Superdeduction at Work

Brauner, Paul; Houtmann, Clément; Kirchner, Claude

doi:10.1007/978-3-540-73147-4_7

Cited by 10 publications

(13 citation statements)

References 22 publications

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“…It was shown that the critical temperature of CPC increases with increasing magnetic field at a given isospin density [48,49]. Besides, the chiral soliton lattice, an inhomogeneous state of neutral pion condensation was predicted in the chiral perturbation theory at finite baryon chemical potential with magnetic field [50]. However, it was shown to be unstable to CPC at large magnetic field or baryon chemical potential [50].…”

Section: Introductionmentioning

confidence: 99%

Rotation induced charged pion condensation in a strong magnetic field: A Nambu–Jona-Lasino model study

Cao

2019

Phys. Rev. D

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We investigate the possibility of charged pion condensation in the presence of parallel rotation and magnetic field within the Nambu-Jona-Lasinio model with quarks as the fundamental degrees of freedom. Previous study based on non-interacting Klein-Gordon theory for pions showed that the charged pions will undergo Bose-Einstein condensation under this circumstance [Y. Liu and I. Zahed, Phys. Rev. Lett. 120, 032001 (2018)]. In this work, we take into account the internal quark structures of charged pions self-consistently through quark polarization loops in an interacting theory, i.e., the Nambu-Jona-Lasino model. The stability of the system against the formation of charged pion condensation, i.e., a nonzero expectation value of the composite charged pion field uiγ5d, is explored. We find that two competing effects are induced by the rotation: the isospin enhancement which favors charged pion condensation and the spin breaking which disfavors the condensation. For a strong magnetic field ( √ eB ∼ 1GeV) and system size of a few fermi, the isospin enhancement effect is stronger than the spin breaking one, and the charged pion condensation becomes energetically favored beyond a critical angular velocity of a few MeV.

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Section: Introductionmentioning

confidence: 99%

Rotation induced charged pion condensation in a strong magnetic field: A Nambu–Jona-Lasino model study

Cao

2019

Phys. Rev. D

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“…A onedimensional superfluid is a simple and useful platform to analyze various macroscopic quantum phenomena such as Josephson dynamics [50][51][52][53]. Moreover, the formation of solitons that we have focused on appears ubiquitously not only in condensed matter physics [21,22] but in high energy physics [25,26]. Our work on the superfluid properties of the one-dimensional annular superfluid would have a wide range of applications and contributions to further theoretical investigations in diverse physical systems.…”

Section: Discussionmentioning

confidence: 99%

“…This is peculiar to effective one-dimensional systems because an extra transverse dimension can destabilize solitons in higher spatial dimensions. Solitons show up in various context of physics from condensed matter physics [21,22], biological systems [23,24] to high energy physics [25,26]. In ultracold atomic systems, the dynamics of soliton has been studied under several conditions such as the quench dynamics [27,28], the dynamics in * koichiro.furutani@phd.unipd.it FIG.…”

Section: Introductionmentioning

confidence: 99%

Superfluid properties of bright solitons in a ring

Furutani,

Salasnich

2021

Preprint

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We theoretically investigate superfluid properties of a one-dimensional annular superfluid with a boost. We derive the formula of the superfluid fraction in the one-dimensional superfluid, which was originally derived by Leggett in the context of supersolid. We see that the superfluid fraction given by Leggett's formula detects the emergence of solitons in the one-dimensional annular superfluid. The formation of a bright soliton at a critical interaction strength decreases the superfluid fraction. At a critical boost velocity, a node appears in the soliton and the superfluid fraction vanishes. With a transverse dimension, the soliton alters to a more localized one and it undergoes dynamical instability at a critical transverse length. Consequently, the superfluid fraction decreases as one increases the length up to the critical length. With a potential barrier along the ring, the uniform density alters to an inhomogeneous configuration and it develops a soliton localized at one of the potential minima by increasing the interaction strength.

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“…Strategies are increasingly useful as a component in systems with computation and deduction explicitly interacting [18,20]. The complementarity between deduction and computation, as emphasized in particular in deduction modulo [18], allows us to now envision a completely new generation of proof assistants where customized deductions are performed modulo appropriate and user definable computations [12,13].…”

Section: Introductionmentioning

confidence: 99%

Extensional and Intensional Strategies

Bourdier

Cirstea

Dougherty

et al. 2010

Electron. Proc. Theor. Comput. Sci.

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This paper is a contribution to the theoretical foundations of strategies. We first present a general definition of abstract strategies which is extensional in the sense that a strategy is defined explicitly as a set of derivations of an abstract reduction system. We then move to a more intensional definition supporting the abstract view but more operational in the sense that it describes a means for determining such a set. We characterize the class of extensional strategies that can be defined intensionally. We also give some hints towards a logical characterization of intensional strategies and propose a few challenging perspectives.

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Superdeduction at Work

Cited by 10 publications

References 22 publications

Rotation induced charged pion condensation in a strong magnetic field: A Nambu–Jona-Lasino model study

Rotation induced charged pion condensation in a strong magnetic field: A Nambu–Jona-Lasino model study

Superfluid properties of bright solitons in a ring

Extensional and Intensional Strategies

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