Pattern Formation in One-Dimensional Polaron Systems and Temporal Orthogonality Catastrophe

Recent studies have demonstrated that higher than two-body bath-impurity correlations are not important for quantitatively describing the ground state of the Bose polaron. Motivated by the above, we employ the so-called Gross Ansatz (GA) approach to unravel the stationary and dynamical properties of the homogeneous one-dimensional Bose-polaron for different impurity momenta and bath-impurity couplings. We explicate that the character of the equilibrium state crossovers from the quasi-particle Bose polaron regime to the collective-excitation stationary dark-bright soliton for varying impurity momentum and interactions. Following an interspecies interaction quench the temporal orthogonality catastrophe is identified, provided that bath-impurity interactions are sufficiently stronger than the intraspecies bath ones, thus generalizing the results of the confined case. This catastrophe originates from the formation of dispersive shock wave structures associated with the zero-range character of the bath-impurity potential. For initially moving impurities, a momentum transfer process from the impurity to the dispersive shock waves via the exerted drag force is demonstrated, resulting in a final polaronic state with reduced velocity. Our results clearly demonstrate the crucial role of non-linear excitations for determining the behavior of the one-dimensional Bose polaron.

Binaural Synthetic Aperture Imaging of the Field of Audition as the Head Rotates and Localisation Perception of Monophonic Sound Listened to through Headphones

A human listening to monophonic sound through headphones perceives the sound to emanate from a point inside the head at the auditory centre at effectively zero range. The extent to which this is predicted by synthetic-aperture calculation performed in response to head rotation is explored. The instantaneous angle between the auditory axis and the acoustic source, lambda, for the zero inter-aural time delay imposed by headphones is 90°. The lambda hyperbolic cone simplifies to the auditory median plane, which intersects a spherical surface centred on the auditory centre, along a prime meridian lambda circle. In a two-dimensional (2-D) synthetic-aperture computation, points of intersection of all lambda circles as the head rotates constitute solutions to the directions to acoustic sources. Geometrically, lambda circles cannot intersect at a point representing the auditory centre; nevertheless, 2-D synthetic aperture images for a pure turn of the head and for a pure lateral tilt yield solutions as pairs of points on opposite sides of the head. These can reasonably be interpreted to be perceived at the sums of the position vectors of the pairs of points on the acoustic image, i.e., at the auditory centre. But, a turn of the head on which a fixed lateral tilt of the auditory axis is concomitant (as in species of owl) yields a 2-D synthetic-aperture image without solution. However, extending a 2-D synthetic aperture calculation to a three-dimensional (3-D) calculation will generate a 3-D acoustic image of the field of audition that robustly yields the expected solution.

Asymmetric Lineshapes of Efimov Resonances in Mass-Imbalanced Ultracold Gases

The resonant profile of the rate coefficient for three-body recombination into a shallow dimer is investigated for mass-imbalanced systems. In the low-energy limit, three atoms collide with zero-range interactions, in a regime where the scattering lengths of the heavy–heavy and the heavy–light subsystems are positive and negative, respectively. For this physical system, the adiabatic hyperspherical representation is combined with a fully semi-classical method and we show that the shallow dimer recombination spectra display an asymmetric lineshape that originates from the coexistence of Efimov resonances with Stückelberg interference minima. These asymmetric lineshapes are quantified utilizing the Fano profile formula. In particular, a closed-form expression is derived that describes the width of the corresponding Efimov resonances and the Fano lineshape asymmetry parameter q. The profile of Efimov resonances exhibits a q-reversal effect as the inter- and intra-species scattering lengths vary. In the case of a diverging asymmetry parameter, i.e., |q|→∞, we show that the Efimov resonances possess zero width and are fully decoupled from the three-body and atom–dimer continua, and the corresponding Efimov metastable states behave as bound levels.

Proof of universality in one-dimensional few-body systems including anisotropic interactions

We provide an analytical proof of universality for bound states in one-dimensional systems of two and three particles, valid for short-range interactions with negative or vanishing integral over space. The proof is performed in the limit of weak pair-interactions and covers both binding energies and wave functions. Moreover, in this limit the results are formally shown to converge to the respective ones found in the case of the zero-range contact interaction.

Neutrino Oscillations in the Model of Interaction of Spinor Fields with Zero-Range Potential Concentrated on a Plane

Symanzik’s approach to the description of quantum field systems in an inhomogeneous space-time is used to construct a model for the interaction of neutrino fields with matter. In this way, the problem of the influence of strong inhomogeneities of the medium on the processes of oscillations is considered. As a simple example, a model of neutrino scattering on a material plane is investigated. Within this model, in the collisions of particles with planes, a special filtration mechanism can be formed. It has a significant impact on the dynamics of subsequent neutrino oscillations which are analogous to the Mikheev-Smirnov-Wolfenstein effect at propagation of these particles in an adiabatic medium. Taking into account the possibility of the filtration process in a highly inhomogeneous environment can be useful in planning and carrying out experimental studies of neutrino physics. It can also be considered by investigations of the role of neutrino in astrophysical processes by means of numerical simulations methods.

The existence of eigenvalues of Schrödinger operator on a lattice in the gap of the essential spectrum

We consider a three-particle discrete Schrödinger operator Hμγ (K), K 2 T3 associated to a system of three particles (two fermions and one different particle) interacting through zero range pairwise potential μ > 0 on the three-dimensional lattice Z 3. It is proved that the operator Hμγ (K), ||K|| < δ, for γ > γ0 has at least two eigenvalues in the gap of the essential spectrum for sufficiently large μ > 0.

A model study on superfluidity of a unitary Fermi gas of atoms interacting with a finite-ranged potential

We calculate Bardeen-Cooper-Schrieffer (BCS) state of a unitary Fermi gas of atoms interacting with the finite-ranged Jost-Kohn potential which has been recently shown to account for the resonant interactions [2019 {\rm J. Phys. B: At. Mol. Opt. Phys.} {\bf 52}, 165004]. Using exact scattering solution of the potential, we derive two-body ${\mathbf T}$-matrix element which is employed to construct the BCS Hamiltonian in momentum space. We present results on the energy- and range-dependence of the pairing gap and superfluid density and the range-dependence of the chemical potential for a wide variation of the scattering length including the \textcolor{red}{unitary} regime. In the zero range limit our calculated gap at the Fermi energy is found to be nearly equal to that calculated \textcolor{red}{in mean-field theory with contact potential}. The mean gap averaged over the full width at half maximum of the gap function in the zero range and unitary limits is found to be $0.42 E_F$ which is quite close to the recent result of the quantum Monte Carlo simulation [2018 {\rm Phys. Rev.A} {\bf 97}, 013601]. The chemical potential in the zero range limit also agrees well with that for the contact potential.