Complexity in parametric Bose-Hubbard Hamiltonians and structural analysis of eigenstates

We consider a family of chaotic Bose-Hubbard Hamiltonians (BHH) parameterized by the coupling strength $k$ between neighboring sites. As $k$ increases the eigenstates undergo changes, reflected in the structure of the Local Density of States. We analyze these changes, both numerically and analytically, using perturbative and semiclassical methods. Although our focus is on the quantum trimer, the presented methodology is applicable for the analysis of longer lattices as well.Comment: 4 pages, 4 figure

Quantum localization and bound state formation in Bose-Einstein condensates

We discuss the possibility of exponential quantum localization in systems of ultracold bosonic atoms with repulsive interactions in open optical lattices without disorder. We show that exponential localization occurs in the maximally excited state of the lowest energy band. We establish the conditions under which the presence of the upper energy bands can be neglected, determine the successive stages and the quantum phase boundaries at which localization occurs, and discuss schemes to detect it experimentally by visibility measurements. The discussed mechanism is a particular type of quantum localization that is intuitively understood in terms of the interplay between nonlinearity and a bounded energy spectrum.Comment: 6 pages, 5 figure

New or ν\nu Missing Energy? Discriminating Dark Matter from Neutrino Interactions at the LHC

Missing energy signals such as monojets are a possible signature of Dark Matter (DM) at colliders. However, neutrino interactions beyond the Standard Model may also produce missing energy signals. In order to conclude that new "missing particles" are observed the hypothesis of BSM neutrino interactions must be rejected. In this paper, we first derive new limits on these Non-Standard neutrino Interactions (NSIs) from LHC monojet data. For heavy NSI mediators, these limits are much stronger than those coming from traditional low-energy $\nu$ scattering or $\nu$ oscillation experiments for some flavor structures. Monojet data alone can be used to infer the mass of the "missing particle" from the shape of the missing energy distribution. In particular, 13 TeV LHC data will have sensitivity to DM masses greater than $\sim$ 1 TeV. In addition to the monojet channel, NSI can be probed in multi-lepton searches which we find to yield stronger limits at heavy mediator masses. The sensitivity offered by these multi-lepton channels provide a method to reject or confirm the DM hypothesis in missing energy searches.Comment: 11 pages, 7 figure

Catching homologies by geometric entropy

A geometric entropy is defined as the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability to single out topological features of networks proceeding in a bottom-up manner: first we consider small size networks by analytical methods and then large size networks by numerical techniques. Two different classes of networks, the random graphs and the scale--free networks, are investigated computing their Betti numbers and then showing the capability of geometric entropy of detecting homologies.Comment: 12 pages, 2 Figure

Topology and phase transitions: a paradigmatic evidence

We report upon the numerical computation of the Euler characteristic \chi (a topologic invariant) of the equipotential hypersurfaces \Sigma_v of the configuration space of the two-dimensional lattice $\phi^4$ model. The pattern \chi(\Sigma_v) vs. v (potential energy) reveals that a major topology change in the family {\Sigma_v}_{v\in R} is at the origin of the phase transition in the model considered. The direct evidence given here - of the relevance of topology for phase transitions - is obtained through a general method that can be applied to any other model.Comment: 4 pages, 4 figure

Lyapunov exponents from geodesic spread in configuration space

The exact form of the Jacobi–Levi-Civita (JLC) equation for geodesic spread is here explicitly worked out at arbitrary dimension for the configuration space manifold [Formula Presented] of a standard Hamiltonian system, equipped with the Jacobi (or kinetic energy) metric [Formula Presented] As the Hamiltonian flow corresponds to a geodesic flow on [Formula Presented] the JLC equation can be used to study the degree of instability of the Hamiltonian flow. It is found that the solutions of the JLC equation are closely resembling the solutions of the standard tangent dynamics equation which is used to compute Lyapunov exponents. Therefore the instability exponents obtained through the JLC equation are in perfect quantitative agreement with usual Lyapunov exponents. This work completes a previous investigation that was limited only to two degrees of freedom systems. © 1997 The American Physical Society

Dynamical Instability in a Trimeric Chain of Interacting Bose-Einstein Condensates

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 figure

Control of unstable macroscopic oscillations in the dynamics of three coupled Bose condensates

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 figure

Spectral Properties of Coupled Bose-Einstein Condensates

We investigate the energy spectrum structure of a system of two (identical) interacting bosonic wells occupied by N bosons within the Schwinger realization of the angular momentum. This picture enables us to recognize the symmetry properties of the system Hamiltonian H and to use them for characterizing the energy eigenstates. Also, it allows for the derivation of the single-boson picture which is shown to be the background picture naturally involved by the secular equation for H. After deriving the corresponding eigenvalue equation, we recast it in a recursive N-dependent form which suggests a way to generate the level doublets (characterizing the H spectrum) via suitable inner parameters. Finally, we show how the presence of doublets in the spectrum allows to recover, in the classical limit, the symmetry breaking effect that characterizes the system classically.Comment: 8 pages, 3 figures; submitted to Phys. Rev. A. The present extended form replaces the first version in the letter forma

Ground-state Properties of Small-Size Nonlinear Dynamical Lattices

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 PR