Structure of the perturbation expansion for the bose liquid at zero temperature

Gavoret, J.; Nozières, P.

doi:10.1016/0003-4916(64)90200-3

Cited by 370 publications

(302 citation statements)

References 9 publications

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“…A systematic study of the implications of WI was originally performed in Ref. 4 . In the following Sections we will exploit extensively the whole set of WI to reduce the set of IR divergent diagrams of PT to only a few independent ones.…”

Section: A Bogoliubov Approximation and The Appearance Of Ir Divergementioning

confidence: 99%

“…The long-wavelength limit of these vertex functions has been obtained long ago. [4][5][6] Here, we will rederive them in a more compact form taking into account the presence of IR divergences. Important information on the scaling of the running coupling will follow from these connections.…”

Section: B Local Ward Identities: Small Kmentioning

confidence: 99%

“…4 Equation (3.36) relates z tt to n/m. Finally, in the limit k → 0 the limit of Γ ll (k) is (βΩ) −1 ∂ 2 Γ/∂ψ 2 lo by definition.…”

Section: B Local Ward Identities: Small Kmentioning

confidence: 99%

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Renormalization-group approach to the infrared behavior of a zero-temperature Bose system

et al. 2004

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We exploit the renormalization-group approach to establish the exact infrared behavior of an interacting Bose system at zero temperature. The local-gauge symmetry in the broken-symmetry phase is implemented through the associated Ward identities, which reduce the number of independent running couplings to a single one. For this coupling the ǫ-expansion can be controlled to all orders in ǫ (= 3−d). For spatial dimensions 1 < d ≤ 3 the Bogoliubov fixed point is unstable towards a different fixed point characterized by the divergence of the longitudinal correlation function. The Bogoliubov linear spectrum, however, is found to be independent from the critical behavior of this correlation function, being exactly constrained by Ward identities. The new fixed point properly gives a finite value of the coupling among transverse fluctuations, but due to virtual intermediate longitudinal fluctuations the effective coupling affecting the transverse correlation function flows to zero. As a result, no transverse anomalous dimension is present. This treatment allows us to recover known results for the quantum Bose gas in the context of a unifying framework and also to reveal the non-trivial skeleton structure of its perturbation theory.

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Section: A Bogoliubov Approximation and The Appearance Of Ir Divergementioning

confidence: 99%

Section: B Local Ward Identities: Small Kmentioning

confidence: 99%

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Renormalization-group approach to the infrared behavior of a zero-temperature Bose system

et al. 2004

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“…This cancellation is a manifestation of the general results of Gavoret and Nozières [24] at least for the combination that enters in the Ward identity.…”

Section: Confirmation At One-loop Ordermentioning

confidence: 57%

Nonequilibrium Relaxation of Bose–Einstein Condensates: Real-Time Equations of Motion and Ward Identities

et al. 2002

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We present a field-theoretical method to obtain consistently the equations of motion for small amplitude condensate perturbations in a homogeneous Bose-condensed gas directly in real time. It is based on linear response, and combines the SchwingerKeldysh formulation of nonequilibrium quantum field theory with the NambuGor'kov formalism of quasiparticle excitations in the condensed phase and the tadpole method in quantum field theory. This method leads to causal equations of motion that allow to study the nonequilibrium evolution as an initial value problem. It also allows to extract directly the Ward identities, which are a consequence of the underlying gauge symmetry and which in equilibrium lead to the HugenholtzPines theorem. An explicit one-loop calculation of the equations of motion beyond the Hartree-Fock-Bogoliubov approximation reveals that the nonlocal, absorptive contributions to the self-energies corresponding to the Beliaev and Landau damping processes are necessary to fulfill the Ward identities in or out of equilibrium. It is argued that a consistent implementation at low temperatures must be based on the loop expansion, which is shown to fulfill the Ward identities order by order in perturbation theory.

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“…Rather the single particle response has the same phonon-like poles (energies) as the density response so that there is only a single mode in the fluid. [4][5][6] The P-R mode is therefore the only mode and can decay only to other P-R modes. At low temperatures the single mode therefore remains sharply defined until its energy is high enough that it can decay to two other modes.…”

mentioning

confidence: 99%

Phonon-roton modes of liquid4He beyond the roton in the porous medium MCM-41

et al. 2013

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We present neutron scattering measurements of the phonon-roton (P-R) mode of superfluid 4 He confined in 47 Å MCM-41 at T = 0.5 K at wave vectors, Q, beyond the roton wave vector (QR = 1.92 Å−1 ). Measurements beyond the roton require access to high wave vectors (up to Q = 4 Å−1 ) with excellent energy resolution and high statistical precision. The present results show for the first time that at T = 0.5 K the P-R mode in MCM-41 extends out to wave-vector Q ≃ 3.6 Å−1 with the same energy and zero width (within precision) as observed in bulk superfluid 4 He. Layer modes in the roton region are also observed. Specifically, the P-R mode energy, ωQ, increases with Q for Q > QR and reaches a plateau at a maximum energy ωQ = 2∆ where ∆ is the roton energy, ∆ = 0.74 ± 0.01 meV in MCM-41. This upper limit means the P-R mode decays to two rotons when its energy exceeds 2∆. It also means that the P-R mode does not decay to two layers modes. If the P-R could decay to two layer modes, ωQ would plateau at a lower energy, ωQ = 2∆L where ∆L = 0.60 meV is the energy of the roton like minimum of the layer mode. The observation of the P-R mode with energy up to 2∆ shows that the P-R mode and the layer modes are independent modes with apparently little interaction between them.

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Structure of the perturbation expansion for the bose liquid at zero temperature

Cited by 370 publications

References 9 publications

Renormalization-group approach to the infrared behavior of a zero-temperature Bose system

Renormalization-group approach to the infrared behavior of a zero-temperature Bose system

Nonequilibrium Relaxation of Bose–Einstein Condensates: Real-Time Equations of Motion and Ward Identities

Phonon-roton modes of liquid4He beyond the roton in the porous medium MCM-41

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