The Theory of Quantum Liquids

Pines, David; Nozières, P.; Corngold, Noel

doi:10.1119/1.1974502

Cited by 915 publications

(124 citation statements)

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“…In general κ, K, v s depend on the magnetic field h and the specific form of the interaction v(k) (such dependence is simple at first order, see (16), but in general quite complex), but our theorem shows that the Kadanoff and Haldane relations (14) and (18) are still true. This is the first example in which such relations are proven in generic non-solvable models.…”

Section: Introduction and Main Resultsmentioning

confidence: 96%

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Universality Relations in Non-solvable Quantum Spin Chains

Benfatto

Mastropietro

2010

J Stat Phys

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Section: Introduction and Main Resultsmentioning

confidence: 96%

“…where X + = K is the critical index (16). Moreover, by definition (see §5.9 of [12]), Ω b x is a sum of multiscale graphs containing only λ-vertices with scale ≤ 0 and in which the the propagators g (h)…”

Section: Proof Of Lemma 21mentioning

confidence: 99%

Universality Relations in Non-solvable Quantum Spin Chains

Benfatto

Mastropietro

2010

J Stat Phys

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“…Such terms turn out to be crucial for an understanding of the Friedel oscillation in Sec.VIII. For the unscreened Coulomb interaction (2.9), the potential (2.12) becomes 17) with the complete elliptic integral K(z) of the first kind [45]. For x ≫ R, one finds V 0 (x) ∼ 1/x again.…”

Section: Forward Scatteringmentioning

confidence: 99%

“…From a fundamental (and theoretical) point of view, a single SWNT is an intriguing system, since Coulomb interactions induce a breakdown of Fermi liquid theory [17] in any one-dimensional (1D) metal. Astonishingly, Tans et al [18] were able to attach contacts to a single 3µm long (10,10) armchair SWNT.…”

Section: Introductionmentioning

confidence: 99%

Correlated transport and non-Fermi-liquid behavior in single-wall carbon nanotubes

1998

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We derive the effective low-energy theory for single-wall carbon nanotubes including the Coulomb interactions among electrons. The generic model found here consists of two spin-1 2 fermion chains which are coupled by the interaction. We analyze the theory using bosonization, renormalization-group techniques, and Majorana refermionization. Several experimentally relevant consequences of the breakdown of Fermi liquid theory observed here are discussed in detail, e.g., magnetic instabilities, anomalous conductance laws, and impurity screening profiles.

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“…4). The dimensionless ratio α = b/r 0 , where b is the dispersion of the nucleon wave-function, and r 0 the typical internucleon distance (∼ 1.2 fm), is the natural parameter to quantify nuclear clustering, in analogy with similar considerations in condensed matter [29].…”

mentioning

confidence: 99%

How atomic nuclei cluster

Ebran

Khan

Nikšić

et al. 2012

Nature

176

244

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Nucleonic matter displays a quantum liquid structure, but in some cases finite nuclei behave like molecules composed of clusters of protons and neutrons. Clustering is a recurrent feature in light nuclei, from beryllium to nickel. For instance, in 12 C the Hoyle state, crucial for stellar nucleosynthesis, can be described as a nuclear molecule consisting of three alpha-particles. The mechanism of cluster formation, however, has not yet been fully understood. We show that the origin of clustering can be traced back to the depth of the confining nuclear potential. By employing the theoretical framework of energy density functionals that encompasses both cluster and quantum liquid-drop aspects of nuclei, it is shown that the depth of the potential determines the energy spacings between single-nucleon orbitals, the localization of the corresponding wave functions and, therefore, the degree of nucleonic density clustering. Relativistic functionals, in particular, are characterized by deep single-nucleon potentials. When compared to non-relativistic functionals that yield similar ground-state properties (binding energy, deformation, radii), they predict the occurrence of much more pronounced cluster structures. More generally, clustering is considered as a transitional phenomenon between crystalline and quantum liquid phases of fermionic systems.The occurrence of molecular states in atomic nuclei and the formation of clusters of nucleons were already predicted in the 30's by von Weizsäcker and Wheeler [1,2]. Even though the description of nuclear dynamics became predominantly based on the concept of independent nucleons in a mean-field potential, a renewed interest in clustering phenomena in the 60's led to the development of dedicated theoretical methods [3]. Numerous experimental studies have revealed a wealth of data on clustering phenomena in light nuclei [4], and modern theoretical approaches use microscopic models that fully take into account single-nucleon degrees of freedom [5][6][7]. Clustering gives rise to nuclear molecules. For instance, in 12 C the second 0 + state the Hoyle state that plays a critical role in stellar nucleosynthesis, is predicted to display a three-α structure [8,9]. The binding energy of the α-particle, formed from two protons and two neutrons, is much larger than in other light nuclei. Cluster radioactivity [10], discovered in the 80's, is another manifestation of clustering in atomic nuclei. Experimental signatures of clustering are usually indirect. Quasi-molecular resonances are probed by scattering one cluster on another, such as in the 12 C+ 12 C system [4,11], and cluster structures are also discernible in the breakup of nuclei. Evidence has been reported for the formation of clusters in ground and excited states of a number of α-conjugate nuclei [4], that is nuclei with an equal even number of protons and neutrons, from 8 Be to 56 Ni.The mechanism of cluster formation in nuclei has not yet been fully understood. Deformation plays an important role because it removes the degenera...

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The Theory of Quantum Liquids

Abstract: A successful integral equation theory of simple quantum liquids

Cited by 915 publications

References 0 publications

Universality Relations in Non-solvable Quantum Spin Chains

Universality Relations in Non-solvable Quantum Spin Chains

Correlated transport and non-Fermi-liquid behavior in single-wall carbon nanotubes

How atomic nuclei cluster

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