Ensemble inequivalence in systems with long-range interactions

Ensemble inequivalence has been observed in several systems. In particular it has been recently shown that negative specific heat can arise in the microcanonical ensemble in the thermodynamic limit for systems with long-range interactions. We display a connection between such behaviour and a mean-field like structure of the partition function. Since short-range models cannot display this kind of behaviour, this strongly suggests that such systems are necessarily non-mean field in the sense indicated here. We illustrate our results showing an application to the Blume-Emery-Griffiths model. We further show that a broad class of systems with non-integrable interactions are indeed of mean-field type in the sense specified, so that they are expected to display ensemble inequivalence as well as the peculiar behaviour described above in the microcanonical ensemble.Comment: 12 pages, no figure

Breaking of ergodicity and long relaxation times in systems with long-range interactions

The thermodynamic and dynamical properties of an Ising model with both short range and long range, mean field like, interactions are studied within the microcanonical ensemble. It is found that the relaxation time of thermodynamically unstable states diverges logarithmically with system size. This is in contrast with the case of short range interactions where this time is finite. Moreover, at sufficiently low energies, gaps in the magnetization interval may develop to which no microscopic configuration corresponds. As a result, in local microcanonical dynamics the system cannot move across the gap, leading to breaking of ergodicity even in finite systems. These are general features of systems with long range interactions and are expected to be valid even when the interaction is slowly decaying with distance.Comment: 4 pages, 5 figure

Supersonic Discrete Kink-Solitons and Sinusoidal Patterns with "Magic" wavenumber in Anharmonic Lattices

The sharp pulse method is applied to Fermi-Pasta-Ulam (FPU) and Lennard-Jones (LJ) anharmonic lattices. Numerical simulations reveal the presence of high energy strongly localized ``discrete'' kink-solitons (DK), which move with supersonic velocities that are proportional to kink amplitudes. For small amplitudes, the DK's of the FPU lattice reduce to the well-known ``continuous'' kink-soliton solutions of the modified Korteweg-de Vries equation. For high amplitudes, we obtain a consistent description of these DK's in terms of approximate solutions of the lattice equations that are obtained by restricting to a bounded support in space exact solutions with sinusoidal pattern characterized by the ``magic'' wavenumber $k=2\pi/3$. Relative displacement patterns, velocity versus amplitude, dispersion relation and exponential tails found in numerical simulations are shown to agree very well with analytical predictions, for both FPU and LJ lattices.Comment: Europhysics Letters (in print

Driven Macroscopic Quantum Tunneling of Ultracold Atoms in Engineered Optical Lattices

Coherent macroscopic tunneling of a Bose-Einstein condensate between two parts of an optical lattice separated by an energy barrier is theoretically investigated. We show that by a pulsewise change of the barrier height, it is possible to switch between tunneling regime and a self-trapped state of the condensate. This property of the system is explained by effectively reducing the dynamics to the nonlinear problem of a particle moving in a double square well potential. The analysis is made for both attractive and repulsive interatomic forces, and it highlights the experimental relevance of our findings

Kinetic theory for non-equilibrium stationary states in long-range interacting systems

We study long-range interacting systems perturbed by external stochastic forces. Unlike the case of short-range systems, where stochastic forces usually act locally on each particle, here we consider perturbations by external stochastic fields. The system reaches stationary states where external forces balance dissipation on average. These states do not respect detailed balance and support non-vanishing fluxes of conserved quantities. We generalize the kinetic theory of isolated long-range systems to describe the dynamics of this non-equilibrium problem. The kinetic equation that we obtain applies to plasmas, self-gravitating systems, and to a broad class of other systems. Our theoretical results hold for homogeneous states, but may also be generalized to apply to inhomogeneous states. We obtain an excellent agreement between our theoretical predictions and numerical simulations. We discuss possible applications to describe non-equilibrium phase transitions.Comment: 11 pages, 2 figures; v2: small changes, close to the published versio

Ruthenium(III) complexes entrapped in liposomes with enhanced cytotoxic and anti-metastatic properties

Metal-based anticancer drugs are pivotal in the fight against cancer pathologies. Since 1978 cis-platin was licensed for medical treatment of a wide number of tumor pathologies(1). However its chemiotherapic use is strongly limited by many and severe side effects and acquired tumor resistance. Since these limitations could be overcome by other metal complexes, in the last thirty years ruthenium compounds have been tested showing a remarkable antitumoral and antimetastatic activity associated with a lower toxicity. A hexacoordinate Ru(III) complex (NAMI-A) is currently undergoing advanced clinical evaluation (2). All data indicate that NAMI-A acts as a pro-drug, but the integrity of ruthenium complexes is essential to store the cytotoxic activity. In this scenario the condition of administration of ruthenium drugs are crucial to exploit their anticancer activity (3). In the last years innovative strategies have been produced to vehicle ruthenium ions in tumor cells like aggregates. This study aims to incorporate the ruthenium complexes in the inner aqueous compartment of liposomes and to test biological properties of two NAMI-A like pyridine derivatives. Specifically, we have investigated the pyridine derivatives of the sodium-compensated analogue of NAMI-A, Na[trans-RuCl4(pyridine)(DMSO)] (NAMI-Pyr) and Na[trans-RuCl4(Pytri)(DMSO)] (NAMI-Pytri). In thelatter complex the pyridine ligand is functionalized with a sugar moiety so as to increase biocompatibility and the ability to cross the cell membrane. The stability of the complexes was studied and compared in solution at different pH following UV-VIS spectra. Lipid formulations based on Egg PC were prepared adding Cholesterol, DSPE-PEG2000 joining molar ratio 57/38 /5% w/w respectively in MeOH/CHCl3 (50/50 v/v) mixture and hydrated with 0.9% w/w of NaCl. This composition was selected to reproduce analog supramolecular aggregates in clinical use to vehicle doxorubicin (Doxil). Ruthenium complexes were loaded into liposomes using the passive equilibration loading method. Full drug containing liposomes were structurally characterized by dynamic light scattering (DLS) measurements. Data indicate the formation of stable aggregates with size and shape in the right range for in vivo applications. The amount of encapsulated ruthenium complexes was quantified by means of ICP-AES. Stability and drug release properties of ruthenium containing liposomes were confirmed in buffer. The growth inhibitory effects of both liposomal and free complexes drug were tested on prostate cancer cells (PC3). Preliminary results show high cytotoxic effect of ruthenium complexes delivered by supramolecular aggregates with respect to free complexes drug

Thermodynamics of the self-gravitating ring model

We present the phase diagram, in both the microcanonical and the canonical ensemble, of the Self-Gravitating-Ring (SGR) model, which describes the motion of equal point masses constrained on a ring and subject to 3D gravitational attraction. If the interaction is regularized at short distances by the introduction of a softening parameter, a global entropy maximum always exists, and thermodynamics is well defined in the mean-field limit. However, ensembles are not equivalent and a phase of negative specific heat in the microcanonical ensemble appears in a wide intermediate energy region, if the softening parameter is small enough. The phase transition changes from second to first order at a tricritical point, whose location is not the same in the two ensembles. All these features make of the SGR model the best prototype of a self-gravitating system in one dimension. In order to obtain the stable stationary mass distribution, we apply a new iterative method, inspired by a previous one used in 2D turbulence, which ensures entropy increase and, hence, convergence towards an equilibrium state

Fingerprinting white marbles of archaeometric interest by means of combined SANS and USANS

We have performed a series of USANS and SANS measurements on a selected group of marble samples characterized by similar chemical composition but wide range of known metamorphic conditions. With these samples we start the building up of a data base in an attempt to correlate metamorphism and mesoscopic structure of white marbles. Experimental data have been analysed in terms of a hierarchical model. The present data highlight the importance of the structure at meso scale in identifying the provenance of the marble samples. A remarkable simple relation between the model parameters and the metamorphic degree has been found. This curve might represent a master curve to allow fingerprinting of white marbles. Also, two coloured marbles from Villa Adriana (Tivoli, Italy) have been investigated by means of the same techniques. Results obtained follow the general trend found for the white marbles

Models with short and long-range interactions: phase diagram and reentrant phase

We study the phase diagram of two different Hamiltonians with competiting local, nearest-neighbour, and mean-field couplings. The first example corresponds to the HMF Hamiltonian with an additional short-range interaction. The second example is a reduced Hamiltonian for dipolar layered spin structures, with a new feature with respect to the first example, the presence of anisotropies. The two examples are solved in both the canonical and the microcanonical ensemble using a combination of the min-max method with the transfer operator method. The phase diagrams present typical features of systems with long-range interactions: ensemble inequivalence, negative specific heat and temperature jumps. Moreover, in a given range of parameters, we report the signature of phase reentrance. This can also be interpreted as the presence of azeotropy with the creation of two first order phase transitions with ensemble inequivalence, as one parameter is varied continuously

Neutron tomography in modern archaeology

The search for non invasive and non destructive techniques is fundamental when dealing with samples of great historical, cultural and artistic value as well as with samples strongly degraded. Among different techniques, Neutron Tomography NT allows a close analysis of samples of Archaeological interest without damaging them. In what follows, a few cases in which the Neutron Tomography instrument of the BENSC at HMI Berlin has been successfully applied will be show