The Mott insulator phase of the one dimensional Bose-Hubbard model: a high order perturbative study

The one dimensional Bose-Hubbard model at a unit filling factor is studied by means of a very high order symbolic perturbative expansion. Analytical expressions are derived for the ground state quantities such as energy per site, variance of on-site occupation, and different correlation functions. These findings are compared to numerics and good agreement is found in the Mott insulator phase. Our results provide analytical approximations to important observables in the Mott phase, and are also of direct relevance to future experiments with ultra cold atomic gases placed in optical lattices. We also discuss the symmetry of the Bose-Hubbard model associated with the sign change of the tunneling coupling.Comment: 7 pages, 4 figures, 1 table. Significantly expanded version with respect to former submission (to appear in Phys. Rev. A

Surfaces immersed in su(N+1) Lie algebras obtained from the CP^N sigma models

We study some geometrical aspects of two dimensional orientable surfaces arrising from the study of CP^N sigma models. To this aim we employ an identification of R^(N(N+2)) with the Lie algebra su(N+1) by means of which we construct a generalized Weierstrass formula for immersion of such surfaces. The structural elements of the surface like its moving frame, the Gauss-Weingarten and the Gauss-Codazzi-Ricci equations are expressed in terms of the solution of the CP^N model defining it. Further, the first and second fundamental forms, the Gaussian curvature, the mean curvature vector, the Willmore functional and the topological charge of surfaces are expressed in terms of this solution. We present detailed implementation of these results for surfaces immersed in su(2) and su(3) Lie algebras.Comment: 32 pages, 1 figure; changes: major revision of presentation, clarifications adde

Interaction and Localization of One-electron Orbitals in an Organic Molecule: Fictitious Parameter Analysis for Multi-physics Simulations

We present a new methodology to analyze complicated multi-physics simulations by introducing a fictitious parameter. Using the method, we study quantum mechanical aspects of an organic molecule in water. The simulation is variationally constructed from the ab initio molecular orbital method and the classical statistical mechanics with the fictitious parameter representing the coupling strength between solute and solvent. We obtain a number of one-electron orbital energies of the solute molecule derived from the Hartree-Fock approximation, and eigenvalue-statistical analysis developed in the study of nonintegrable systems is applied to them. Based on the results, we analyze localization properties of the electronic wavefunctions under the influence of the solvent.Comment: 4 pages, 5 figures, the revised version will appear in J. Phys. Soc. Jpn. Vol.76 (No.1

Spontaneous emission of non-dispersive Rydberg wave packets

Non dispersive electronic Rydberg wave packets may be created in atoms illuminated by a microwave field of circular polarization. We discuss the spontaneous emission from such states and show that the elastic incoherent component (occuring at the frequency of the driving field) dominates the spectrum in the semiclassical limit, contrary to earlier predictions. We calculate the frequencies of single photon emissions and the associated rates in the "harmonic approximation", i.e. when the wave packet has approximately a Gaussian shape. The results agree well with exact quantum mechanical calculations, which validates the analytical approach.Comment: 14 pages, 4 figure

Ionization via Chaos Assisted Tunneling

A simple example of quantum transport in a classically chaotic system is studied. It consists in a single state lying on a regular island (a stable primary resonance island) which may tunnel into a chaotic sea and further escape to infinity via chaotic diffusion. The specific system is realistic : it is the hydrogen atom exposed to either linearly or circularly polarized microwaves. We show that the combination of tunneling followed by chaotic diffusion leads to peculiar statistical fluctuation properties of the energy and the ionization rate, especially to enhanced fluctuations compared to the purely chaotic case. An appropriate random matrix model, whose predictions are analytically derived, describes accurately these statistical properties.Comment: 30 pages, 11 figures, RevTeX and postscript, Physical Review E in pres

A realistic example of chaotic tunneling: The hydrogen atom in parallel static electric and magnetic fields

Statistics of tunneling rates in the presence of chaotic classical dynamics is discussed on a realistic example: a hydrogen atom placed in parallel uniform static electric and magnetic fields, where tunneling is followed by ionization along the fields direction. Depending on the magnetic quantum number, one may observe either a standard Porter-Thomas distribution of tunneling rates or, for strong scarring by a periodic orbit parallel to the external fields, strong deviations from it. For the latter case, a simple model based on random matrix theory gives the correct distribution.Comment: Submitted to Phys. Rev.

Infinitesimal deformations of a formal symplectic groupoid

Given a formal symplectic groupoid $G$ over a Poisson manifold $(M, \pi_0)$, we define a new object, an infinitesimal deformation of $G$, which can be thought of as a formal symplectic groupoid over the manifold $M$ equipped with an infinitesimal deformation $\pi_0 + \epsilon \pi_1$ of the Poisson bivector field $\pi_0$. The source and target mappings of a deformation of $G$ are deformations of the source and target mappings of $G$. To any pair of natural star products $(\ast, \tilde\ast)$ having the same formal symplectic groupoid $G$ we relate an infinitesimal deformation of $G$. We call it the deformation groupoid of the pair $(\ast, \tilde\ast)$. We give explicit formulas for the source and target mappings of the deformation groupoid of a pair of star products with separation of variables on a Kaehler- Poisson manifold. Finally, we give an algorithm for calculating the principal symbols of the components of the logarithm of a formal Berezin transform of a star product with separation of variables. This algorithm is based upon some deformation groupoid.Comment: 22 pages, the paper is reworked, new proofs are adde

Supersymmetric WZW σ\sigma Model on Full and Half Plane

We study classical integrability of the supersymmetric U(N) $\sigma$ model with the Wess-Zumino-Witten term on full and half plane. We demonstrate the existence of nonlocal conserved currents of the model and derive general recursion relations for the infinite number of the corresponding charges in a superfield framework. The explicit form of the first few supersymmetric charges are constructed. We show that the considered model is integrable on full plane as a concequence of the conservation of the supersymmetric charges. Also, we study the model on half plane with free boundary, and examine the conservation of the supersymmetric charges on half plane and find that they are conserved as a result of the equations of motion and the free boundary condition. As a result, the model on half plane with free boundary is integrable. Finally, we conclude the paper and some features and comments are presented.Comment: 12 pages. submitted to IJMP

Dynamics of cold bosons in optical lattices: Effects of higher Bloch bands

The extended effective multiorbital Bose-Hubbard-type Hamiltonian which takes into account higher Bloch bands, is discussed for boson systems in optical lattices, with emphasis on dynamical properties, in relation with current experiments. It is shown that the renormalization of Hamiltonian parameters depends on the dimension of the problem studied. Therefore, mean field phase diagrams do not scale with the coordination number of the lattice. The effect of Hamiltonian parameters renormalization on the dynamics in reduced one-dimensional optical lattice potential is analyzed. We study both the quasi-adiabatic quench through the superfluid-Mott insulator transition and the absorption spectroscopy, that is energy absorption rate when the lattice depth is periodically modulated.Comment: 23 corrected interesting pages, no Higgs boson insid

Statistical properties of energy levels of chaotic systems: Wigner or non-Wigner

For systems whose classical dynamics is chaotic, it is generally believed that the local statistical properties of the quantum energy levels are well described by Random Matrix Theory. We present here two counterexamples - the hydrogen atom in a magnetic field and the quartic oscillator - which display nearest neighbor statistics strongly different from the usual Wigner distribution. We interpret the results with a simple model using a set of regular states coupled to a set of chaotic states modeled by a random matrix.Comment: 10 pages, Revtex 3.0 + 4 .ps figures tar-compressed using uufiles package, use csh to unpack (on Unix machine), to be published in Phys. Rev. Let