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Micro-pattern gaseous detectors (MPGDs) are a promising readout technology for hadronic calorimeters (HCAL) thanks to their good space resolution, longevity and rate capability. We describe the development of a HCAL based on MPGDs for an experiment at the proposed Muon Collider. The design of a semi-digital MPGD-HCAL is shown and its performance is calculated with Monte Carlo simulations with high-energy pions, showing an energy resolution down to 8\% for \SI{80}{\giga\eV} pions. We also present the performance of twelve MPGD prototypes with different technologies (MicroMegas, $\mu$-RWELL and RPWELL) assembled and operated in test beam first with high-energy muons and later with pions in a hadronic calorimeter prototype of $\sim1\,\lambda_\text{I}$ length; the detectors have a good response uniformity (lower than 17\%) and space resolution and their performance in the calorimeter shows very good agreement with the Monte Carlo shower calculation.

Very recently, the validity of the concept of negative temperature has been challenged by several authors since they consider Boltzmann's entropy (that allows negative temperatures) inconsistent from a mathematical and statistical point of view, whereas they consider Gibbs' entropy (that does not admit negative temperatures) the correct definition for microcanonical entropy. In the present paper we prove that for systems with equivalence of the statistical ensembles Boltzmann entropy is the correct microcanonical entropy. Analytical results on two systems supporting negative temperatures, confirm the scenario we propose. In addition, we corroborate our proof by numeric simulations on an explicit lattice system showing that negative temperature equilibrium states are accessible and obey standard statistical mechanics prevision., Comment: To appear in Annals of Physics

Open many-body quantum systems have attracted renewed interest in the context of quantum information science and quantum transport with biological clusters and ultracold atomic gases. The physical relevance in many-particle bosonic systems lies in the realization of counter-intuitive transport phenomena and the stochastic preparation of highly stable and entangled many-body states due to engineered dissipation. We review a variety of approaches to describe an open system of interacting ultracold bosons which can be modeled by a tight-binding Hubbard approximation. Going along with the presentation of theoretical and numerical techniques, we present a series of results in diverse setups, based on a master equation description of the dissipative dynamics of ultracold bosons in a one-dimensional lattice. Next to by now standard numerical methods such as the exact unravelling of the master equation by quantum jumps for small systems and beyond mean-field expansions for larger ones, we present a coherent-state path integral formalism based on Feynman-Vernon theory applied to a many-body context.

The notion of negative absolute temperature emerges naturally from Boltzmann's definition of "surface" microcanonical entropy in isolated systems with a bounded energy density. Recently, the well-posedness of such construct has been challenged, on account that only the Gibbs "volume" entropy ---and the strictly positive temperature thereof--- would give rise to a consistent thermodynamics. Here we present analytical and numerical evidence that Boltzmann microcanonical entropy provides a consistent thermometry for both signs of the temperature. In particular, we show that Boltzmann (negative) temperature allows the description of phase transitions occurring at high energy densities, at variance with Gibbs temperature. Our results apply to nonlinear lattice models standardly employed to describe the propagation of light in arrays of coupled waveguides and the dynamics of ultracold gases trapped in optical lattices. Optically induced photonic lattices, characterized by saturable nonlinearity, are particularly appealing because they offer the possibility of observing states ---and phase transitions--- at both signs of the temperature., Comment: 14 pages, 8 figures. Expanded some concepts. Added one figure in the Appendix and some new references

We address the stability of superfluid currents in a system of interacting lattice bosons. We consider various Gutzwiller trial states for the quantum phase model which provides a good approximation for the Bose-Hubbard model in the limit of large interactions and boson populations. We thoroughly analyze the current-carrying stationary states of the dynamics ensuing from a Gaussian ansatz, and derive analytical results for the critical lines signaling their modulational and energetic instability, as well as the maximum of the carried current. We show that these analytical results are in good qualitative agreement with those obtained numerically in previous works on the Bose-Hubbard model, and in the present work for the quantum phase model., Comment: 10 pages, 5 figures

In this paper we consider a bosonic Josephson junction described by a two-mode Bose-Hubbard model, and we thoroughly analyze a quantum phase transition occurring in the system in the limit of infinite bosonic population. We discuss the relation between this quantum phase transition and the dynamical bifurcation occurring in the spectrum of the Discrete Self Trapping equations describing the system at the semiclassical level. In particular, we identify five regimes depending on the strength of the effective interaction among bosons, and study the finite-size effects arising from the finiteness of the bosonic population. We devote a special attention to the critical regime which reduces to the dynamical bifurcation point in the thermodynamic limit of infinite bosonic population. Specifically, we highlight an anomalous scaling in the population imbalance between the two wells of the trapping potential, as well as in two quantities borrowed from Quantum Information Theory, i.e. the entropy of entanglement and the ground-state fidelity. Our analysis is not limited to the zero temperature case, but considers thermal effects as well., Comment: 13 pages, 10 figures

We consider an ultra-small system of polarized bosons on an optical lattice with a ring topology interacting via long range dipole-dipole interactions. Dipoles polarized perpendicular to the plane of the ring reveal sharp transitions between different density wave phases. As the strength of the dipolar interactions is varied the behavior of the transitions is first-order like. For dipoles polarized in the plane of the ring the transitions between possible phases show pronounced sensitivity to the lattice depth. The abundance of possible configurations may be useful for quantum information applications., Comment: decompressed version now reaching 6 pages

We illustrate how dynamical transitions in nonlinear semiclassical models can be recognized as phase transitions in the corresponding -- inherently linear -- quantum model, where, in a Statistical Mechanics framework, the thermodynamic limit is realized by letting the particle population go to infinity at fixed size. We focus on lattice bosons described by the Bose-Hubbard (BH) model and Discrete Self-Trapping (DST) equations at the quantum and semiclassical level, respectively. After showing that the gaussianity of the quantum ground states is broken at the phase transition, we evaluate finite populations effects introducing a suitable scaling hypothesis; we work out the exact value of the critical exponents and we provide numerical evidences confirming our hypothesis. Our analytical results rely on a general scheme obtained from a large-population expansion of the eigenvalue equation of the BH model. In this approach the DST equations resurface as solutions of the zeroth-order problem., Comment: 4 pages, 3 figures; a few changes made in the layout of equations; improved visibility of some figures; added some references and endnotes

We consider correlated L\'evy walks on a class of two- and three-dimensional deterministic self-similar structures, with correlation between steps induced by the geometrical distribution of regions, featuring different diffusion properties. We introduce a geometric parameter $\alpha$, playing a role analogous to the exponent characterizing the step-length distribution in random systems. By a {\it single-long jump} approximation, we analytically determine the long-time asymptotic behavior of the moments of the probability distribution, as a function of $\alpha$ and of the dynamic exponent $z$ associated to the scaling length of the process. We show that our scaling analysis also applies to experimentally relevant quantities such as escape-time and transmission probabilities. Extensive numerical simulations corroborate our results which, in general, are different from those pertaining to uncorrelated L\'evy-walks models., Comment: 10 pages, 11 figures; some concepts rephrased to improve on clarity; a few references added; symbols and line styles in some figures changed to improve on visibility

We consider the Bose-Hubbard model describing attractive bosonic particles hopping across the sites of a translation-invariant lattice, and compare the relevant ground-state properties with those of the corresponding symmetry-breaking semiclassical nonlinear theory. The introduction of a suitable measure allows us to highlight many correspondences between the nonlinear theory and the inherently linear quantum theory, characterized by the well-known self-trapping phenomenon. In particular we demonstrate that the localization properties and bifurcation pattern of the semiclassical ground-state can be clearly recognized at the quantum level. Our analysis highlights a finite-number effect., Comment: 9 pages, 8 figures

We study the dynamical stability of the macroscopic quantum oscillations characterizing a system of three coupled Bose-Einstein condensates arranged into an open-chain geometry. The boson interaction, the hopping amplitude and the central-well relative depth are regarded as adjustable parameters. After deriving the stability diagrams of the system, we identify three mechanisms to realize the transition from an unstable to stable behavior and analyze specific configurations that, by suitably tuning the model parameters, give rise to macroscopic effects which are expected to be accessible to experimental observation. Also, we pinpoint a system regime that realizes a Josephson-junction-like effect. In this regime the system configuration do not depend on the model interaction parameters, and the population oscillation amplitude is related to the condensate-phase difference. This fact makes possible estimating the latter quantity, since the measure of the oscillating amplitudes is experimentally accessible., Comment: 25 pages, 12 figures

We study a two-dimensional Bose-Hubbard model at a zero temperature with random local potentials in the presence of either uniform or binary disorder. Many low-energy metastable configurations are found with virtually the same energy as the ground state. These are characterized by the same blotchy pattern of the, in principle, complex nonzero local order parameter as the ground state. Yet, unlike the ground state, each island exhibits an overall random independent phase. The different phases in different coherent islands could provide a further explanation for the lack of coherence observed in experiments on Bose glasses., Comment: 14 pages, 4 figures

We consider strongly interacting boson-boson mixtures on one-dimensional lattices and, by adopting a qualitative mean-field approach, investigate their quantum phases as the interspecies repulsion is increased. In particular, we analyze the low-energy "quantum emulsion" metastable states occurring at large values of the interspecies interaction, which are expected to prevent the system from reaching its true ground state. We argue a significant decrease in the visibility of the time-of-flight images in the case of these spontaneously disordered states., Comment: 10 pages, 2 figures - to appear in the topical issue on "Novel Quantum Phases and Mesoscopic Physics in Quantum Gases" of the European Physical Journal B (2009)

Recently it has been suggested that fermions whose hopping amplitude is quenched to extremely low values provide a convenient source of local disorder for lattice bosonic systems realized in current experiment on ultracold atoms. Here we investigate the phase diagram of such systems, which provide the experimental realization of a Bose-Hubbard model whose local potentials are randomly extracted from a binary distribution. Adopting a site-dependent Gutzwiller description of the state of the system, we address one- and two-dimensional lattices and obtain results agreeing with previous findings, as far as the compressibility of the system is concerned. We discuss the expected peaks in the experimental excitation spectrum of the system, related to the incompressible phases, and the superfluid character of the {\it partially compressible phases} characterizing the phase diagram of systems with binary disorder. In our investigation we make use of several analytical results whose derivation is described in the appendices, and whose validity is not limited to the system under concern., Comment: 12 pages, 5 figures. Some adjustments made to the manuscript and to figures. A few relevant observations added throughout the manuscript. Bibliography made more compact (collapsed some items)

The mean-field pictures based on the standard time-dependent variational approach have widely been used in the study of nonlinear many-boson systems such as the Bose-Hubbard model. The mean-field schemes relevant to Gutzwiller-like trial states $|F>$, number-preserving states $|\xi >$ and Glauber-like trial states $|Z>$ are compared to evidence the specific properties of such schemes. After deriving the Hamiltonian picture relevant to $|Z>$ from that based on $|F>$, the latter is shown to exhibit a Poisson algebra equipped with a Weyl-Heisenberg subalgebra which preludes to the $|Z>$-based picture. Then states $|Z>$ are shown to be a superposition of $\cal N$-boson states $|\xi>$ and the similarities/differences of the $|Z>$-based and $|\xi>$-based pictures are discussed. Finally, after proving that the simple, symmetric state $|\xi>$ indeed corresponds to a SU(M) coherent state, a dual version of states $|Z>$ and $|\xi>$ in terms of momentum-mode operators is discussed together with some applications., Comment: 16 pages

We investigate the properties of strongly interacting heteronuclear boson-boson mixtures loaded in realistic optical lattices, with particular emphasis on the physics of interfaces. In particular, we numerically reproduce the recent experimental observation that the addition of a small fraction of K induces a significant loss of coherence in Rb, providing a simple explanation. We then investigate the robustness against the inhomogeneity typical of realistic experimental realizations of the glassy quantum emulsions recently predicted to occur in strongly interacting boson-boson mixtures on ideal homogeneous lattices., Comment: 10 pages, 3 figures; some changes in the text and abstract have been introduced; coherence now given in terms of visibility; a couple of new reference added

We use the fidelity approach to quantum critical points to study the zero temperature phase diagram of the one-dimensional Hubbard model. Using a variety of analytical and numerical techniques, we analyze the fidelity metric in various regions of the phase diagram, with particular care to the critical points. Specifically we show that close to the Mott transition, taking place at on-site repulsion U=0 and electron density n=1, the fidelity metric satisfies an hyper-scaling form which we calculate. This implies that in general, as one approaches the critical point U=0, n=1, the fidelity metric tends to a limit which depends on the path of approach. At half filling, the fidelity metric is expected to diverge as U^{-4} when U is sent to zero., Comment: 8 pages, 4 figures, added results on the hyper-scaling form of the fidelity metric

Going beyond the currently investigated regimes in experiments on quantum transport of ultracold atoms in disordered potentials, we predict a crossover between regular and quantum-chaotic dynamics when varying the strength of disorder. Our spectral approach is based on the Bose-Hubbard model describing interacting atoms in deep random potentials. The predicted crossover from localized to diffusive dynamics depends on the simultaneous presence of interactions and disorder, and can be verified in the laboratory by monitoring the evolution of typical experimental initial states., Comment: 4 pages, 4 figures (improved version), to be published in PRA

In the present paper we describe the properties induced by disorder on an ultracold gas of Bosonic atoms loaded into a two-dimensional optical lattice with global confinement ensured by a parabolic potential. Our analysis is centered on the spatial distribution of the various phases, focusing particularly on the superfluid properties of the system as a function of external parameters and disorder amplitude. In particular, it is shown how disorder can suppress superfluidity, while partially preserving the system coherence., Comment: Accepted for publication on JPB-FTC

In this paper we derive an analytic approximation to the density of states for atoms in a combined optical lattice and harmonic trap potential as used in current experiments with quantum degenerate gases. We compare this analytic density of states to numerical solutions and demonstrate its validity regime. Our work explicitly considers the role of higher bands and when they are important in quantitative analysis of this system. Applying our density of states to a degenerate Fermi gas we consider how adiabatic loading from a harmonic trap into the combined harmonic-lattice potential affects the degeneracy temperature. Our results suggest that occupation of excited bands during loading should lead to more favourable conditions for realizing degenerate Fermi gases in optical lattices., Comment: 11 pages, 9 figures

We analyze the quantum phase transition in the Bose-Hubbard model borrowing two tools from quantum-information theory, i.e. the ground-state fidelity and entanglement measures. We consider systems at unitary filling comprising up to 50 sites and show for the first time that a finite-size scaling analysis of these quantities provides excellent estimates for the quantum critical point.We conclude that fidelity is particularly suited for revealing a quantum phase transition and pinning down the critical point thereof, while the success of entanglement measures depends on the mechanisms governing the transition., Comment: 7 pages, 5 figures (endfloats used due to problems with figures and latex. Sorry about that); final version, similar to the published one

The zero-temperature phase diagram for ultracold Bosons in a random 1D potential is obtained through a site-decoupling mean-field scheme performed over a Bose-Hubbard (BH) Hamiltonian whose hopping term is considered as a random variable. As for the model with random on-site potential, the presence of disorder leads to the appearance of a Bose-glass phase. The different phases -i.e. Mott insulator, superfluid, Bose-glass- are characterized in terms of condensate fraction and superfluid fraction. Furthermore, the boundary of the Mott lobes are related to an off-diagonal Anderson model featuring the same disorder distribution as the original BH Hamiltonian., Comment: 7 pages, 6 figures. Submitted to Laser Physics

We analyze thoroughly the mean-field dynamics of a linear chain of three coupled Bose-Einstein condensates, where both the tunneling and the central-well relative depth are adjustable parameters. Owing to its nonintegrability, entailing a complex dynamics with chaos occurrence, this system is a paradigm for longer arrays whose simplicity still allows a thorough analytical study.We identify the set of dynamics fixed points, along with the associated proper modes, and establish their stability character depending on the significant parameters. As an example of the remarkable operational value of our analysis, we point out some macroscopic effects that seem viable to experiments., Comment: 5 pages, 3 figures

We show that a site-dependent mean-field approach captures the quantum phases of the disordered Bose-Hubbard model commonly adopted to describe ultracold bosons in random optical lattice potentials. The different phases, namely superfluid, Mott insulator, Bose-glass and -- at finite temperature -- normal fluid, are characterized by means of the superfluid and condensate fractions, and compressibility of the system. We point out that both the boundaries of the Mott lobes and the nature of the phase surrounding them are related to the spectral features of a purely off-diagonal non-interacting Anderson model. We compare our results to other works., Comment: 5 pages, 4 figures, added some references and reformulated some sentences

We investigate the ground state of a system of interacting particles in small nonlinear lattices with M > 2 sites, using as a prototypical example the discrete nonlinear Schroedinger equation that has been recently used extensively in the contexts of nonlinear optics of waveguide arrays, and Bose-Einstein condensates in optical lattices. We find that, in the presence of attractive interactions, the dynamical scenario relevant to the ground state and the lowest-energy modes of such few-site nonlinear lattices reveals a variety of nontrivial features that are absent in the large/infinite lattice limits: the single-pulse solution and the uniform solution are found to coexist in a finite range of the lattice intersite coupling where, depending on the latter, one of them represents the ground state; in addition, the single-pulse mode does not even exist beyond a critical parametric threshold. Finally, the onset of the ground state (modulational) instability appears to be intimately connected with a non-standard (``double transcritical'') type of bifurcation that, to the best of our knowledge, has not been reported previously in other physical systems., Comment: 7 pages, 4 figures; submitted to PRE

We determine the low-energy spectrum and the eigenstates for a two-bosonic mode nonlinear model by applying the In\"{o}n\"{u}-Wigner contraction method to the Hamiltonian algebra. This model is known to well represent a Bose-Einstein condensate rotating in a thin torus endowed with two angular-momentum modes as well as a condensate in a double-well potential characterized by two space modes. We consider such a model in the presence of both an attractive and a repulsive boson interaction and investigate regimes corresponding to different values of the inter-mode tunneling parameter. We show that the results ensuing from our approach are in many cases extremely satisfactory. To this end we compare our results with the ground state obtained both numerically and within a standard semiclassical approximation based on su(2) coherent states., Comment: 24 pages, 5 figures, accepted for publication on J. Phys. A

We study the ground state properties of the Bose-Hubbard model with attractive interactions on a M-site one-dimensional periodic -- necklace-like -- lattice, whose experimental realization in terms of ultracold atoms is promised by a recently proposed optical trapping scheme, as well as by the control over the atomic interactions and tunneling amplitudes granted by well-established optical techniques. We compare the properties of the quantum model to a semiclassical picture based on a number-conserving su(M) coherent state, which results into a set of modified discrete nonlinear Schroedinger equations. We show that, owing to the presence of a correction factor ensuing from number conservation, the ground-state solution to these equations provides a remarkably satisfactory description of its quantum counterpart not only -- as expected -- in the weak-interaction, superfluid regime, but even in the deeply quantum regime of large interactions and possibly small populations. In particular, we show that in this regime, the delocalized, Schroedinger-cat-like quantum ground state can be seen as a coherent quantum superposition of the localized, symmetry-breaking ground-state of the variational approach. We also show that, depending on the hopping to interaction ratio, three regimes can be recognized both in the semiclassical and quantum picture of the system., Comment: 11 pages, 7 figures; typos corrected and references added; to appear in Phys. Rev. A

Ultracold bosons in optical superlattices are expected to exhibit fractional-filling insulating phases for sufficiently large repulsive interactions. On strictly 1D systems, the exact mapping between hard-core bosons and free spinless fermions shows that any periodic modulation in the lattice parameters causes the presence of fractional-filling insulator domains. Here, we focus on two recently proposed realistic 2D structures where such mapping does not hold, i.e. the two-leg ladder and the trimerized kagome' lattice. Based on a cell strong-coupling perturbation technique, we provide quantitatively satisfactory phase diagrams for these structures, and give estimates for the occurrence of the fractional-filling insulator domains in terms of the inter-cell/intra-cell hopping amplitude ratio., Comment: 4 pages, 3 figures

The phase diagram of ultracold bosons in realistic optical superlattices is addressed via second-order {\it cell} strong coupling perturbative expansions for the Bose-Hubbard model describing the system. Taking advantage of the cell partition inherent in the complex periodic modulation of a superlattice, this technique allows for the description of the unusual loophole-shaped insulator domains that may occur in the phase diagram of the system, unlike the standard perturbative approach. Furthermore, comparisons with quantum Monte Carlo simulations show that our approach provides quantitatively satisfactory results at a significantly lower computational cost than brute force numerical methods. We explicitly consider the phase diagrams for two realistic 3-periodic optical superlattices. These show that many insulator domains exhibit an unusual reentrant character, which we discuss, and suggest that the quantum phase transition relevant to the loophole-shaped insulating domains does not require extreme experimental condition in order to be observed., Comment: 11 pages, 4 figures; final version. Title and abstract slightly changed. Minor typos corrected. Acknowledgments added and references updated

We report a multiple-site mean-field analysis of the zero-temperature phase diagram for ultracold bosons in realistic optical superlattices. The system of interacting bosons is described by a Bose-Hubbard model whose site-dependent parameters reflect the nontrivial periodicity of the optical superlattice. An analytic approach is formulated based on the analysis of the stability of a fixed-point of the map defined by the self-consistency condition inherent in the mean-field approximation. The experimentally relevant case of the period-2 one-dimensional superlattice is briefly discussed. In particular, it is shown that, for a special choice of the superlattice parameters, the half-filling insulator domain features an unusual loophole shape that the single-site mean-field approach fails to capture., Comment: 7 pages, 1 figure

The zero-temperature phase diagram of a Bose-Einstein condensate confined in realistic one-dimensional $\ell$-periodic optical superlattices is investigated. The system of interacting bosons is modeled in terms of a Bose-Hubbard Hamiltonian whose site-dependent local potentials and hopping amplitudes reflect the periodicity of the lattice partition in $\ell$-site cells. Relying on the exact mapping between the hard-core limit of the boson Hamiltonian and the model of spinless noninteracting fermions, incompressible insulator domains are shown to exist for rational fillings that are predicted to be compressible in the atomic limit. The corresponding boundaries, qualitatively described in a {\it multiple-site} mean-field approach, are shown to exhibit an unusual loophole shape. A more quantitative description of the loophole domain boundaries at half filling for the special case $\ell$ = 2 is supplied in terms of analytic strong-coupling expansions and quantum Monte Carlo simulations., Comment: 5 pages, 3 figures; final version; bibliography updated; acknowledgments included

We consider a Bose-Hubbard model with an arbitrary hopping term and provide the boundary of the insulating phase thereof in terms of third-order strong coupling perturbative expansions for the ground state energy. In the general case two previously unreported terms occur, arising from triangular loops and hopping inhomogeneities, respectively. Quite interestingly the latter involves the entire spectrum of the hopping matrix rather than its maximal eigenpair, like the remaining perturbative terms. We also show that hopping inhomogeneities produce a first order correction in the local density of bosons. Our results apply to ultracold bosons trapped in confining potentials with arbitrary topology, including the realistic case of optical superlattices with uneven hopping amplitudes. Significant examples are provided. Furthermore, our results can be extented to magnetically tuned transitions in Josephson junction arrays., Comment: 5 pages, 2 figures,final version

We report the first study of the zero-temperature phase diagram of the Bose-Hubbard model on topologically inhomogeneous arrays. We show that the usual Mott-insulator and superfluid domains, in the paradigmatic case of the comb lattice, are separated by regions where the superfluid behaviour of the bosonic system is confined along the comb backbone. The existence of such {\it confined superfluidity}, arising from topological inhomogeneity, is proved by different analytical and numerical techniques which we extend to the case of inhomogeneous arrays. We also discuss the relevance of our results to real system exhibiting macroscopic phase coherence, such as coupled Bose condensates and Josephson arrays., Comment: 6 pages, 4 figures, final version

We present an analytic description of the finite-temperature phase diagram of the Bose-Hubbard model, successfully describing the physics of cold bosonic atoms trapped in optical lattices and superlattices. Based on a standard statistical mechanics approach, we provide the exact expression for the boundary between the superfluid and the normal fluid by solving the self-consistency equations involved in the mean-field approximation to the Bose-Hubbard model. The zero-temperature limit of such result supplies an analytic expression for the Mott lobes of superlattices, characterized by a critical fractional filling., Comment: 8 pages, 6 figures, submitted to Phys. Rev. A

We consider a system formed by an array of Bose-Einstein condensates trapped in a harmonic potential with a superimposed periodic optical potential. Starting from the boson field Hamiltonian, appropriate to describe dilute gas of bosonic atoms, we reformulate the system dynamics within the Bose-Hubbard model picture. Then we analyse the effective dynamics of the system when the optical potential depth is suddenly varied according to a procedure applied in many of the recent experiments on superfluid-Mott transition in Bose-Einstein condensates. Initially the condensates' array generated in a weak optical potential is assumed to be in the superfluid ground-state which is well described in terms of coherent states. At a given time, the optical potential depth is suddenly increased and, after a waiting time, it is quickly decreased so that the initial depth is restored. We compute the system-state evolution and show that the potential jump brings on an excitation of the system, incorporated in the final condensate wave functions, whose effects are analysed in terms of two-site correlation functions and of on-site population oscillations. Also we show how a too long waiting time can destroy completely the coherence of the final state making it unobservable., Comment: 10 pages, 4 figures, to appear on Journal of Physics B (Special Issue: Levico BEC workshop). Publication status updated

The Bose-Hubbard Hamiltonian capturing the essential physics of the arrays of interacting Bose-Einstein condensates is addressed, focusing on arrays consisting of two (dimer) and three (trimer) sites. In the former case, some results concerning the persistence of mean-field features in the energy spectrum of the symmetric dimer are extended to the asymmetric version of the system, where the two sites are characterized by different on-site energies. Based on a previous systematic study of the mean-field limit of the trimer, where the dynamics is exhaustively described in terms of its fixed points for every choice of the significant parameters, an interesting mapping between the dimer and the trimer is emphasized and used as a guide in investigating the persistence of mean-field features in the rather complex energy spectrum of the trimer. These results form the basis for the systematic investigation of the purely quantum trimer extending and completing the existing mean-field analysis. In this respect we recall that, similar to larger arrays, the trimer is characterized by a non-integrable mean-field dynamics featuring chaotic trajectories. Hence, the correspondence between mean-field fixed points and quantum energy levels emphasized in the present work may provide a key to investigate the quantum counterpart of classical instability., Comment: 12 pages, 6 figures, to appear on Journal of Physics B (Special Issue: Levico BEC workshop). Publication status updated

The dynamics of a mean-field model of three coupled condensates is studied for initial states characterized by twin condensates. Condensates occupy an open three-well chain, where the central potential-well depth is an independent parameter. Despite its diversity from the closed-chain symmetric model, such model is shown to have an integrable regime involving a predictable evolution for twin-condensate initial states. After establishing the dependence of the phase-space topology on the model parameters, the latter are shown to allow the control of various macroscopic effects such as rapid population inversions, pulsed phase changes, self-trapping and long-duration periodic oscillations. Finally, based on quantizing the system in terms of suitable ``microscopic'' canonical variables, the stability conditions of the integrable regime are related to the su(1,1) structure of the Hamiltonian spectrum., Comment: 12 pages, 8 figures, to appear on Laser Physics 4, 2004. In the new version of the paper figures inserted accidentally in the previous version have been removed

We study the filling of states in a pure hopping boson model on the comb lattice, a low dimensional discrete structure where geometrical inhomogeneity induces Bose-Einstein condensation (BEC) at finite temperature. By a careful analysis of the thermodynamic limit on combs we show that, unlike the standard lattice case, BEC is characterized by a macroscopic occupation of a finite number of states with energy belonging to a small neighborhood of the ground state energy. Such remarkable feature gives rise to an anomalous behaviour in the large distance two-point correlation functions. Finally, we prove a general theorem providing the conditions for the pure hopping model to exhibit the standard behaviour, i.e. to present a macroscopic occupation of the ground state only., Comment: 8 pages, 5 eps figures, to appear in Phys. Rev. B 66

We introduce a thermal dynamics for the Ising ferromagnet where the energy variations occurring within the system exhibit a diffusive character typical of thermalizing agents such as e.g. localized excitations. Time evolution is provided by a walker hopping across the sites of the underlying lattice according to local probabilities depending on the usual Boltzmann weight at a given temperature. Despite the canonical hopping probabilities the walker drives the system to a stationary state which is not reducible to the canonical equilibrium state in a trivial way. The system still exhibits a magnetic phase transition occurring at a finite value of the temperature larger than the canonical one. The dependence of the model on the density of walkers realizing the dynamics is also discussed. Interestingly the differences between the stationary state and the Boltzmann equilibrium state decrease with increasing number of walkers., Comment: 9 pages, 14 figures. Accepted for publication on PRE

Complex molecules and mesoscopic structures are naturally described by general networks of elementary building blocks and tight-binding is one of the simplest quantum model suitable for studying the physical properties arising from the network topology. Despite the simplicity of the model, topological complexity can make the evaluation of the spectrum of the tight-binding Hamiltonian a rather hard task, since the lack of translation invariance rules out such a powerful tool as Fourier transform. In this paper we introduce a rigorous analytical technique, based on topological methods, for the exact solution of this problem on branched structures. Besides its analytic power, this technique is also a promising engineering tool, helpful in the design of netwoks displaying the desired spectral features., Comment: 19 pages, 14 figures