On the collective properties of a boson system

Valatin, J. G.; Butler, D.

doi:10.1007/bf02859603

Cited by 108 publications

(55 citation statements)

References 7 publications

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“…BCS-like Fermi-liquid) to Fermi-gas takes place) and not by change of the lattice structures. Indeed, if we assume that the observed in Y-Ba-Cu-O energy gap 2∆(30)(31)(32)(33)(34)(35)(36)(37)(38)(39)(40) meV and (60-70) meV is equal to the binding energy of two types of bipolarons, then from the BCS-like relation (4.4) it follows T F (100-130) K and (200-230) K in accordance with the above observations. Further, if in BSC at T F2 < T c1 (= T B1 ) and T c1 < T F1 the temperature dependence of the ∆ SC are identified improperly as ∆ T ) = ∆ F1 (T ), then such ∆ SC (T ) should deviate down and up, respectively, from their assumed BCS-dependence.…”

supporting

confidence: 77%

“…37) and SC properties of electronic liquids in superconductors. Another most often discussed model of superfluidity based on the c-number condensate of a repulsive BG, proposed first by Bogolubov 37 and then developed by many others 38,41,46 is not suitable also for this purpose. 42,131 As the theory of a repulsive BG superfluidity (or c-numbercondensate theory 46 ) cannot explain a number SF properties of 4 He, such as, the observed half-integer values of circulation, 43 the observed 4 He specific heat departure from the phonon-like dependence, 44 the condensate fraction n B0 = N B0 /N B (e.g., c-number theory 42,131 predicts n B0 > 1 which is unphysical), and the depletion of the zero-momentum k = 0 state, where N B0 is the number of Bose particles with k = 0.…”

Section: Ground State Of Bose-liquidmentioning

confidence: 99%

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The Microscopic Theory of Superfluidity and Superconductivity Driven by Single Particle and Pair Condensation of Attracting Bosons

Dzhumanov

1998

Int. J. Mod. Phys. B

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A original microscopic theory of superfluidity and superconductivity driven by the single particle (SPC) and pair condensation (PC) of attracting bosons both in Fermi and in Bose systems is developed. This theory (as distinct from the existing theories) for Fermi systems contains two order parameters ∆ F and ∆ B characterizing the attracting fermion pairs and boson pairs, respectively. In such systems superconducting (SC) phase transition is accompanied, as a rule, by the formation of k-space composite bosons (e.g. Cooper pairs and bipolarons) with their subsequent transition to the superfluid (SF) state by attractive SPC and PC. A novel Fermi-liquid and SF Bose-liquid theories are elaborated for description this two-stage Fermi-Bose-liquid (FBL) scenario of SC (or SF) transition. The crossover from k-to real (r)-space pairing regime for BCS-like coupling constants γ F 0.7 − 0.9 and the irrelevance of r-space pairs to the superconductivity are shown. The developed SF Bose-liquid theory predicts the first-order phase transition SPC ↔ PC of attracting 3d-bosons with the kink-like behaviors of all SC (SF) parameters near T = T * B < Tc in accordance with the observations in 4 He, 3 He and superconductors. It is argued that the coexistence of the order parameters ∆ F and ∆ B leads to the superconductivity by two FBL scenarios. One of these scenarios is realized in the so-called fermion (type I, II and III) superconductors (FSC) (where formation of k-space composite bosons and their condensation occur at the same temperature) and the other in the boson (type II and III) superconductors (BSC) (where BCS-like pairing take place in the normal state with manifesting of the second-order phase transition and opening of the pseudogap at T = T F > Tc). There the gapless superfluidity (superconductivity) is caused by the gapless excitation spectrum of bosons at T ≤ T * B and not by the presence of point or line nodes of the BCS-like gap ∆ F assumed in some s-, pand d-pairing models. The 3D-and 2D-insulator-metal-superconductor phase diagrams are presented. The necessary and sufficient microscopic criterions for superfluidity is formulated. The theory proposed are in close agreement with the observations in 4 He, 3 He, superconductors, nuclear and neutron star matter, cosmology, etc.

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supporting

confidence: 77%

Section: Ground State Of Bose-liquidmentioning

confidence: 99%

The Microscopic Theory of Superfluidity and Superconductivity Driven by Single Particle and Pair Condensation of Attracting Bosons

Dzhumanov

1998

Int. J. Mod. Phys. B

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“…The Bogoliubov model for weakly interacting bosons [5,6,7] has long been the starting point for more detailed theories [8,9,10,11,12]. The ground state is approximated by an ideal Bose gas, and number conservation is violated by anomalous operator averages of the zero momentum condensate operator.…”

Section: Introductionmentioning

confidence: 99%

Number-conserving model for boson pairing

et al. 2002

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An independent pair ansatz is developed for the many body wavefunction of dilute Bose systems. The pair correlation is optimized by minimizing the expectation value of the full hamiltonian (rather than the truncated Bogoliubov one) providing a rigorous energy upper bound. In contrast with the Jastrow model, hypernetted chain theory provides closed-form exactly solvable equations for the optimized pair correlation. The model involves both condensate and coherent pairing with number conservation and kinetic energy sum rules satisfied exactly and the compressibility sum rule obeyed at low density. We compute, for bulk boson matter at a given density and zero temperature, (i) the two-body distribution function, (ii) the energy per particle, (iii) the sound velocity, (iv) the chemical potential, (v) the momentum distribution and its condensate fraction and (vi) the pairing function, which quantifies the ODLRO resulting from the structural properties of the two-particle density matrix. The connections with the low-density expansion and Bogoliubov theory are analyzed at different density values, including the density and scattering length regime of interest of trappedatoms Bose-Einstein condensates. Comparison with the available Diffusion Monte Carlo results is also made.

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“…7) a variational functional resembling ours is used but an equation corresponding to Eq. (32) is lacking, because No is not treated as a variational parameter.…”

mentioning

confidence: 99%

A Note on the Pair Theory of a Degenerate System of Bosons

Yamasaki

1984

Progress of Theoretical Physics

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A degenerate system of interacting bosons is analyzed in terms of the quasi-particle operators defined by the Bogoliubov transformation and their canonical products introduced in a previous paper. The analysis leads to a version of the pair theory. It is shown that, contrary to Luban's conclusion, the entropy suffers no di.scontinuous change when the number of zero-momentum particles decreases to zero and the system becomes non-degenerate.In a recent paper,') the present author has called attention to certain polynomials of creation and / or annihilation operators obeying boson-type (or fermion-type) commutation relations. These polynomials were named canonical products of creation and/ or annihilation operators because they possess many properties analogous to the ones possessed by normal products. The canonical products are symmetric (or antisymmetric) with respect to the exchange of the operators forming them. Like the normal products whose unperturbed ground, state averages vanish, canonical products have vanishing thermal averages in the unperturbed state. Normal products constitute a set of orthogonal polynomials (in fact monomials) when the inner product of two polynomials is defined to be the unperturbed ground-state average of one polynomial left-multiplied by the Hermitian conjugate of another. Similarly, the canonical products constitute a set of orthogonal polynomials when the inner product of two polynomials is defined to be the thermal average in place of the ground-state average. Wick's theorem can be generalized so as to be appropriate at finite temperature using the canonical products instead of normal products. Canonical products have proved useful in decomposing the Hamiltonian of a many-body system so that the thermodynamic potential, the excitation energies and the residual interaction in the Hartree-Fock approximation can be made manifest in a single formula.In this note we shall discuss the decomposition of the Hamiltonian of a degenerate system of bosons into the canonical products of quasi-particle operators a k and/ or a k * which are defined by the Bogoliubov transformation (1) where ak is the annihilation operator of a bose particle with the wave number k. It will be found that our analysis leads naturally to a scheme known as the pair theory.")-n*) The literature is motivated by the analogy with the BCS theory8) .• ) of superconductivity in which only pairs of particles with zero net momenta are assumed to interact. But such an analogy is not tenable as it fails in reproducing the phonon spectrum and hence superfluidity. Interaction between pairs with non-zero momerita cannot be omitted. As we shall see, our scheme is simply the consequence of an attempt to make the best of the Bogoliubov transformation. It also provides an example showing that the canonical products, instead of normal products, are convenient tools in describing the residual interaction of quasiparticles in a finite temperature system.The canonical products of the operators a p and / or a p * are defined with referen...

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On the collective properties of a boson system

Cited by 108 publications

References 7 publications

The Microscopic Theory of Superfluidity and Superconductivity Driven by Single Particle and Pair Condensation of Attracting Bosons

The Microscopic Theory of Superfluidity and Superconductivity Driven by Single Particle and Pair Condensation of Attracting Bosons

Number-conserving model for boson pairing

A Note on the Pair Theory of a Degenerate System of Bosons

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