Quantum Breathing Mode of Interacting Particles in a One-dimensional Harmonic Trap

Extending our previous work, we explore the breathing mode---the [uniform] radial expansion and contraction of a spatially confined system. We study the breathing mode across the transition from the ideal quantum to the classical regime and confirm that it is not independent of the pair interaction strength (coupling parameter). We present the results of time-dependent Hartree-Fock simulations for 2 to 20 fermions with Coulomb interaction and show how the quantum breathing mode depends on the particle number. We validate the accuracy of our results, comparing them to exact Configuration Interaction results for up to 8 particles

Phase transition in the Higgs model of scalar dyons

In the present paper we investigate the phase transition "Coulomb--confinement" in the Higgs model of abelian scalar dyons -- particles having both, electric $e$ and magnetic $g$, charges. It is shown that by dual symmetry this theory is equivalent to scalar fields with the effective squared electric charge e^{*2}=e^2+g^2. But the Dirac relation distinguishes the electric and magnetic charges of dyons. The following phase transition couplings are obtained in the one--loop approximation: \alpha_{crit}=e^2_{crit}/4\pi\approx 0.19, \tilde\alpha_{crit}=g^2_{crit}/4\pi\approx 1.29 and \alpha^*_{crit}\approx 1.48.Comment: 16 pages, 2 figure

Superfluid state of magnetoexcitons in double layer graphene structures

The possibility of realization of a superfluid state of bound electron-hole pairs (magnetoexcitons) with spatially separated components in a graphene double layer structure (two graphene layers separated by a dielectric layer) subjected by a strong perpendicular to the layers magnetic field is analyzed. We show that the superfluid state of magnetoexcitons may emerge only under certain imbalance of filling factors of the layers. The imbalance can be created by an electrostatic field (external gate voltage). The spectrum of elementary excitations is found and the dependence of the Berezinskii-Kosterlitz-Thouless transition temperature on the interlayer distance is obtained. The advantages of use graphene double layer systems instead of double quantum well GaAs heterostructures are discussed

On passage through resonances in volume-preserving systems

Resonance processes are common phenomena in multiscale (slow-fast) systems. In the present paper we consider capture into resonance and scattering on resonance in 3-D volume-preserving slow-fast systems. We propose a general theory of those processes and apply it to a class of viscous Taylor-Couette flows between two counter-rotating cylinders. We describe the phenomena during a single passage through resonance and show that multiple passages lead to the chaotic advection and mixing. We calculate the width of the mixing domain and estimate a characteristic time of mixing. We show that the resulting mixing can be described using a diffusion equation with a diffusion coefficient depending on the averaged effect of the passages through resonances.Comment: 23 pages and 9 Figure

Nonlinear Bogolyubov-Valatin transformations and quaternions

In introducing second quantization for fermions, Jordan and Wigner (1927/1928) observed that the algebra of a single pair of fermion creation and annihilation operators in quantum mechanics is closely related to the algebra of quaternions H. For the first time, here we exploit this fact to study nonlinear Bogolyubov-Valatin transformations (canonical transformations for fermions) for a single fermionic mode. By means of these transformations, a class of fermionic Hamiltonians in an external field is related to the standard Fermi oscillator.Comment: 6 pages REVTEX (v3: two paragraphs appended, minor stylistic changes, eq. (39) corrected, references [10]-[14], [36], [37], [41], [67]-[69] added; v4: few extensions, references [62], [63] added, final version to be published in J. Phys. A: Math. Gen.

Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder

We study the Anderson localization of Bogoliubov quasiparticles (elementary many-body excitations) in a weakly interacting Bose gas of chemical potential $\mu$ subjected to a disordered potential $V$. We introduce a general mapping (valid for weak inhomogeneous potentials in any dimension) of the Bogoliubov-de Gennes equations onto a single-particle Schr\"odinger-like equation with an effective potential. For disordered potentials, the Schr\"odinger-like equation accounts for the scattering and localization properties of the Bogoliubov quasiparticles. We derive analytically the localization lengths for correlated disordered potentials in the one-dimensional geometry. Our approach relies on a perturbative expansion in $V/\mu$, which we develop up to third order, and we discuss the impact of the various perturbation orders. Our predictions are shown to be in very good agreement with direct numerical calculations. We identify different localization regimes: For low energy, the effective disordered potential exhibits a strong screening by the quasicondensate density background, and localization is suppressed. For high-energy excitations, the effective disordered potential reduces to the bare disordered potential, and the localization properties of quasiparticles are the same as for free particles. The maximum of localization is found at intermediate energy when the quasicondensate healing length is of the order of the disorder correlation length. Possible extensions of our work to higher dimensions are also discussed.Comment: Published versio

Anderson Localization of Bogolyubov Quasiparticles in Interacting Bose-Einstein Condensates

We study the Anderson localization of Bogolyubov quasiparticles in an interacting Bose-Einstein condensate (with healing length \xi) subjected to a random potential (with finite correlation length \sigma_R). We derive analytically the Lyapunov exponent as a function of the quasiparticle momentum k and we study the localization maximum k_{max}. For 1D speckle potentials, we find that k_{max} is proportional to 1/\xi when \xi is much larger than \sigma_R while k_{max} is proportional to 1/\sigma_R when \xi is much smaller than \sigma_R, and that the localization is strongest when \xi is of the order of \sigma_R. Numerical calculations support our analysis and our estimates indicate that the localization of the Bogolyubov quasiparticles is accessible in current experiments with ultracold atoms.Comment: published version (no significant changes compared to last version

Bare vs effective pairing forces. A microscopic finite-range interaction for HFB calculations in coordinate space

We propose a microscopic effective interaction to treat pairing correlations in the $^{1}S_0$ channel. It is introduced by recasting the gap equation written in terms of the bare force into a fully equivalent pairing problem. Within this approach, the proposed interaction reproduces the pairing properties provided by the realistic $AV18$ force very accurately. Written in the canonical basis of the actual Bogolyubov transformation, the force takes the form of an off-shell in-medium two-body matrix in the superfluid phase multiplied by a BCS occupation number $2 \rho_{m}$. This interaction is finite ranged, non local, total-momentum dependent and density dependent. The factor $2 \rho_{m}$ emerging from the recast of the gap equation provides a natural cut-off and makes zero-range approximations of the effective vertex meaningful. Performing such an approximation, the roles of the range and of the density dependence of the interaction can be disentangled. The isoscalar and isovector density-dependences derived ab-initio provide the pairing force with a strong predictive power when extrapolated toward the drip-lines. Although finite ranged and non local, the proposed interaction makes HFB calculations of finite nuclei in coordinate space tractable. Through the two-basis method, its computational cost is of the same order as for a zero-range force.Comment: 43 pages, 13 figures. Published versio

Electronic Orbital Currents and Polarization in Mott Insulators

The standard view is that at low energies Mott insulators exhibit only magnetic properties while charge degrees of freedom are frozen out as the electrons become localized by a strong Coulomb repulsion. We demonstrate that this is in general not true: for certain spin textures {\it spontaneous circular electric currents} or {\it nonuniform charge distribution} exist in the ground state of Mott insulators. In addition, low-energy ``magnetic'' states contribute comparably to the dielectric and magnetic functions $\epsilon_{ik}(\omega)$ and $\mu_{ik}(\omega)$ leading to interesting phenomena such as rotation the electric field polarization and resonances which may be common for both functions producing a negative refraction index in a window of frequencies

On radiative damping in plasma-based accelerators

Radiative damping in plasma-based electron accelerators is analyzed. The electron dynamics under combined influence of the constant accelerating force and the classical radiation reaction force is studied. It is shown that electron acceleration cannot be limited by radiation reaction. If initially the accelerating force was stronger than the radiation reaction force then the electron acceleration is unlimited. Otherwise the electron is decelerated by radiative damping up to a certain instant of time and then accelerated without limits. Regardless of the initial conditions the infinite-time asymptotic behavior of an electron is governed by self-similar solution providing unlimited acceleration. The relative energy spread induced by the radiative damping decreases with time in the infinite-time limit