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Josephson-like junctions, transiently established in heavy ion collisions between superfluid nuclei, few MeV below the Coulomb barrier, allow for the back and forth transfer of a nuclear Cooper pair of effectively charged nucleons and thus the emission of $\gamma$-rays. The second order DWBA $T$-matrix formulation of single Cooper pair alternating current is shown to contain the gauge phases and gauge rotational frequencies as required by the Josephson (ac) effect, in keeping with the derivation of the transfer (tunneling) Hamiltonian in a gauge invariant representation. We describe the emergence of two strongly convergent parameters (conserved quantities) within the time the abnormal densities of the two superfluid nuclei overlap: a) the correlation length (dc); b) the number of emitted $\gamma$-rays per cycle (ac), and thus the dipole moment of the successively transferred nucleons. Result which leads to a nuclear parallel with the direct current (dc) and alternating current (ac) Josephson effects, and which testifies to the validity of BCS theory of superconductivity down to few Cooper pair condensates, and single Cooper pair alternating currents. The physics at the basis of a quantitative description of Cooper pair tunneling between weakly coupled superconductors or superfluid nuclei at energies below the Coulomb barrier, is that the process is dominated by the successive transfer of the two partner fermions entangled over distances of the order of the coherence length, $\approx10^4$\AA ${}$ in the case of lead, and 13.5 fm in the case of the reaction $^{116}\text{Sn}+^{60}\text{Ni}\to^{114}\text{Sn(gs)}+^{62}\text{Ni(gs)}$ at few MeV below the Coulomb barrier.

Effective charged neutrons involved in one- and two- nucleon tunneling processes in heavy ion collisions between superfluid nuclei are expected to emit photons. Although the centroid, width and integrated energy area characterizing the associated gamma-strength functions are rather similar, the corresponding line shapes reflect the thermal equilibrated-like character of the quasiparticle transfer (1n-channel, blackbody spectral functional dependence), and the quantal coherent character of the Cooper pair transfer (2n-channel, Gaussian functional dependence) respectively. The predicted angular distributions, polarizations and analyzing power provide further insight into the profoundly different physics to be found at the basis of what can be considered a transient Joule-like and a (ac) Josephson-like nuclear processes

The phenomenon of low-temperature superconductivity is intimately associated with the condensation of weakly bound, very extended, strongly overlapping Cooper pairs, and systematic experimental studies of the associated mean square radius (coherence length) have been made. While the extension of BCS theory to the atomic nucleus has been successful beyond expectation, to our knowledge, no measurement of the nuclear coherence length (expected to be much larger than nuclear dimensions) has been reported in the literature. Recent studies of Cooper pair transfer across a Josephson-like junction, transiently established in a heavy ion collision between superfluid nuclei, have likely changed the situation, providing the experimental input for a quantitative estimate of the nuclear coherence length, as well as the basis for a nuclear analogue of the (ac) Josephson effect.

While Josephson-like junctions, transiently established in heavy ion collisions ($\tau_{coll}\approx10^{-21}$ s) between superfluid nuclei --through which Cooper pair tunneling ($Q$-value $Q_{2n}$) proceeds mainly in terms of successive transfer of entangled nucleons-- is deprived from the macroscopic aspects of a supercurrent, it displays many of the special effects associated with spontaneous symmetry breaking in gauge space (BCS condensation), which can be studied in terms of individual quantum states and of tunneling of single Cooper pairs. From the results of studies of one- and two- neutron transfer reactions carried out at energies below the Coulomb barrier we estimate the value of the mean square radius (correlation length) of the nuclear Cooper pair. A quantity related to the largest distance of closest approach for which the absolute two-nucleon tunneling cross section is of the order of the single-particle one. Furthermore, emission of $\gamma$-rays of (Josephson) frequency $\nu_J=Q_{2n}/h$ distributed over an energy range $\hbar/\tau_{coll}$ is predicted.

The properties of the two-quasiparticle-like soft E1-modes and PDR have been and are systematically studied with the help of inelastic and electromagnetic experiments which essentially probe the particle-hole components of these vibrations. It is shown that further insight in their characterisation can be achieved with the help of two-nucleon transferreactions, in particular concerning the particle-particle components of the modes, in terms of absolute differential cross sections which take properly into account successive and simultaneous transfer mechanisms corrected for non-orthogonality, able to reproduce the experimental findings at the 10% level. The process $^9$Li$(t,p)^{11}$Li(1$^-$) is discussed, and absolute cross sections predicted., Comment: Typo corrected with respect to previous version

The properties of the quantum electrodynamic (QED) vacuum in general, and of the nuclear vacuum (ground) state in particular are determined by virtual processes implying the excitation of a photon and of an electron--positron pair in the first case and of, for example, the excitation of a collective quadrupole surface vibration and a particle--hole pair in the nuclear case. Signals of these processes can be detected in the laboratory in terms of what can be considered a nuclear analogue of Hawking radiation. An analogy which extends to other physical processes involving QED vacuum fluctuations like the Lamb shift, pair creation by $\gamma-$rays, van der Waals forces and the Casimir effect, to the extent that one concentrates on the eventual outcome resulting by forcing a virtual process to become real, and not on the role of the black hole role in defining the event horizon. In the nuclear case, the role of this event is taken over at a microscopic, fully quantum mechanical level, by nuclear probes (reactions) acting on a virtual particle of the zero point fluctuation (ZPF) of the nuclear vacuum in a similar irreversible, no--return, fashion as the event horizon does, letting the other particle, entangled with the first one, escape to infinity, and eventually be detected. With this proviso in mind one can posit that the reactions $^1$H($^{11}$Be,$^{10}$Be$(2^+$;3.37 ${\rm MeV}$))$^2$H and $^{1}$H($^{11}$Li,$^9$Li($1/2^-$; 2.69 ${\rm MeV}$))$^3$H together with the associated $\gamma-$decay processes indicate a possible nuclear analogy of Hawking radiation.

We show, within the framework of renormalized nuclear field theory and of the induced reaction surrogate formalism, that the highly debated $^{10}$Li structure, observed in a recent $^9$Li(d,p)$^{10}$Li one--neutron transfer experiment is consistent with or better, requires the presence of a virtual $1/2^+$ state of similar single--particle strength than that of the $1/2^-$ resonance at 0.45$\pm$ 0.03 MeV. Based on continuum spectroscopy self-energy techniques, we find that the physical mechanism responsible for parity inversion in $^{10}_3$Li is the same as that at the basis of the similar phenomenon observed in $^{11}_4$Be and to that needed in $^{11}$Li to have an important $s$--wave ground state component. Furthermore, it is also consistent with the (normal) sequence of the $1p_{1/2}$ and $2s_{1/2}$ levels in the $N=7$ isotones $^{12}_5$B and $^{13}_6$C., Comment: Revised text and figures. The paper includes supplemental material

The nuclei 11Be and 11Li provide paradigmatic examples of one-and two- neutron halo systems. Because the reaction 1H(11Li,9Li)3H is dominated by successive transfer, one can use the quantitative picture emerging from a nu- clear field theory description of the structure and reaction mechanism of the above Cooper pair transfer process and of the 2H(10Be,11Be)1H and 1H(11Be,10Be)2H reactions, to shed light on the structure of 10Li. This analysis provides important support for a parity inverted scenario with a 1/2+ virtual state at about 0.2 MeV., Comment: Proceedings of the 15th Varenna Conference on Nuclear Reaction Mechanisms

The centroid, width and percentage of energy weighted sum rule of dipole resonances can be strongly affected by dynamical fluctuations and static deformations of the nuclear surface, deformations and fluctuations which, in turn, depend on pairing, and thus on Cooper pairs. Because of angular momentum conservation, such insight is restricted, to lowest order, to deformations of quadrupole and monopole type. The latter being closely connected with the neutron (excess) skin and thus with soft dipole modes. From the values $(N-Z)/A \approx 0.18$, 0.21, and 0.45 for the nuclei $^{122}$Sn, $^{208}$Pb, and $^{11}$Li, it is expected that the latter system, which is weakly bound by pairing effects (spatially extended single Cooper pair and odd proton acting as spectator), constitutes an attractive laboratory to study the properties of soft $E1$--modes and thus of isospin nuclear deformation. From the calculation of the full dipole response function in QRPA, discretizing the continuum in a spherical box of radius of 40 fm, one finds a GDR with centroid $E_x \approx 24$ MeV, width $\Gamma \approx$ 11 MeV and carrying 90\% of the EWSR, and a low--lying collective resonance characterized by $E_X = 0.75$ MeV, $\Gamma = 0.5$ MeV and $6.2\%$ EWSR The wave function of the latter resonance is built out of about fifteen components (both protons and neutrons), typical of a collective mode. The transition densities indicate this soft $E1$--mode to be generated by surface density oscillation of the neutron skin ($\Delta r_{np} \approx 1.71$ fm) relative to an approximately isospin--saturated core. Through a detailed study of the full dipole response of $^{11}$Li we will draw a comparison between the soft $E1$--mode of this halo nucleus and the PDR of heavy stable nuclei, pointing to the physical similarities and also to the basic differences., Comment: submitted to Physica Scripta, Focus-issue-on-Nuclear-Shapes-and-Symmetries-From-Experiment-to-Theory

The physical reason why one can calculate with similar accuracy, as compared to the experimental data, the absolute cross section associated with two-nucleon transfer processes between members of pairing rotational bands, making use of simple BCS (constant matrix elements) or of many-body (Nambu-Gorkov (NG), nuclear field theory (NFT)) spectroscopic amplitudes, is not immediately obvious. Restoration of spontaneous symmetry breaking and associated emergent generalised rigidity in gauge space provides the answer, and points to a new emergence: a physical sum rule resulting from the intertwining of structure and reaction processes and closely connected with the central role induced pairing interaction plays in structure together with the fact that successive transfer dominates Cooper pair tunnelling.

The exotic nucleus 11Be has been extensively studied and much experimental information is available on the structure of this system. Treating, within the framework of empirically renormalised nuclear field theory in both configuration and 3D-space, the mixing of bound and continuum single-particle states through the coupling to collective particle-hole (p,h) and pairing vibrations of the 10Be core, as well as Pauli principle acting not only between the particles explicitly considered and those participating in the collective states, but also between fermions involved in two-phonon virtual states it is possible, for the first time, to simultaneously and quantitatively account for the energies of the 1/2+,1/2- low-lying states, the centroid and line shape of the 5/2+ resonance, the one-nucleon stripping and pickup absolute differential cross sections involving 11Be as either target or residual nucleus, and the dipole transitions connecting the 1/2+ and 1/2- parity inverted levels as well as the charge radius, thus providing a unified and exhaustive characterisation of the many-body effects which are at the basis of this paradigmatic one-neutron halo system., Comment: Supplemental materials included

Nuclear Field Theory of structure and reactions is confronted with observations made on neutron halo dripline nuclei, resulting in the prediction of a novel (symbiotic) mode of nuclear excitation, and on the observation of the virtual effect of the halo phenomenon in the apparently non-halo nucleus $^7$Li. This effect is forced to become real by intervening the virtual process with an external (t,p) field which, combined with accurate predictive abilities concerning the absolute differential cross section, reveals an increase of a factor 2 in the cross section due to the presence of halo ground state correlations, and is essential to reproduce the value of the observed $d \sigma(^7$Li(t,p)$^9$Li)/d$\Omega$., Comment: Submitted to CERN proceedings for the 14th International Conference on Nuclear Reaction mechanisms, Varenna, June 15 - 19, 2015

A complete characterization of the structure of nuclei can be obtained by combining information arising from inelastic scattering, Coulomb excitation and $\gamma-$decay, together with one- and two-particle transfer reactions. In this way it is possible to probe the single-particle and collective components of the nuclear many-body wavefunction resulting from their mutual coupling and diagonalising the low-energy Hamiltonian. We address the question of how accurately such a description can account for experimental observations. It is concluded that renormalizing empirically and on equal footing bare single-particle and collective motion in terms of self-energy (mass) and vertex corrections (screening), as well as particle-hole and pairing interactions through particle-vibration coupling allows theory to provide an overall, quantitative account of the data.

An essentially "complete" description of the low-energy nuclear structure of the superfluid nucleus $^{120}$Sn and of its odd-$A$ neighbors is provided by the observations carried out with the help of Coulomb excitation and of one-- and of two-- particle transfer reactions, specific probes of vibrations, quasiparticle and pairing degrees of freedom respectively, and of their mutual couplings. These experimental findings are used to stringently test the predictions of a similarly "complete" description of $^{119,120,121}$Sn carried out in terms of elementary modes of excitation which, through their interweaving, melt together into effective fields, each displaying properties reflecting that of all others, there individuality resulting from the actual relative importance of each one. Its implementation is done by solving the Nambu-Gor'kov equations including, for the first time, all medium polarization effects resulting from the interweaving of quasiparticles, spin and surface vibrations, taking into account, within the framework of nuclear field theory (NFT), the variety of processes leading to self-energy, vertex and Pauli principle corrections, and to the induced pairing interaction. Theory provides an overall quantitative account of the experimental findings. From these results one can, not only obtain strong circumstantial evidence for the inevitability for the dual origin of pairing in nuclei but also, extract information which can be used at profit to quantitatively disentangle the contributions to pairing correlations in general and to the pairing gap in particular, arising from the bare and from the induced pairing interactions., Comment: 13 pages, 5 figures

The second order DWBA implementation of two-particle transfer direct reactions which includes simultaneous and successive transfer, properly corrected by non-orthogonality effects is tested with the help of controlled nuclear structure and reaction inputs against data spanning the whole mass table, and showed to constitute a quantitative probe of nuclear pairing correlations.

Pairing rotations and pairing vibrations are collective modes associated with a field, the pair field, which changes the number of particles by two. Consequently, they can be studied at profit with the help of two-particle transfer reactions on superfluid and in normal nuclei, respectively. The advent of exotic beams has opened, for the first time, the possibility to carry out such studies in medium heavy nuclei, within the same isotopic chain. In the case studied in the present paper that of the Sn-isotopes (essentially from closed (Z=N=50) to closed (Z=50,N=82) shells). The static and dynamic off-diagonal, long range order phase coherence in gauge space displayed by pairing rotations and vibrations respectively, leads to coherent states which behave almost classically. Consequently, these modes are amenable to an accurate nuclear structure description in terms of simple models containing the right physics, in particular BCS plus QRPA and HF mean field plus RPA respectively. The associated two- nucleon transfer spectroscopic amplitudes predicted by such model calculations can thus be viewed as essentially "exact". This fact, together with the availability of optical potentials for the different real and virtual channels involved in the reactions considered, namely (A+2)Sn+p, (A+1)Sn+d and (A)Sn+t, allows for the calculation of the associated absolute cross sections without, arguably, free parameters. The numerical predictions of the absolute differential cross sections, obtained making use of the above mentioned nuclear structure and optical potential inputs, within the framework of second order DWBA, taking into account simultaneous, successive and non-orthogonality contributions provide, within experimental errors an overall account of the experimental findings for all of the measured (A+2)Sn(p,t)(A)Sn(gs) reactions, for which absolute cross sections have been reported to date., Comment: 71 pages, 17 figures

Many of the concepts which are at the basis of the development associated with a quantitative treatment of the variety of phenomena associated with the spontaneous breaking of gauge symmetry in nuclei have been instrumental in connection with novel studies of soft matter, namely of protein evolution and protein folding. Although the route to these subjects and associated development does not necessarily imply the nuclear physics connection, such a connection has proven qualitatively and quantitatively inspiring. In particular to model protein evolution in terms of the alignment of quasispins displaying twenty different projections, one for each of the twenty amino acids occurring in nature, and the associated symmetry breaking in information (sequence) space. Emergent properties of the corresponding phase transition are domain walls which stabilize local elementary structures (LES), few groups of 10-20 aminoacids which become structured already in the denatured state provide the molecular recognition directing protein folding. In fact, their docking is closely related to the transition state of the process. While the two-step, yes or no, folding process, does not provide direct information concerning LES, one can force LES from virtual to become real, observable final state entities. Getting again inspiration from the nuclear case (virtual processes contributing to pair correlations can be forced to become real with the help of a probe which itself changes particle number by two), one would expect that to make real virtual LES, that is segments of the protein which already at an early stage of the folding process flicker in and out of their native conformation, one needs a probe which itself displays a similar behaviour. Peptides displaying a sequence identical to LES are such probes., Comment: Contribution to the Volume 50 years of Nuclear BCS edited by World Scientific

Learning how proteins fold will hardly have any impact in the way conventional -- active site centered -- drugs are designed. On the other hand, this knowledge is proving instrumental in defining a new paradigm for the identification of drugs against any target protein: folding inhibition. Targeting folding renders drugs less prone to elicit spontaneous genetic mutations which in many cases, notably in connection with viruses like the Human Immunodeficiency Virus (HIV), can block therapeutic action. From the progress which has taken place during the last years in the understanding of the becoming of a protein, and how to read from the corresponding sequences the associated three-dimensional, biologically active, native structure, the idea of non-conventional (folding) inhibitors and thus of leads to eventual drugs to fight disease, arguably, without creating resistance, emerges as a distinct possibility.

Absolute values of two-particle transfer cross sections along the Sn-isotopic chain from closed shell to closed shell (100Sn,132Sn) are calculated taking properly into account nuclear correlations, as well as the successive, simultaneous and non-orthogonality contributions to the differential cross sections. The results are compared with systematic, homogeneous bombarding conditions (p, t) data. The observed agreement, almost within statistical errors and without free parameters, testify to the fact that theory is able to be quantitative in its predictions.

We study the linear response of the inner crust of neutron stars within the Random Phase Approximation, employing a Skyrme-type interaction as effective interaction. We adopt the Wigner-Seitz approximation, and consider a single unit cell of the Coulomb lattice which constitutes the inner crust, with a nucleus at its center, surrounded by a sea of free neutrons. With the use of an appropriate operator, it is possible to analyze in detail the properties of the vibrations of the surface of the nucleus and their interaction with the modes of the sea of free neutrons, and to investigate the role of shell effects and of resonant states.

We present a calculation of the properties of vibrational states in deformed, axially--symmetric even--even nuclei, within the framework of a fully self--consistent Quasparticle Random Phase Approximation (QRPA). The same Skyrme energy density and density-dependent pairing functionals are used to calculate the mean field and the residual interaction in the particle-hole and particle-particle channels. We have tested our software in the case of spherical nuclei against fully self consistent calculations published in the literature, finding excellent agreement. We investigate the consequences of neglecting the spin-orbit and Coulomb residual interactions in QRPA. Furthermore we discuss the improvement obtained in the QRPA result associated with the removal of spurious modes. Isoscalar and isovector responses in the deformed ${}^{24-26}$Mg, $^{34}$Mg isotopes are presented and compared to experimental findings.

The bare NN-potential, parametrized so as to reproduce the nuclear phase shifts leads to a sizable Cooper pair binding energy in nuclei along the stability valley. It is a much debated matter whether this value accounts for the "empirical" value of the pairing gap or whether a similarly important contribution arises from the exchange of collective vibrations between Cooper pair partners. In keeping with the fact that two-particle transfer reactions are the specific probe of pairing in nuclei, and that exotic halo nuclei like 11Li are extremely polarizable, we find that the recent studied reaction, namely 11Li+p -> 9Li+t, provides direct evidence of phonon mediated pairing in nuclei.

With the help of a unified description of the nuclear structure and of the direct reaction mechanism we show that a recent 1H(11Li,9Li)3H experiment provides, for the first time in nuclear physics, direct evidence of phonon mediated pairing., Comment: 9 pages, 4 figures. Major changes

The line shape of the plasma resonance in both neutral and charged small sodium clusters is calculated. The overall properties of the multipeak structure observed in the photoabsorption cross section of spherical Na_8 and Na_20 neutral clusters can be understood in terms of Landau damping. Quantal configurations are shown to play an important role. In the case of charged Na_9+ and Na_21^+ clusters a single peak is predicted that carries most of the oscillator strength., Comment: This early (1989) jellium matrix-RPA/LDA (TDLDA in Fock space) study: 1) introduced the physics of spectral Landau-damping fragmentation for metal clusters; 2) explained the double line of the neutral Na_20; 3) predicted a 25% strength at high energies (recently seen experimentally); 4) predicted reduced fragmentation for cationic clusters (later seen experimentally)

We discuss in this paper both the past and the present of two-nucleon transfer reactions, as well as try to foresee the near future of such studies in nuclei, induced by light as well as by heavy ion reactions., Comment: Massive changes, 64 pages, submitted to Physics Reports

The high computational cost of carrying out molecular dynamics simulations of even small-size proteins is a major obstacle in the study, at atomic detail and in explicit solvent, of the physical mechanism which is at the basis of the folding of proteins. Making use of a biasing algorithm, based on the principle of the ratchet-and-pawl, we have been able to calculate eight folding trajectories (to an RMSD between 1.2A and 2.5A) of the B1 domain of protein G in explicit solvent without the need of high-performance computing. The simulations show that in the denatured state there is a complex network of cause-effect relationships among contacts, which results in a rather hierarchical folding mechanism. The network displays few local and nonlocal native contacts which are cause of most of the others, in agreement with the NOE signals obtained in mildly-denatured conditions. Also nonnative contacts play an active role in the folding kinetics. The set of conformations corresponding to the transition state display phi-values with a correlation coefficient of 0.69 with the experimental ones. They are structurally quite homogeneous and topologically native-like, although some of the side chains and most of the hydrogen bonds are not in place.

Here we present a program aimed at free-energy calculations in molecular systems. It consists of a series of routines that can be interfaced with the most popular classical molecular dynamics (MD) codes through a simple patching procedure. This leaves the possibility for the user to exploit many different MD engines depending on the system simulated and on the computational resources available. Free-energy calculations can be performed as a function of many collective variables, with a particular focus on biological problems, and using state-of-the-art methods such as metadynamics, umbrella sampling and Jarzynski-equation based steered MD. The present software, written in ANSI-C language, can be easily interfaced with both fortran and C/C++ codes., Comment: to be submitted to Computer Physics Communications

The 1S0 pairing gap associated with the inner crust of a neutron star is calculated, taking into account the coexistence of the nuclear lattice with the sea of free neutrons (finite size effects), as well as medium polarization effects associated with the exchange of density and spin fluctuations. Both effects are found to be important and to lead to an overall quenching of the pairing gap. This result, whose quantitative value is dependent on the effective interaction used to generate the single-particle levels, is a consequence of the balance between the attractive (repulsive) induced interaction arising from the exchange of density (spin) modes, balance which in turn is influenced by the presence of the protons and depends on the single-particle structure of the system., Comment: 10 pages, 9 figures. Version 2: a new figure inserted, some misprints fixed

The structure of a vortex in the inner crust of neutron stars is calculated within the framework of quantum mean field theory taking into account the interaction with the nuclei composing the Coulomb lattice. Making use of the results obtained with different nuclear interactions, the pinning energy, relevant in the study of glitches, is worked out. Quantal size and density dependent effects are found to be important.

The bare nucleon-nucleon interaction is essential for the production of pair correlations in nuclei, but an important contribution also arises from the induced interaction resulting from the exchange of collective vibrations between nucleons moving in time reversal states close to the Fermi energy. The pairing field resulting from the summed interaction is strongly peaked at the nuclear surface. It is possible to reproduce the detailed spatial dependence of this field using a Local Density Approximation (LDA) and a contact interaction, with parameters which are quite different from those commonly used in more phenomenological approaches.

Metadynamics is a powerful computational tool to obtain the free energy landscape of complex systems. The Monte Carlo algorithm has proven useful to calculate thermodynamic quantities associated with simplified models of proteins, and thus to gain an ever-increasing understanding on the general principles underlying the mechanism of protein folding. We show that it is possible to couple metadynamics and Monte Carlo algorithms to obtain the free energy of model proteins in a way which is computationally very economical., Comment: Submitted to Gene

The free-energy landscape of the alpha-helix of protein G is studied by means of metadynamics coupled with a solute tempering algorithm. Metadynamics allows to overcome large energy barriers, whereas solute tempering improves the sampling with an affordable computational effort. From the sampled free-energy surface we are able to reproduce a number of experimental observations, such as the fact that the lowest minimum corresponds to a globular conformation displaying some degree of beta-structure, that the helical state is metastable and involves only 65% of the chain. The calculations also show that the system populates consistently a pi-helix state and that the hydrophobic staple motif is present only in the free-energy minimum associated with the helices, and contributes to their stabilization. The use of metadynamics coupled with solute tempering results then particularly suitable to provide the thermodynamics of a short peptide, and its computational efficiency is promising to deal with larger proteins.

The Metropolis implementation of the Monte Carlo algorithm has been developed to study the equilibrium thermodynamics of many-body systems. Choosing small trial moves, the trajectories obtained applying this algorithm agree with those obtained by Langevin's dynamics. Applying this procedure to a simplified protein model, it is possible to show that setting a threshold of 1 degree on the movement of the dihedrals of the protein backbone in a single Monte Carlo step, the mean quantities associated with the off-equilibrium dynamics (e.g., energy, RMSD, etc.) are well reproduced, while the good description of higher moments requires smaller moves. An important result is that the time duration of a Monte Carlo step depends linearly on the temperature, something which should be accounted for when doing simulations at different temperatures., Comment: corrections to the text and to the figures