Chemiluminescence, Electrogenerated

Nepomnyashchii, Alexander B.; Bard, Allen J.; Leland, Jonathan K.; Debad, Jeff D.; Sigal, George B.; Wilbur, James L.; Wohlstadter, Jacob N.

doi:10.1002/9780470027318.a5302.pub2

Cited by 14 publications

(25 citation statements)

References 57 publications

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“…This unphysical result is absent in the Bogoliubov approximation [4] and the (HFB)-Popov approximation [2,[5][6][7][8] (i.e., Shohno model [9]). However, they do not satisfy the identity proved by Nepomnyashchii and Nepomnyashchii [10,11], stating the vanishing off-diagonal self-energy in the low-energy and low-momentum limit in the BEC phase.…”

Section: Introductionmentioning

confidence: 82%

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Comparative studies of many-body corrections to an interacting Bose-Einstein condensate

Watabe

Ōhashi

2013

Phys. Rev. A

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We compare many-body theories describing fluctuation corrections to the mean-field theory in a weakly interacting Bose-condensed gas. Using a generalized random-phase approximation, we include both density fluctuations and fluctuations in the particle-particle scattering channel in a consistent manner. We also separately examine effects of the fluctuations within the framework of the random-phase approximation. Effects of fluctuations in the particle-particle scattering channel are also separately examined by using the many-body T -matrix approximation. We assess these approximations with respect to the transition temperature T c , the order of phase transition, as well as the so-called Nepomnyashchii-Nepomnyashchii identity, which states the vanishing off-diagonal self-energy in the low-energy and low-momentum limit. Since the construction of a consistent theory for interacting bosons which satisfies various required conditions is a long standing problem in cold atom physics, our results would be useful for this important challenge.

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Section: Introductionmentioning

confidence: 82%

“…Nepomnyashchii and Nepomnyashchii proved that the off-diagonal self-energy in the lowenergy and low-momentum limit exactly vanishes below T c [10,11]. This Nepomnyashchii-Nepomnyashchii (NN) identity is, however, not satisfied in the mean-field theory, where Σ 12 = n 0 U > 0.…”

Section: Nepomnyashchii-nepomnyashchii Identitymentioning

confidence: 99%

Comparative studies of many-body corrections to an interacting Bose-Einstein condensate

Watabe

Ōhashi

2013

Phys. Rev. A

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“…One difficulty faced by such approaches is that the ungapped propagators for the Goldstone modes lead to infrared (IR) divergences in many of these contributions. However there are strong cancellations between these divergences that follow from Ward identities for the spontaneously broken U(1) symmetry [17,18]. These cancellations are lost if an expansion of, say, a self-energy is truncated at finite order.…”

Section: Introductionmentioning

confidence: 99%

Application of the functional renormalization group to Bose gases: From linear to hydrodynamic fluctuations

2018

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We study weakly interacting Bose gases using the functional renormalization group with a hydrodynamic effective action. We use a scale-dependent parametrization of the boson fields that interpolates between a Cartesian representation at high momenta and an amplitude-phase one for low momenta. We apply this to Bose gases in two and three dimensions near the superfluid phase transition where they can be described by statistical O(2) models. We are able to give consistent physical descriptions of the infrared regime in both two and three dimensions. In particular, and in contrast to previous studies using the functional renormalization group, we find a stable superfluid phase at finite temperatures in two dimensions. We compare our results for the superfluid and boson densities with Monte-Carlo simulations, and we find they are in reasonable agreement. arXiv:1806.10373v2 [cond-mat.quant-gas] 21 Sep 2018 in the physical limit will depend on the choices made in setting up the flow equations. These include the form of the regulator, and ways of optimizing this choice have been developed [29,30].There are many versions of the FRG; in this work we use the one introduced by Wetterich [26, 27] for the average effective action, which is based on the Legendre transform of the logarithm of the partition function. The exact flow equation for this effective action has a one-loop structure. However, in practice, a truncation scheme needs to be used in order to solve for the RG flow. In this work we employ a derivative expansion; other choices can be found in the literature [31][32][33]. Truncations based on derivative expansions have been widely used in applications of the FRG and, despite the approximations introduced, they have been successful in describing phase transitions and critical exponents in a variety of systems [27,28].In particular, with fields in the Cartesian representation, the FRG has had some success in describing the weaklyinteracting Bose gas and related O(N ) models in three dimensions. In the critical regime, it yields results that are in good agreement with Monte-Carlo simulations. Away from that region, it has also been used to investigate bulk thermodynamic properties [18,27,31,[34][35][36][37][38]. As shown by Dupuis [18,39], one appealing aspect of this FRG approach is that, despite the potential IR divergences of loop diagrams as the physical limit is approached, it does respect the relevant Ward identity [17], giving a vanishing anomalous self-energy.This self-energy, and the resulting IR-divergent propagator for the longitudinal mode, arise from a momentumindependent interaction that vanishes in the physical limit. This treatment thus fails to capture the interaction between the amplitude fluctuations of the condensate that is present in Popov's effective theory. It also omits the leading interaction between the Goldstone modes, which is of second order in momenta. These limitations may be remedied by the inclusion of higher-order terms in the derivative expansion of the action. However, in current ...

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“…In fact, similar divergences are encountered in the theory of the interacting Bose gas where interaction corrections to Bogoliubov's celebrated mean-field theory for the condensed phase are known to be infrared divergent in two and three dimensions. [14][15][16][17][18] Note, however, that these divergencies do not arise in the spin-wave expansion of many other quantum magnets because spin conservation forces this coupling to vanish in the long wavelength limit. For- tunately, in the Bose gas nonperturbative resummations of these divergencies are available, leading to a nonanalytic contribution to the longitudinal part of the bosonic two-point function.…”

Section: Introductionmentioning

confidence: 99%

Singular spin-wave theory and scattering continua in the cone state ofCs2CuCl4

2014

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For temperatures below 0.6 K the geometrically frustrated layered quantum antiferromagnet Cs2CuCl4 in a magnetic field perpendicular to the layers orders magnetically in a so-called cone state, where the magnetic moments have a finite component in the field direction while their projection onto the layers forms a spiral. Modeling this system by a two-dimensional spatially anisotropic quantum Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interaction, we find that even for vanishing temperature the usual spin-wave expansion is plagued by infrared divergencies which are due to the coupling between longitudinal and transverse spin fluctuations in the cone state. Similar divergencies appear also in the ground state of the interacting Bose gas in two and three dimensions. Using known results for the correlation functions of the interacting Bose gas, we present a non-perturbative expression for the dynamic structure factor in the cone state of Cs2CuCl4. We show that in this state the spectral line shape of spin fluctuations exhibits singular scattering continua which can be understood in terms of the well-known anomalous longitudinal fluctuations in the ground state of the two-dimensional Bose gas.

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Chemiluminescence, Electrogenerated

Cited by 14 publications

References 57 publications

Comparative studies of many-body corrections to an interacting Bose-Einstein condensate

Comparative studies of many-body corrections to an interacting Bose-Einstein condensate

Application of the functional renormalization group to Bose gases: From linear to hydrodynamic fluctuations

Singular spin-wave theory and scattering continua in the cone state ofCs2CuCl4

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