Limit Of Weak Interactions Research Articles

Possible quantum phase manipulation of a two-leg ladder in mixed-dimensional fermionic cold atoms

The recent realization of mixed-dimensional systems of cold atoms has attracted much attention from both experimentalists and theorists. In this article we investigate a two-species Fermi atom mixture: one species of atom exists in two hyperfine states and is confined to move in a two-leg ladder, interacting with an on-site interaction, and the other moves freely in a two-dimensional square lattice that contains the two-leg ladder. The two species of atoms interact via an on-site interaction on the ladder. In the limit of weak interspecies interactions, the two-dimensional gas can be integrated out, leading to an effective long-range mediated interaction in the ladder, generated by the on-site interspecies interaction. We show that the form of the mediated interaction can be controlled by the density of the two-dimensional gas and that it enhances the charge-density wave instability in the two-leg ladder after the renormalization-group transformation. Parametrizing the phase diagram with various experimentally controllable quantities, we discuss the possible tuning of the macroscopic quantum many-body phases of the two-leg ladder in this mixed-dimensional fermionic cold atom system.

Symmetry breaking for ratchet transport in the presence of interactions and a magnetic field

We study the microwave induced ratchet transport of two-dimensional electrons on an oriented semidisk Galton board. The magnetic field symmetries of ratchet transport are analyzed in the presence of electron-electron interactions. Our results show that a magnetic field asymmetric ratchet current can appear due to two contributions, a Hall drift of the rectified current that depends only weakly on electron-electron interactions and a breaking of the time reversal symmetry due to the combined effects of interactions and magnetic field. In the latter case, the asymmetry between positive and negative magnetic fields vanishes in the weak interaction limit. We also discuss the recent experimental results on ratchet transport in asymmetric nanostructures.

Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions

We study the thermal conductivity, at fixed positive temperature, of a disordered lattice of harmonic oscillators, weakly coupled to each other through anharmonic potentials. The interaction is controlled by a small parameter ϵ > 0. We rigorously show, in two slightly different setups, that the conductivity has a non-perturbative origin. This means that it decays to zero faster than any polynomial in ϵ as ϵ → 0. It is then argued that this result extends to a disordered chain studied by Dhar and Lebowitz (2008 Phys. Rev. Lett. 100 134301), and to a classic spin chain recently investigated by Oganesyan, Pal and Huse (2009 Phys. Rev. B 80 115104).

STELLAR ENERGY RELAXATION AROUND A MASSIVE BLACK HOLE

[abridged] Energy relaxation around a massive black hole (MBH) is key to establishing the dynamical state of galactic nuclei, and the nature of close stellar interactions with the MBH. The standard description of relaxation as diffusion provides a perturbative 2nd-order solution in the weak two-body interaction limit. We run N-body simulations and find that this solution fails to describe the non-Gaussian relaxation on short timescale, which is strongly influenced by extreme events even in the weak limit, and is thus difficult to characterize and measure. We derive a non-perturbative solution for relaxation as an anomalous diffusion process, and develop a robust estimation technique to measure it in simulations. These enable us to analyze and model our numerical results, and validate in detail, for the first time, this model of energy relaxation around an MBH on all timescales. We derive the relation between the energy diffusion time, t_E, and the time for a small perturbation to return to steady state, t_r, in a relaxed, single mass cusp around a MBH. We constrain the contribution of strong encounters, measure that of the weakest encounters, determine the value of the Coulomb logarithm, and provide a robust analytical estimate for t_E in a finite nuclear stellar cusp. We find that t_r ~ 10t_E ~(5/32)Q^2P_h/N_h log Q, where Q=M_bh/M_* is the MBH to star mass ratio, the orbital period P_h and number of stars N_h are evaluated at the energy scale corresponding to the MBH's sphere of influence, E_h=sigma_inf^2, where sigma_inf is the velocity dispersion far from the MBH. We conclude, using the observed cosmic M_bh/sigma correlation, that cusps around lower-mass MBHs (M_bh<10^7 Mo), which evolved passively over a Hubble time, should be relaxed. We consider the effects of anomalous energy diffusion on orbital perturbations of stars observed near the Galactic MBH.

Quantum effects on one-dimensional collision dynamics of fermion clusters

Recently, many experiments with cold atomic gases have been conducted from interest in the non-equilibrium dynamics of correlated quantum systems. Of these experiments, the mixing dynamics of fermion clusters motivates us to research cluster-cluster collision dynamics in one-dimensional Fermi systems. We adopt the one-dimensional Fermi-Hubbard model and apply the time-dependent density matrix renormalization group method. We simulate collisions between two fermion clusters of spin-up and spin-down and calculate reflectance of the clusters R changing the particle number in each cluster and the interaction strength between two fermions with up and down spins. We also evaluate the quasi-classical (independent collision) reflectance Rqc to compare it with R. The quasi-classical picture is quantitatively valid in the limit of weak interaction, but it is not valid when interaction is strong.

Excitation spectrum of a two-component Bose–Einstein condensate in a ring potential

A mixture of two distinguishable Bose–Einstein condensates confined in a ring potential has numerous interesting properties under rotational and solitary-wave excitation. The lowest energy states for a fixed angular momentum coincide with a family of solitary-wave solutions. In the limit of weak interactions, exact diagonalization of the many-body Hamiltonian is possible and permits evaluation of the complete excitation spectrum of the system.

Emergence of collective behavior in dynamical networks

One of the main paradigms of the theory of weakly interactingchaotic systems is the absence of phase transitions in genericsituation. We propose a new type of multicomponent systemsdemonstrating in the weak interaction limit both collective andindependent behavior of local components depending on fineproperties of the interaction. The model under consideration isrelated to dynamical networks and sheds a new light to the problemof synchronization under weak interactions.

Behavior of the anomalous correlation function in a uniform two-dimensional Bose gas

We investigate the behavior of the anomalous correlation function in two dimensional Bose gas. In the local case, we find that this quantity has a finite value in the limit of weak interactions at zero temperature. The effects of the anomalous density on some thermodynamic quantities are also considered. These effects can modify in particular the chemical potential, the ground sate energy, the depletion and the superfluid fraction. Our predictions are in good agreement with recent analytical and numerical calculations. We show also that the anomalous density presents a significant importance compared to the non-condensed one at zero temperature. The single-particle anomalous correlation function is expressed in two dimensional homogenous Bose gases by using the density-phase fluctuation. We then confirm that the anomalous average accompanies in analogous manner the true condensate at zero temperature while it does not exist at finite temperature.

Localized Phase Structures Growing Out of Quantum Fluctuations in a Quench of Tunnel-coupled Atomic Condensates

We investigate the relative phase between two weakly interacting 1D condensates of bosonic atoms after suddenly switching on the tunnel coupling. The following phase dynamics is governed by the quantum sine-Gordon equation. In the semiclassical limit of weak interactions, we observe the parametric amplification of quantum fluctuations leading to the formation of breathers with a finite lifetime. The typical lifetime and density of these "quasibreathers" are derived employing exact solutions of the classical sine-Gordon equation. Both depend on the initial relative phase between the condensates, which is considered as a tunable parameter.

Quantum walk of two interacting bosons

We study the effect of interactions on the propagation of quantum correlations in the bosonic two-body quantum walk. The combined effect of interactions and Hanbury Brown--Twiss interference results in unique spatial correlations which depend on the strength of the interaction, but not on its sign. We experimentally measure the weak interaction limit of these effects using light propagating in a highly nonlinear photonic lattices. Finally, we propose an experimental approach to observe the strong interaction limit using few atoms in optical lattices.

The glass to superfluid transition in dirty bosons on a lattice

We investigate the interplay between disorder and interactions in a Bose gas on a lattice in the presence of randomly localized impurities. We compare the performance of two theoretical methods, namely the simple version of multi-orbital Hartree–Fock and the common Gross–Pitaevskii approach, and show how the former gives a very good approximation to the ground state in the limit of weak interactions, where the superfluid fraction is small. We further prove rigorously that for this class of disorder the fractal dimension of the ground state d* tends to the physical dimension in the thermodynamic limit. This allows us to introduce a quantity called the fractional occupation, which gives useful information on the crossover from a Lifshits to a Bose glass. Finally, we compare the temperature and interaction effects and highlight their similarities and intrinsic differences.

Confinedp-band Bose-Einstein condensates

We study bosonic atoms on the $p$ band of a two-dimensional optical square lattice in the presence of a confining trapping potential. Using a mean-field approach, we show how the anisotropic tunneling for $p$-band particles affects the cloud of condensed atoms by characterizing the ground-state density and the coherence properties of the atomic states both between sites and atomic flavors. In contrast to the usual results based on the local-density approximation, the atomic density can become anisotropic. This anisotropic effect is especially pronounced in the limit of weak atom-atom interactions and of weak lattice amplitudes, i.e., when the properties of the ground state are mainly driven by the kinetic energies. We also investigate how the trap influences known properties of the nontrapped case. In particular, we focus on the behavior of the antiferromagnetic vortex-antivortex order, which for the confined system is shown to disappear at the edges of the condensed cloud.

Quantum entanglement in exactly soluble atomic models: the Moshinsky model with three electrons, and with two electrons in a uniform magnetic field

We investigate the entanglement-related features of the eigenstates of two exactly soluble atomic models: a one-dimensional three-electron Moshinsky model, and a three-dimensional two-electron Moshinsky system in an external uniform magnetic field. We analytically compute the amount of entanglement exhibited by the wavefunctions corresponding to the ground, first and second excited states of the three-electron model. We found that the amount of entanglement of the system tends to increase with energy, and in the case of excited states we found a finite amount of entanglement in the limit of vanishing interaction. We also analyze the entanglement properties of the ground and first few excited states of the two-electron Moshinsky model in the presence of a magnetic field. The dependence of the eigenstates' entanglement on the energy, as well as its behaviour in the regime of vanishing interaction, are similar to those observed in the three-electron system. On the other hand, the entanglement exhibits a monotonically decreasing behavior with the strength of the external magnetic field. For strong magnetic fields the entanglement approaches a finite asymptotic value that depends on the interaction strength. For both systems studied here we consider a perturbative approach in order to shed some light on the entanglement's dependence on energy and also to clarify the finite entanglement exhibited by excited states in the limit of weak interactions. As far as we know, this is the first work that provides analytical and exact results for the entanglement properties of a three-electron model.

Damping of Bloch Oscillations in the Hubbard Model

Using nonequilibrium dynamical mean-field theory, we study the isolated Hubbard model in a static electric field in the limit of weak interactions. Linear response behavior is established at long times, but only if the interaction exceeds a critical value, below which the system exhibits an ac-type response with Bloch oscillations. The transition from ac to dc response is defined in terms of the universal long-time behavior of the system, which does not depend on the initial condition.

Exact diagonalization study of 2D Hubbard model on honeycomb lattice: Semi-metal to insulator transition

Phase transition in a honeycomb lattice is studied by the means of the two-dimensional Hubbard model and the exact diagonalization dynamical mean field theory at zero temperature. At low energies, the dispersion relation is shown to be a linear function of the momentum. In the limit of weak interactions, the system is in the semi-metal phase. By increasing the on site interaction a semi-metal to insulator transition takes place in the paramagnetic phase. Calculation of double occupancy shows such a phase transition is of the second order. The respective phase transition point and critical on-site interaction are determined using renormalized Fermi velocity factor.

Density functional of a two-dimensional gas of dipolar atoms: Thomas-Fermi-Dirac treatment

We derive the density functional for the ground-state energy of a two-dimensional, spin-polarized gas of neutral fermionic atoms with magnetic-dipole interaction, in the Thomas-Fermi-Dirac approximation. For many atoms in a harmonic trap, we give analytical solutions for the single-particle spatial density and the ground-state energy, in dependence on the interaction strength, and we discuss the weak-interaction limit that is relevant for experiments. We then lift the restriction of full spin polarization and account for a time-independent inhomogeneous external magnetic field. The field strength necessary to ensure full spin polarization is derived.

Conservation issue of pairwise quantum discord and entanglement of two coupled qubits in a two-mode vacuum cavity

The conservation issues of pairwise quantum discord and entanglement of two qubits coupled to a two-mode vacuum cavity are investigated by considering the dipole–dipole interaction between two qubits. It is found that the sum of the square of the pairwise quantum discords and the sum of the square of the pairwise concurrences are both conserved in the strong dipole-dipole interaction limit. However, in the middle dipole-dipole and weak dipole-dipole interaction limits, the sum of the square of the pairwise concurrences is still conserved while the sum of the square of the pairwise discords is not. The crucial reason for this is that the quantum discords are not equivalent if the measurements are performed on different subsystems in a general situation. So it is very important for quantum computation depending on the quantum discord to select the target performed by the measurements.

Finite-temperature density-functional theory of Bose-Einstein condensates

The thermodynamic approach to density functional theory (DFT) is used to derive a versatile theoretical framework for the treatment of finite-temperature (and in the limit, zero temperature) Bose-Einstein condensates (BECs). The simplest application of this framework, using the overall density of bosons alone, would yield the DFT of Nunes (1999). It is argued that a significant improvement in accuracy may be obtained by using additional density fields: the condensate amplitude and the anomalous density. Thus, two advanced schemes are suggested, one corresponding to a generalized two-fluid model of condensate systems, and another scheme which explicitly accounts for anomalous density contributions and anomalous effective potentials. The latter reduces to the Hartree-Fock-Bogoliubov approach in the limit of weak interactions. For stronger interactions, a local density approximation is suggested, but its implementation requires accurate data for the thermodynamic properties of uniform interacting BEC systems, including fictitious perturbed states of such systems. Provided that such data becomes available, e.g., from quantum Monte Carlo computation, DFT can be used to obtain high-accuracy theoretical results for the equilibrium states of BECs of various geometries and external potentials.

Self-consistent mappings and systems of interacting particles

In recent paper (1), we suggested a new model for the dynamics of locally interacting particles (with meanfieldtype interaction) and proved that, in the limit of weak interactions, finite systems of particles (or CML) may exhibit both a synchronized and an independent behavior (i.e., a phase transition may occur), depending on subtle properties of the interac� tion operator. The fundamental technical limitation was the finiteness of the number of particles. In this paper, we introduce a new construction in the theory of dynamical systems, namely, that of selfconsistent mappings; its application has made it possible to study the infiniteparticle version of our model.

Continuous Hawking-Page transitions in Einstein-scalar gravity

We investigate continuous Hawking-Page transitions in Einstein’s gravity coupled to a scalar field with an arbitrary potential in the weak gravity limit. We show that this is only possible in a singular limit where the black-hole horizon marginally traps a curvature singularity. Depending on the subleading terms in the potential, a rich variety of continuous phase transitions arise. Our examples include second and higher order, including the Berezinskii-Kosterlitz-Thouless type. In the case when the scalar is dilaton, the condition for continuous phase transitions lead to (asymptotically) linear-dilaton background. We obtain the scaling laws of thermodynamic functions, as well as the viscosity coefficients near the transition. In the limit of weak gravitational interactions, the bulk viscosity asymptotes to a universal constant, independent of the details of the scalar potential. As a byproduct of our analysis we obtain a one-parameter family of kink solutions in arbitrary dimension d that interpolate between AdS near the boundary and linear-dilaton background in the deep interior. The continuous Hawking-Page transitions found here serve as holographic models for normal-to superfluid transitions.