Microscopic Derivation of the Fröhlich Hamiltonian for the Bose Polaron in the Mean-Field Limit

Myśliwy, Krzysztof; Seiringer, Robert

doi:10.1007/s00023-020-00969-3

Cited by 5 publications

(6 citation statements)

References 28 publications

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“…Thus the system is -for a large number of bosons -in good approximation described by the Bogoliubov-Fröhlich Hamiltonian, given in (9) below. Our result is in agreement with recent findings by Mysliwy and Seiringer, who analyzed the spectral properties of the same system [30].…”

Section: Introductionsupporting

confidence: 94%

“…Bogoliubov theory has also been justified in this context [42,16,11,43,27,38,39,40,2], and allows for a resolution of the spectrum close to the ground state [11,16,42,27,3]. Recently, higher order corrections [7] and the interaction with a tracer particle [30] have also been considered in the static context.…”

Section: Mean-field Equations and Correctionsmentioning

confidence: 99%

“…The excitations can thus be described by a non-interacting theory and, in the case of the torus, the energy levels can be computed explicitly (see e.g. [30]).…”

Section: Heuristics Of Bogoliubov Theorymentioning

confidence: 99%

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Dynamics of a Tracer Particle Interacting with Excitations of a Bose–Einstein Condensate

Lampart

Pickl²

2022

Ann. Henri Poincaré

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We consider the quantum dynamics of a large number N of interacting bosons coupled a tracer particle, i.e. a particle of another kind, on a torus. We assume that in the initial state the bosons essentially form a homogeneous Bose-Einstein condensate, with some excitations. With an appropriate mean-field scaling of the interactions, we prove that the effective dynamics for N → ∞ is generated by the Bogoliubov-Fröhlich Hamiltonian, which couples the tracer particle linearly to the excitation field.

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Section: Introductionsupporting

confidence: 94%

Section: Mean-field Equations and Correctionsmentioning

confidence: 99%

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Dynamics of a Tracer Particle Interacting with Excitations of a Bose–Einstein Condensate

Lampart

Pickl²

2022

Ann. Henri Poincaré

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“…In order to calculate the correlation, we invoke the expression for the dimensionless momenta and make use of Eqs. (23) and (22) which results in…”

Section: D-dimensional Spectral Densitymentioning

confidence: 99%

“…In the context of the Bose polaron problem, a large part of the theoretical effort deals with the weak regime, described by the so called Fröhlich Hamiltonian. This theoretical approach studies effective mass, quantum dynamics, [16][17][18][19][20][21][22], collision dynamics [23], the behavior in a d-dimensional BEC near the critical temperature [24], particularly in two dimensions [24,25], and related aspects of the system. Some studies in the weak regime considered the impurity as a quantum Brownian particle in a BEC or in a so called Luttinger liquid [26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Quantum dynamics of a Bose polaron in a d -dimensional Bose-Einstein condensate

et al. 2021

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We study the quantum motion of an impurity atom immersed in a Bose-Einstein condensate in arbitrary dimensions. It was shown, for all dimensions, that the Bogoliubov excitations of the Bose-Einstein condensate act as a bosonic bath for the impurity, where linear coupling is possible for a certain regime of validity, which was assessed only in one dimension. Here we present the detailed derivation of the d-dimensional Langevin equations that describe the quantum dynamics of the system, and of the associated generalized tensor that describes the spectral density in the full generality, and assesses the linear assumption in all dimensions. As results, we obtain, when the impurity is not trapped, the mean square displacement in all dimensions, showing that the motion is superdiffusive. We obtain also explicit expressions for the superdiffusive coefficient in the small and large temperature limits. We find that, in the latter case, the maximal value of this coefficient is the same in all dimensions, but is only reachable in one dimension, within the validity of the assumptions. We study also the behavior of the average energy and compare the results for various dimensions. In the trapped case, we study squeezing and find that the stronger position squeezing can be obtained in lower dimensions. We quantify the non-Markovianity of the particle's motion and find that it increases with dimensionality.

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Magnetic impurity inducing local defect of polarization and depletion of magnetization in magnetic cluster: blended ferron formation

Jipdi,

Dongmo,

Fai

et al. 2023

Phys. Scr.

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This paper presents a blended ferron in a ferromagnetic cluster wherethe electric polarization and magnetization tailor the quasi-particle characteristics.The resulting quasi-particle has coupled acoustic-polaron and ferron characteristics.The constant competition between electric polarization and magnetization alters theeffective mass thereby reducing the global inertia of the quasi-particle. The impuritysignificantly affects the environment, and the resulting defects in the polarization andmagnetization are soliton-like. It was observed that any gain in electric polarizationis conveyed by a drop in magnetization, where the hybridization of magnetization andpolarization gives rise to a new quasi-particle concept: a blended ferron. The latter ismanifested by the local deformation of the electric polarization and depletion of themagnetization in the cluster’s signature of magnetic reordering

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Microscopic Derivation of the Fröhlich Hamiltonian for the Bose Polaron in the Mean-Field Limit

Cited by 5 publications

References 28 publications

Dynamics of a Tracer Particle Interacting with Excitations of a Bose–Einstein Condensate

Dynamics of a Tracer Particle Interacting with Excitations of a Bose–Einstein Condensate

Quantum dynamics of a Bose polaron in a d -dimensional Bose-Einstein condensate

Magnetic impurity inducing local defect of polarization and depletion of magnetization in magnetic cluster: blended ferron formation

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