Momentum Of Impurity Research Articles

Quantum flutter from the nonlinear Luttinger liquid perspective

Abstract Quantum flutter is a ubiquitous phenomenon which can be observed from the fast moving impurity
injected into a fermionic or bosonic medium of quantum liquid. In this scenario, one usually consider
a medium of a fully polarized state and inject a spin-flipped impurity as the initial state. When the
initial velocity of the impurity is beyond the intrinsic sound velocity of the medium, the impurity
momentum dramatically exhibits a long-lived periodic oscillation with the periodicity remaining
invariant with respect to the initial velocity. In this letter, we show that such a novel phenomenon
can be explained by a linear Luttinger liquid coupled to a deep hole in the Fermi sea. Once the
deep hole excitations are involved and the impurity momentum surpass the Fermi momentum,
the propagator thus displays a periodic oscillation after a quick relaxation decay. The oscillation
periodicity is solely determined by the energy of the deepest hole excitation. Our result provides
deep insights into the dynamical behavior of quantum impurities immersed into one-dimensional
quantum liquids.

Poloidal impurity asymmetries, flow and neoclassical transport in pedestals in the plateau and banana regimes

Charge exchange recombination spectroscopy (CXRS) measures the radial electric field in the pedestal by measuring the impurity density, temperature and flow. Combined outboard and inboard CXRS measurements allow poloidal variations that arise due to the poloidal variation of the magnetic field to be determined. At present, impurity neoclassical pedestal models avoid the complications of treating finite poloidal gyroradius effects by assuming the impurity charge number is large compared with the main ion charge number. These models are extended slightly by retaining the impurity radial pressure gradient to demonstrate that no substantial effect occurs due to impurity diamagnetic effects. More importantly, the neoclassical model is significantly extended to obtain a more comprehensive treatment of the main ions in the plateau and banana regimes. A parallel impurity momentum equation is derived that is consistent with previous results in the banana regime and reduces to the proper large aspect ratio form required in the plateau regime. The implications for interpreting the CXRS measurements are discussed by writing all results in terms of the gradient drive and poloidal flow.

Mobile impurity in a one-dimensional gas at finite temperatures

We consider the McGuire model of a one-dimensional gas of free fermions interacting with a single impurity. We compute the static one-body function and momentum distribution of the impurity at finite temperatures. The results involve averages over Fredholm determinants that we further analyse using the effective form factors approach. With this approach, we derive the large-distance behaviour of the one-body function, which takes the form of an averaged exponential decay. This method allows us to study an experimentally important regime of small momenta of the impurity's momentum distribution. We also consider the one-body function at short distances and compute finite temperature Tan's contact.

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.

Stochastic-field approach to the quench dynamics of the one-dimensional Bose polaron

We consider the dynamics of a quantum impurity after a sudden interaction quench into a one-dimensional degenerate Bose gas. We use the Keldysh path integral formalism to derive a truncated Wigner like approach that takes the back action of the impurity onto the condensate into account already on the mean-field level and further incorporates thermal and quantum effects up to one-loop accuracy. This framework enables us not only to calculate the real space trajectory of the impurity but also the absorption spectrum. We find that quantum corrections and thermal effects play a crucial role for the impurity momentum at weak to intermediate impurity-bath couplings.Furthermore, we see the broadening of the absorption spectrum with increasing temperature.

Dynamics of impurity in the environment of Dirac fermions

We study the dynamics of a nonmagnetic impurity interacting with the surface states of a 3D and 2D topological insulator (TI). Employing the linked cluster technique we develop a formalism for obtaining the Green’s function of the mobile impurity interacting with the low-energy Dirac fermions. We show that for the non-recoil case in 2D, the Green’s function in the long-time limit has a power-law decay in time implying the breakdown of the quasiparticle description of the impurity. The spectral function in turn exhibits a weak power-law singularity. In the recoil case, however, the reduced phase-space for scattering processes implies a non-zero quasiparticle weight and the presence of a coherent part in the spectral function. Performing a weak coupling analysis we find that the mobility of the impurity reveals a T−3/2 divergence at low temperatures. In addition, we show that the Green’s function of an impurity interacting with the helical edge modes (surface states of 2D TI) exhibit power-law decay in the long-time limit for both the non-recoil and recoil case (with low impurity momentum), indicating the break down of the quasiparticle picture. However, for impurity with high momentum, the quasiparticle picture is restored. The mobility of the heavy impurity interacting with the helical edge modes exhibits unusual behaviour. It has an exponential divergence at low temperatures which can be tuned to a power-law divergence, T−4, by the application of the magnetic field.

Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas.

A kinetic theory describing the motion of an impurity particle in a degenerate Tonks-Girardeau gas is presented. The theory is based on the one-dimensional Boltzmann equation. An iterative procedure for solving this equation is proposed, leading to the exact solution in a number of special cases and to an approximate solution with the explicitly specified precision in a general case. Previously we reported that the impurity reaches a nonthermal steady state, characterized by an impurity momentum p(∞) depending on its initial momentum p(0) [E. Burovski, V. Cheianov, O. Gamayun, and O. Lychkovskiy, Phys. Rev. A 89, 041601(R) (2014)]. In the present paper the detailed derivation of p(∞)(p(0)) is provided. We also study the motion of an impurity under the action of a constant force F. It is demonstrated that if the impurity is heavier than the host particles, m(i)>m(h), damped oscillations of the impurity momentum develop, while in the opposite case, m(i)<m(h), oscillations are absent. The steady-state momentum as a function of the applied force is determined. In the limit of weak force it is found to be force independent for a light impurity and proportional to √[F] for a heavy impurity.

Quantum Flutter: Signatures and Robustness

We investigate the motion of an impurity particle injected with finite velocity into an interacting one-dimensional quantum gas. Using large-scale numerical simulations based on matrix product states, we observe and quantitatively analyze long-lived oscillations of the impurity momentum around a nonzero saturation value, called quantum flutter. We show that the quantum flutter frequency is equal to the energy difference between two branches of collective excitations of the model. We propose an explanation of the finite saturation momentum of the impurity based on the properties of the edge of the excitation spectrum. Our results indicate that quantum flutter exists away from integrability and provide parameter regions in which it could be observed in experiments with ultracold atoms using currently available technology.

Nonlinear momentum relaxation of an impurity in a harmonic chain

A microscopic derivation of the generalized Langevin equation for arbitrary powers of the momentum of an impurity in a harmonic chain is presented. As a direct consequence of the Gaussian character of the conditional momentum distribution function, nonlinear momentum coupling effects are absent for this system and the Langevin equation takes on a particularly simple form. The kernels which characterize the decay of higher powers of the impurity momentum depend on the ratio of the masses of the impurity and bath particles, in contrast to the situation for the momentum Langevin equation for this system. The simplicity of the harmonic chain dynamics is exploited in order to investigate several features of the relaxation, such as the factorization approximation for time-dependent correlation functions and the decay of the kinetic energy autocorrelation function.

Excitation Spectrum of an Impurity in the Hard-Sphere Bose Gas

The impurity excitation spectrum is calculated for the hard-sphere Bose gas with dilute impurity concentration, using the pseudopotential method of Lee, Huang, and Yang. The spectrum for the ideal case, in which the mass and interaction of impurity are the same with those of the bosons in the gas, is k2 in the unit of 2ma = h/ = 1 (ma being the mass of boson, and k the momentum of impurity), with an effective mass correction of −6445[(ρa3)12/π12]k2+O[(ρa3)k2,k4], where ρ is the density of the boson gas, and a is the hard-sphere diameter of the boson. The general impurity case is also calculated and found to have an impurity spectrum rk2, with a similar effective mass correction, where r is the mass ratio of the boson to the impurity.