Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1003.0652

Reply to arXiv:1002.4366, "Comment on `Motion of an impurity in an ultracold quasi-one-dimensional gas of hard-core bosons`", by S. Giraud and R. Combescot

Marvin D. Girardeau, Anna Minguzzi

Published Mar 2, 2010• 1 citation
arXivHTMLPDF

Abstract

In their Comment [1] Giraud and Combescot point out that the contribution to the impurity-boson distribution function $ρ_{bi}(x-y)$ of a term we dropped is not negligible, rather than being negligible in the thermodynamic limit as we had conjectured. We now agree with them, but nevertheless our results for $ρ_{bi}$ are highly accurate for large impurity-boson mass ratio $m_i/m$ and remain qualitatively correct for all values of $m_i/m$ and all values of the boson-impurity coupling constant.

DOI
10.48550/arxiv.1003.0652

Related papers

Reply to “Comment on ‘Motion of an impurity particle in an ultracold quasi-one-dimensional gas of hard-core bosons’ ”

Marvin D. Girardeau, Anna Minguzzi

In their Comment Giraud and Combescot (GC) [Phys. Rev. A 82, 037603 (2010)] point out that the contribution to the impurity-boson distribution function ${\ensuremath{\rho}}_{\mathit{bi}}(x\ensuremath{-}y)$ of a term we dropped is not negligible, rather than being negligible in the thermodynamic limit as we had conjectured. We now agree with them, but our results for ${\ensuremath{\rho}}_{\mathit{bi}}$ are highly accurate for large impurity-boson mass ratio ${m}_{i}/m$, for all values of $x\ensuremath{-}y$ and boson-impurity coupling constant.

Physical Review A•Sep 7, 2010•2 citations

Comment on “Motion of an impurity particle in an ultracold quasi-one-dimensional gas of hard-core bosons”

S. Giraud, R. Combescot

Very recently Girardeau and Minguzzi [Phys. Rev. A 79, 033610 (2009)] have studied an impurity in a one-dimensional gas of hard-core bosons. In particular they dealt with the general case where the mass of the impurity is different from the mass of the bosons and the impurity-boson interaction is not necessarily infinitely repulsive. We show that one of their initial steps is unjustified, contradicting known exact results. Their results in the general case apply only actually when the mass of the impurity is infinite.

arXiv:1002.4366•Physical Review A•Sep 7, 2010•2 citations

Reply to “Comment on ‘Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas’ ”

Oleksandr Gamayun, Oleg Valentinovich Lychkovskiy, Vadim Cheianov

In our recent paper [O. Gamayun, O. Lychkovskiy, and V. Cheianov, Phys. Rev. E 90, 032132 (2014)] we studied the dynamics of a mobile impurity particle weakly interacting with the Tonks-Girardeau gas and pulled by a small external force F. Working in the regime when the thermodynamic limit is taken prior to the small force limit, we found that the Bloch oscillations of the impurity velocity are absent in the case of a light impurity. Further, we argued that for a light impurity the steady-state drift velocity V(D) remains finite in the limit F→0. These results are in contradiction with earlier works by Gangardt and co-workers [D. M. Gangardt and A. Kamenev, Phys. Rev. Lett. 102, 070402 (2009); M. Schecter, D. M. Gangardt, and A. Kamenev, Ann. Phys. (NY) 327, 639 (2012)]. One of us has conjectured [O. Lychkovskiy, Phys. Rev. A 91, 040101 (2015)] that the central assumption of these works, the adiabaticity of the dynamics, can break down in the thermodynamic limit. In the preceding Comment [M. Schecter, D. M. Gangardt, and A. Kamenev, Phys. Rev. E 92, 016101 (2015)], Schecter et al. have argued against this conjecture and in support of the existence of Bloch oscillations and the linearity of V(D)(F). They have suggested that the ground state of the impurity-fluid system is a quasibound state and that this is sufficient to ensure adiabaticity in the thermodynamic limit. Their analytical argument is based on a certain truncation of the Hilbert space of the system. We argue that extending the results and intuition based on their truncated model on the original many-body problem lacks justification.

arXiv:1407.4433•Physical Review E•Jul 8, 2015•11 citations

Reply to the "Comment on 'Neel order in doped quasi one-dimensional antiferromagnets'"

Sebastian Eggert, Ian K. Affleck, Matthew D. P. Horton

In a recent comment by A.A. Zvyagin to our Letter [Phys. Rev. Lett. 89, 47202 (2002)] it was pointed out that the bosonization treatment of the antiferromagnetic Heisenberg chain is only valid in the low temperature and long length limit. We support this statement and quantify the limits of validity by explicitly showing the crossover to the high temperature and/or short length limit using a combination of bosonization formulas and numerical results.

arXiv:cond-mat/0210002•Sep 30, 2002•0 citations

Comment on “Kinetic theory for a mobile impurity in a degenerate Tonks-Girardeau gas”

Michael Schecter, Dimitri M. Gangardt, Alex Kamenev

In a recent paper Gamayun et al. [O. Gamayun, O. Lychkovskiy, and V. Cheianov, Phys. Rev. E 90, 032132 (2014)] studied the dynamics of a mobile impurity weakly coupled to a one-dimensional Tonks-Girardeau gas of strongly interacting bosons. Employing the Boltzmann equation approach, they, in particular, arrived at the following conclusions: (i) a light impurity, being accelerated by a constant force F, does not exhibit Bloch oscillations, which were predicted and studied by Gangardt and co-workers [D. M. Gangardt and A. Kamenev, Phys. Rev. Lett. 102, 070402 (2009); M. Schecter, D. M. Gangardt, and A. Kamanev, Ann. Phys. (N.Y.) 327, 639 (2012)]; (ii) a heavy impurity does undergo Bloch oscillations, accompanied by a drift with the velocity v(D)∝√[F]. In this Comment we argue that result (i) is an artifact of the classical Boltzmann approximation. The latter misses the formation of the quasibound state between the impurity and a hole. Its dispersion relation E(b)(P,ρ) is a smooth periodic function of momentum P with the period 2k(F)=2πℏρ, where ρ is a density of the host gas. Being accelerated by a small force, such a bound-state exhibits Bloch oscillations superimposed with the drift velocity v(D)=μF. The mobility μ may be expressed exactly [M. Schecter et al., Ann. Phys. (N.Y.) 327, 639 (2012)] in terms of E(b)(P,ρ). Result (ii), while not valid at exponentially small forces, indeed reflects an interesting intermediate-force behavior.

arXiv:1404.4366•Physical Review E•Jul 8, 2015•14 citations

Reply to ‘‘Comment on ‘Undetermined-constant method in the boson Green’s-function theory’ ’’

Jingbo Zhang

In this Reply to the preceding Comment by Brown [Phys. Rev. A 43, XXXX (1991)], the following two points are discussed. (1) The undetermined-constant method solves problems by using only boson Green's functions, but the method given by Brown in the Comment must use both boson and fermion Green's functions. (2) When the undetermined-constant method is applied to the example given by Ramos and Gomes [Nuovo Cimento 3A, 441 (1971)], exactly the same results can be obtained.

Physical Review A•Apr 1, 1991•1 citation
In their Comment [1] Giraud and Combescot point out that the contribution to the impurity-boson distribution function ρbi(x−y)ρ_{bi}(x-y)ρbi​(x−y) of a term we dropped is not negligible, rather than being negligible in the thermodynamic limit as we had conjectured. We now agree with them, but nevertheless our results for ρbiρ_{bi}ρbi​ are highly accurate for large impurity-boson mass ratio mi/mm_i/mmi​/m and remain qualitatively correct for all values of mi/mm_i/mmi​/m and all values of the boson-impurity coupling constant.
In their Comment Giraud and Combescot (GC) [Phys. Rev. A 82, 037603 (2010)] point out that the contribution to the impurity-boson distribution function ${\ensuremath{\rho}}_{\mathit{bi}}(x\ensuremath{-}y)$ of a term we dropped is not negligible, rather than being negligible in the thermodynamic limit as we had conjectured. We now agree with them, but our results for ${\ensuremath{\rho}}_{\mathit{bi}}$ are highly accurate for large impurity-boson mass ratio mi/m{m}_{i}/mmi​/m, for all values of $x\ensuremath{-}y$ and boson-impurity coupling constant.
Very recently Girardeau and Minguzzi [Phys. Rev. A 79, 033610 (2009)] have studied an impurity in a one-dimensional gas of hard-core bosons. In particular they dealt with the general case where the mass of the impurity is different from the mass of the bosons and the impurity-boson interaction is not necessarily infinitely repulsive. We show that one of their initial steps is unjustified, contradicting known exact results. Their results in the general case apply only actually when the mass of the impurity is infinite.
In our recent paper [O. Gamayun, O. Lychkovskiy, and V. Cheianov, Phys. Rev. E 90, 032132 (2014)] we studied the dynamics of a mobile impurity particle weakly interacting with the Tonks-Girardeau gas and pulled by a small external force F. Working in the regime when the thermodynamic limit is taken prior to the small force limit, we found that the Bloch oscillations of the impurity velocity are absent in the case of a light impurity. Further, we argued that for a light impurity the steady-state drift velocity V(D) remains finite in the limit F→0. These results are in contradiction with earlier works by Gangardt and co-workers [D. M. Gangardt and A. Kamenev, Phys. Rev. Lett. 102, 070402 (2009); M. Schecter, D. M. Gangardt, and A. Kamenev, Ann. Phys. (NY) 327, 639 (2012)]. One of us has conjectured [O. Lychkovskiy, Phys. Rev. A 91, 040101 (2015)] that the central assumption of these works, the adiabaticity of the dynamics, can break down in the thermodynamic limit. In the preceding Comment [M. Schecter, D. M. Gangardt, and A. Kamenev, Phys. Rev. E 92, 016101 (2015)], Schecter et al. have argued against this conjecture and in support of the existence of Bloch oscillations and the linearity of V(D)(F). They have suggested that the ground state of the impurity-fluid system is a quasibound state and that this is sufficient to ensure adiabaticity in the thermodynamic limit. Their analytical argument is based on a certain truncation of the Hilbert space of the system. We argue that extending the results and intuition based on their truncated model on the original many-body problem lacks justification.
In a recent paper Gamayun et al. [O. Gamayun, O. Lychkovskiy, and V. Cheianov, Phys. Rev. E 90, 032132 (2014)] studied the dynamics of a mobile impurity weakly coupled to a one-dimensional Tonks-Girardeau gas of strongly interacting bosons. Employing the Boltzmann equation approach, they, in particular, arrived at the following conclusions: (i) a light impurity, being accelerated by a constant force F, does not exhibit Bloch oscillations, which were predicted and studied by Gangardt and co-workers [D. M. Gangardt and A. Kamenev, Phys. Rev. Lett. 102, 070402 (2009); M. Schecter, D. M. Gangardt, and A. Kamanev, Ann. Phys. (N.Y.) 327, 639 (2012)]; (ii) a heavy impurity does undergo Bloch oscillations, accompanied by a drift with the velocity v(D)∝√[F]. In this Comment we argue that result (i) is an artifact of the classical Boltzmann approximation. The latter misses the formation of the quasibound state between the impurity and a hole. Its dispersion relation E(b)(P,ρ) is a smooth periodic function of momentum P with the period 2k(F)=2πℏρ, where ρ is a density of the host gas. Being accelerated by a small force, such a bound-state exhibits Bloch oscillations superimposed with the drift velocity v(D)=μF. The mobility μ may be expressed exactly [M. Schecter et al., Ann. Phys. (N.Y.) 327, 639 (2012)] in terms of E(b)(P,ρ). Result (ii), while not valid at exponentially small forces, indeed reflects an interesting intermediate-force behavior.