Microscopic theory of the friction force exerted on a quantum impurity in one-dimensional quantum liquids

Abstract

We study the motion of a slow quantum impurity in one-dimensional environments focusing on systems of strongly interacting bosons and weakly interacting fermions. While at zero temperature the impurity motion is frictionless, at low temperatures finite friction appears. The dominant process is the scattering of the impurity off two fermionic quasiparticles. We evaluate the friction force and show that, at low temperatures, it scales either as the fourth or the sixth power of temperature, depending on the system parameters. This is a result of the scattering of the impurity off two fermionic quasiparticles that are situated around different Fermi points. It is the dominant process at low temperatures. We also evaluate the contribution to the friction force originating from the scattering of the impurity off two fermionic quasiparticles that are situated around different Fermi points. It behaves as the tenth power of temperature.

Exact result for the polaron mass in a one-dimensional Bose gas

“…Many theoretical papers addressed polaron properties in one-dimensional bosonic systems [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Several of them [12,14,15,18,23,27] rely on models solvable by Bethe ansatz [32][33][34].…”

Mobile impurity in a one-dimensional gas at finite temperatures

“…The total momentum P (k) = k j . The summation in ( 27) can be performed exactly, using a slight variation of the Cauchy-Binet formula [67] and the result is (28) with A ij = A(k i , k j ) and B ij = B(k i , k j ) where A(q, q ) = − e(q) − e(q ) q − q B(q, q ), B(q, q ) = 2 L exp g(q) + g(q ) − ix(q + q ) 2 × sin πν(q) sin πν(q ), (29) and…”

“…For instance, various mean-field approaches [20][21][22][23][24] can be used to describe properties of the ground state. Instead, perturbation theories for the weak impurity-gas coupling allows one to describe dynamics of the impurity [25][26][27][28][29]. Numerical methods such as the time-dependent densitymatrix renormalization-group has been successfully applied to extract breathing mode [30] and time-evolving block decimation methods can be used to describe various non-equilibrium aspects of the impurity [31], including the quantum flutter phenomenon [32].…”

Microscopic theory of thermalization in 1D with nonlinear bath coupling

“…In recent years, there have been significant advances in understanding the dynamics of impurities immersed in bosonic [12][13][14][15][16] and fermionic [12,17,18] systems. In recent work, linearized approaches have been used to show the emergence of Brownian motion in D-dimensional Bose-Einstein Condensates [19], as well as the microscopic origins of friction in one-dimensional quantum liquids [20].…”