Determination of the chemical potential using energy-biased sampling

An energy-biased method to evaluate ensemble averages requiring test-particle insertion is presented. The method is based on biasing the sampling within the subdomains of the test-particle configurational space with energies smaller than a given value freely assigned. These energy-wells are located via unbiased random insertion over the whole configurational space and are sampled using the so called Hit&Run algorithm, which uniformly samples compact regions of any shape immersed in a space of arbitrary dimensions. Because the bias is defined in terms of the energy landscape it can be exactly corrected to obtain the unbiased distribution. The test-particle energy distribution is then combined with the Bennett relation for the evaluation of the chemical potential. We apply this protocol to a system with relatively small probability of low-energy test-particle insertion, liquid argon at high density and low temperature, and show that the energy-biased Bennett method is around five times more efficient than the standard Bennett method. A similar performance gain is observed in the reconstruction of the energy distribution.Comment: 10 pages, 4 figure

La riabilitazione termale nel 150° Anniversario dell'Unità d'Italia. Un testimonial d'eccezione: Giuseppe Garibaldi.

Nell’anno in cui si celebra il 150° Anniversario dell’Unità d’Italia, il riemergere di alcune lettere di Giuseppe Garibaldi - che fanno riferimento ad un periodo di cure termali effettuato presso le Terme della Ficoncella e di Traiano (vicino Civitavecchia, Roma) - ci ha dato lo spunto per questo lavoro che intende considerare i numerosi trattamenti effettuati presso diverse stazioni termali italiane dall’Eroe dei Due Mondi per una patologia reumatica (probabilmente una poliartrite reumatoide) e per gli esiti di varie ferite di guerra, in particolare la ben nota ferita da arma da fuoco subita a livello dell’arto inferiore destro nel corso della battaglia d’Aspromonte, nel 1862

Efficient numerical integrators for stochastic models

The efficient simulation of models defined in terms of stochastic differential equations (SDEs) depends critically on an efficient integration scheme. In this article, we investigate under which conditions the integration schemes for general SDEs can be derived using the Trotter expansion. It follows that, in the stochastic case, some care is required in splitting the stochastic generator. We test the Trotter integrators on an energy-conserving Brownian model and derive a new numerical scheme for dissipative particle dynamics. We find that the stochastic Trotter scheme provides a mathematically correct and easy-to-use method which should find wide applicability.Comment: v

Using Weyl operators to study Mermin's inequalities in Quantum Field Theory

Mermin's inequalities are investigated in a Quantum Field Theory framework by using von Neumann algebras built with Weyl operators. We devise a general construction based on the Tomita-Takesaki modular theory and use it to compute the vacuum expectation value of the Mermin operator, analyzing the parameter space and explicitly exhibiting a violation of Mermin's inequalities. Therefore, relying on the power of modular operators, we are able to demonstrate that Mermin's inequalities are violated when examined within the vacuum state of a scalar field theory.Comment: 8 pages, 1 figure, revised version. Accepted for publication in PR

Weyl operators, Tomita-Takesaki theory and Bell-CHSH inequality violations

The violation of the Bell-CHSH inequality in the vacuum state of a relativistic free real scalar field is established by means of the Tomita-Takesaki construction and of the direct computation of the correlation functions of Weyl operators.Comment: 9 pages, 2 figure