metals in dielectric based on criteria that limit these structures in photonic applications, i.e. thermal heating and two-photon absorption. The device independent results predict extremely large values of FOM_{C} for a specific combination of the metal and insulator dielectric constant given by \epsilon_{h}=\frac{\epsilon_{1}-\epsilon_{2}}{2}, where \epsilon_{h} is the dielectric constant of the host and \epsilon_{1} and \epsilon_{2} are the real and imaginary parts for the metal.Comment: Appearing in Appl. Phys. Lett. (2006

Price setting behaviour in Spain: evidence from micro PPI data

This paper identifies the basic features of price setting behaviour at the producer level in the Spanish economy using a large dataset containing the micro data underlying the construction of the PPI over the period 1991-1999. It explores how these general features are affected by some specific factors (cost structure, degree of competition, demand conditions, government intervention, level of inflation, seasonality, and the practice of using attractive prices) and presents a comparison of price setting practices at the producer and at the consumer level to ascertain whether the retail sector augments or mitigates price stickiness. We find that prices do not change often but do so by a large amount. The cost structure, proxied by the labour share and the relevance of raw materials, and the degree of competition, proxied by import penetration, affect price flexibility. We also find some evidence that producer prices are more flexible than consumer prices. JEL Classification: E31, D40frequency of price changes, price setting, producer prices

Do decreasing hazard functions for price changes make any sense?

A common finding in empirical studies using micro data on consumer and producer prices is that hazard functions for price changes are decreasing. This means that a firm will have a lower probability of changing its price the longer it has kept it unchanged. This result is at odds with standard models of price setting. Here a simple explanation is proposed: decreasing hazards may result from aggregating heterogeneous price setters. We show analytically the form of this heterogeneity effect for the most commonly used pricing rules and find that the aggregate hazard is (nearly always decreasing. Results are illustrated using Spanish producer and consumer price data. We find that a very accurate representation of individual data is obtained by considering just 4 groups of agents: one group of flexible Calvo agents, one group of intermediate Calvo agents and one group of sticky Calvo agents plus an annual Calvo process. JEL Classification: C40, D40, E30hazard function, Heterogeneous Agents, mixture models, price setting models

Determinants of domestic and cross-border bank acquisitions in the European Union

This paper analyzes the determinants of bank acquisitions both within and across 25 members of the European Union (EU-25) during the period 1997–2004. Our results suggest that poorly managed banks (those with a high cost-to-income ratio) and larger banks are more likely to be acquired by other banks in the same country. The probability of being a target in a cross-border deal is larger for banks that are quoted in the stock market. Finally, banks operating in more concentrated markets are less likely to be acquired by other banks in the same country but are more likely to be acquired by banks in other EU-25 countries.Banks and banking - Europe