The exciton many-body theory extended to any kind of composite bosons

We have recently constructed a many-body theory for composite excitons, in which the possible carrier exchanges between N excitons can be treated exactly through a set of dimensionless “Pauli scatterings” between two excitons. Many-body effects with free excitons turn out to be rather simple because these excitons are the exact one-pair eigenstates of the semiconductor Hamiltonian, in the absence of localized traps. They consequently form a complete orthogonal basis for one-pair states. As essentially all quantum particles known as bosons are composite bosons, it is highly desirable to extend this free exciton many-body theory to other kinds of “cobosons” — a contraction for composite bosons — the physically relevant ones being possibly not the exact one-pair eigenstates of the system Hamiltonian. The purpose of this paper is to derive the “Pauli scatterings” and the “interaction scatterings” of these cobosons in terms of their wave functions and the interactions which exist between the fermions from which they are constructed. It is also explained how to calculate many-body effects in such a very general composite boson system.     

Ground state energy of N Frenkel excitons

By using the composite many-body theory for Frenkel excitons we have recently developed, we here derive the ground state energy of N Frenkel excitons in the Born approximation through the Hamiltonian mean value in a state made of N identical Q = 0 excitons. While this quantity reads as a density expansion in the case of Wannier excitons, due to many-body effects induced by fermion exchanges between N composite particles, we show that the Hamiltonian mean value for N Frenkel excitons only contains a first order term in density, just as for elementary bosons. Such a simple result comes from a subtle balance, difficult to guess a priori, between fermion exchanges for two or more Frenkel excitons appearing in Coulomb term and the ones appearing in the N exciton normalization factor – the cancellation being exact within terms in 1/N_s where N_s is the number of atomic sites in the sample. This result could make us naively believe that, due to the tight binding approximation on which Frenkel excitons are based, these excitons are just bare elementary bosons while their composite nature definitely appears at various stages in the precise calculation of the Hamiltonian mean value.     

Shiva diagrams for composite-boson many-body effects: how they work

The purpose of this paper is to show how the diagrammatic expansion in fermion exchanges of scalar products of N-composite-boson (“coboson”) states can be obtained in a practical way. The hard algebra on which this expansion is based, will be given in an independent publication. Due to the composite nature of the particles, the scalar products of N-coboson states do not reduce to a set of Kronecker symbols, as for elementary bosons, but contain subtle exchange terms between two or more cobosons. These terms originate from Pauli exclusion between the fermionic components of the particles. While our many-body theory for composite bosons leads to write these scalar products as complicated sums of products of “Pauli scatterings” between two cobosons, they in fact correspond to fermion exchanges between any number P of quantum particles, with 2 ≤P≤N. These P-body exchanges are nicely represented by the so-called “Shiva diagrams”, which are topologically different from Feynman diagrams, due to the intrinsic many-body nature of the Pauli exclusion from which they originate. These Shiva diagrams in fact constitute the novel part of our composite-exciton many-body theory which was up to now missing to get its full diagrammatic representation. Using them, we can now “see” through diagrams the physics of any quantity in which enters N interacting excitons — or more generally N composite bosons —, with fermion exchanges included in an exact — and transparent — way.     

Composite boson many-body theory for Frenkel excitons

We present a many-body theory for Frenkel excitons which takes into account their composite nature exactly. Our approach is based on four commutators similar to the ones we previously proposed for Wannier excitons. They allow us to calculate any physical quantity dealing with N excitons in terms of “Pauli scatterings” for carrier exchange in the absence of carrier interaction and “interaction scatterings” for carrier interactions in the absence of carrier exchange. We show that Frenkel excitons have a novel “transfer assisted exchange scattering”, specific to these excitons. It comes from indirect Coulomb processes between localized atomic states. These indirect processes, commonly called “electron-hole exchange” in the case of Wannier excitons and most often neglected, are crucial for Frenkel excitons, as they are the only ones responsible for the excitation transfer. We also show that in spite of the fact that Frenkel excitons are made of electrons and holes on the same atomic site, so that we could naively see them as elementary particles, they definitely are composite objects, their composite nature appearing through various properties, not always easy to guess. The present many-body theory for Frenkel excitons is thus going to appear as highly valuable to securely tackle their many-body physics, as in the case of nonlinear optical effects in organic semiconductors.     

Bose–Fermi mixtures in a three-dimensional optical lattice

Using the dynamical mean-field theory and the Gutzwiller method, we study the Mott transition in Bose–Fermi mixtures confined in a three-dimensional optical lattice and analyze the effect of fermions on the coherence of bosons. We conclude that increasing fermion composition reduces bosonic coherence in the presence of strong Bose–Fermi interactions and under the condition of the integer filling factors for composite fermions, which consist of one fermion and one or more bosonic holes. Various phases of the mixtures have been demonstrated including phase separation of two species, coexisting regions of superfluid bosons and fermionic liquids, and Mott regions in the phase space spanned by the chemical potentials of the bosons and the fermions.     

The Girardeau's fermion-boson procedure in the light of the composite-boson many-body theory

We reconsider the procedure developed for atoms a few decades ago by Girardeau, in the light of the composite-boson many-body theory we recently proposed. The Girardeau's procedure makes use of a so called “unitary Fock-Tani operator” which in an exact way transforms one composite bound atom into one bosonic “ideal” atom. When used to transform the Hamiltonian of interacting atoms, this operator generates an extremely complex set of effective scatterings between ideal bosonic atoms and free fermions which makes the transformed Hamiltonian impossible to write explicitly, in this way forcing to some truncation. The scatterings restricted to the ideal-atom subspace are shown to read rather simply in terms of the two elementary scatterings of the composite-boson many-body theory, namely, the energy-like direct interaction scatterings — which describe fermion interactions without fermion exchange — and the dimensionless Pauli scatterings — which describe fermion exchanges without fermion interaction. We here show that, due to a fundamental difference in the scalar products of elementary and composite bosons, the Hamiltonian expectation value for N ground state atoms obtained by staying in the ideal-atom subspace and working with boson operators only, differ from the exact ones even for N = 2 and a mapping to the ideal-atom subspace performed, as advocated, from the fully antisymmetrical atomic state, i.e., the state which obeys the so-called “subsidiary condition”. This shows that, within this Girardeau's procedure too, we cannot completely forget the underlying fermionic components of the particles if we want to correctly describe their interactions.     

Polarized antiquark flavor asymmetry in Drell–Yan pair production

We investigate the role of the flavor asymmetry of the nucleon's polarized antiquark distributions in Drell–Yan lepton pair production in polarized nucleon–nucleon collisions at HERA (fixed–target) and RHIC energies. It is shown that the large polarized antiquark flavor asymmetry predicted by model calculations in the large– limit (chiral quark–soliton model) has a dramatic effect on the double spin asymmetries in high mass lepton pair production, as well as on the single spin asymmetries in lepton pair production through –bosons at . Received: 31 May 2000 / Revised version: 1 December 2000 / Published online: 5 February 2001     

A hartree-bose mean-field approximation for IBM-3

A Hartree-Bose mean-field approximation for the IBM-3 is presented. A Hartree-Bose transformation from the spherical to the deformed bosons with charge-dependent parameters is proposed which allows bosonic pair correlations and includes higher angular momentum bosons. The formalism contains previously proposed IBM-2 and IBM-3 intrinsic states as particular limits. Presented by J.E. García-Ramos at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997. This work has been supported in part by the Spanish DGICYT under contracts No. PB 95/0123 and PB95-0533, a DGICYT-IN2P3 agreement and by the European Commission under contract CI1*-CT94-0072.     

A unified theory of weak interactions

A gauge model for the weak interactions of the leptons (v _e, e, μ, ν_μ) and the quarks (q _p, q_n,qλ,q _p′) is presented in which deviations from universality, such as the Cabibbo suppression, are explicitly and spontaneously generated. The gauge group is, to begin with SU(4). There are three quartets of Higgs scalars with suitable vacuum expectation values, sufficient and necessary to give masses to all gauge bosons. It turns out that this gauge group is too ‘large’ and fails to account for many observed symmetries of weak interactions, especially electron-muon symmetry. This symmetry corresponds to a discrete transformationR which is an element of SU(4). To accommodate it, the gauge group is restricted to the subgroup of SU(4) which commutes withR. There are now 7 gauge bosons, 4 charged and 3 neutral. One pair of charged bosons is necessarily heavier than the other pair (denotedW ^±) and two neutrals are necessarily heavier than the third (W ⁰). The electron and the muon become massive while the neutrinos and the quark fields remain massless. The dominant charged weak currents coupling toW ^± havee-μ universality and Cabibbo universality for both of whichR-symmetry is essential—the Cabibbo angle is a simple function of the vacuum expectation values. The same symmetry ensurese-μ symmetry and the absence of flavour-changing components in the neutral currents. The currents coupling to the heavier gauge bosons break all these symmetries but these bosons can be made arbitrarily heavy and so are relevant only in the domain of ‘ultraweak’ interactions. The Cabibbo angleϑ _c itself is determined by minimising a very general class of Higgs potentials, leading to a numerical valueϑ _c = ±π/8, | tanϑ _c | = √2 − 1 (an alternative solution | tanϑ _c | = (√2+1) is rejected), independent of the parameters and of the precise form of the potential. This is the ‘bare’ϑ _c; in low energy/momentum transfer processes, this value is renormalised by the structure of the hadrons. A model is given for this renormalisation which reduces the renormalised value of | tanϑ _c | to about 0.2–0.3 from the bare value 0.41. Recent data on highly inelastic neutrino interactions are shown to be not inconsistent with | tanϑ _c | = 0.4.     

Solitons in Bose–Einstein condensates

The Gross–Pitaevskii equation (GPE) describing the evolution of the Bose–Einstein condensate (BEC) order parameter for weakly interacting bosons supports dark solitons for repulsive interactions and bright solitons for attractive interactions. After a brief introduction to BEC and a general review of GPE solitons, we present our results on solitons that arise in the BEC of hard-core bosons, which is a system with strongly repulsive interactions. For a given background density, this system is found to support both a dark soliton and an antidark soliton (i.e., a bright soliton on a pedestal) for the density profile. When the background has more (less) holes than particles, the dark (antidark) soliton solution dies down as its velocity approaches the sound velocity of the system, while the antidark (dark) soliton persists all the way up to the sound velocity. This persistence is in contrast to the behaviour of the GPE dark soliton, which dies down at the Bogoliubov sound velocity. The energy–momentum dispersion relation for the solitons is shown to be similar to the exact quantum low-lying excitation spectrum found by Lieb for bosons with a delta-function interaction.     

Excitons dressed by a sea of excitons

We here consider an exciton i embedded in a sea of N identical excitons 0. If the excitons are taken as true bosons, a bosonic enhancement factor N is found for i=0. If the exciton composite nature is kept, this enhancement not only exists for i=0, but also for any exciton having a center of mass momentum equal to the sea exciton momentum. This physically comes from the fact that an exciton with such a momentum can be transformed into a sea exciton by Pauli scattering, i.e., carrier exchange with the sea, making this exciton i not so much different from a sea exciton. This possible scattering, directly linked to the composite nature of the excitons, is irretrievably lost when the excitons are bosonized. The underlying interest of this work is in fact the calculation of the scalar products of N-exciton states, which turns out to be quite tricky, due to possible carrier exchanges between excitons. This work actually constitutes a crucial piece of our many-body theory for interacting composite bosons, because all physical effects involving composite bosons ultimately end by the calculation of such scalar products. The skeleton diagrams we here introduce to represent them, allow to visualize many-body effects linked to carrier exchanges in an easy way. They are conceptually different from Feynman diagrams, because of the special feature of the Pauli scatterings which originate from boson statistics departure.     

Size shrinking of composite bosons for increasing density in the BCS to Bose-Einstein crossover

We consider a system of fermions in the continuum case at zero temperature, in the strong-coupling limit of a short-range attraction when composite bosons form as bound-fermion pairs. We examine the density dependence of the size of the composite bosons at leading order in the density (“dilute limit”), and show on general physical grounds that this size should decrease with increasing density, both in three and two dimensions. We then compare with the analytic zero-temperature mean-field solution, which indeed exhibits the size shrinking of the composite bosons both in three and two dimensions. We argue, nonetheless, that the two-dimensional mean-field solution is not consistent with our general result in the “dilute limit”, to the extent that mean field treats the scattering between composite bosons in the Born approximation which is known to break down at low energy in two dimensions. Received 3 June 1999 and Received in final form 29 July 1999     

Luminescence centers in Sc2O3

Sc₂O₃ luminescence spectra are studied. The spectra are separated into elementary bands by the Alentsev–Fock method. It is established that the luminescence spectra consist of a number of overlapping bands with maxima at 3.5; 3.05; 2.65; 2.35, and 2.05 eV. The band at 3.5 eV is interpreted as emission of self-localized excitons, and the other bands, as defect-center recombination. L’vov State University, 50, Dragomanov St., L’vov, 290005, Ukraine. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 6, pp. 776–778, November–December, 1997.     

Some issues in a gauge model of unparticles

We address in a recent gauge model of unparticles the issues that are important for consistency of a gauge theory, i.e., unitarity and the Ward identity of the physical amplitudes. We find that non-integrable singularities arise in physical quantities like the cross section and the decay rate from the gauge interactions of unparticles. We also show that the Ward identity is violated due to the lack of a dispersion relation for charged unparticles although the Ward–Takahashi identity for general Green functions is incorporated in the model. A previous observation that the contribution of the unparticle (with scaling dimension d) to the gauge boson self-energy is a factor (2−d) of the particle’s self-energy has been extended to the Green function of triple gauge bosons. This (2−d) rule may be generally true for Green functions for any number of points of the gauge bosons. This implies that the model would be trivial even as one that mimics certain dynamical effects on gauge bosons in which unparticles serve as an interpolating field.     

Microscopic theory of single particle and pair condensation of an attracting bose gas as the basis for superfluidity and superconductivity

A consistent and unified microscopic theory of superfluidity and superconductivity is developed on the basis of two-stage Fermi-Bose-liquid (FBL) (in particular case, one-stage Bose-liquid) scenarios. It is shown that these phase transition scenarios is accompanied, as a rule, by the formation of composite bosons (Cooper pair and bipolarons) with their subsequent single particle (SPC) and pair condensation (PC). A brief outline of the modified and generalized BCS-like pairing theory of fermions is presented. In an analogy to that, a detailed boson pairing theory is developed. The SPC and PC features of an attracting 3d- and 2d-BG as a function of the interboson coupling constant in the complete range 0≤T≤T _B is studied in detail. It is argued that the coexistence of the order parameters of attracting fermions Δ_F and bosons Δ_B leads to the superfluidity (in³He) and superconductivity (in superconductors) by two FBL scenarios. One of these scenarios is realized in the so-called fermion superconductors (FSC) and the other in the boson superconductors (BSC) in which the gapless superconductivity is caused by the absence of the gap Δ_SF in the excitation spectrum of bosons and not by the presence of point or line nodes of the BCS-like gap Δ_F. The new adequate definitions for basic superconducting parameters of FSC and BSC are given. The theory proposed is consistent with the experimental data available.     

II. The standard model in the isotopic Foldy-Wouthuysen representation without higgs bosons in the fermion sector

The Standard Model with massive fermions is formulated in the isotopic Foldy-Wouthuysen representation. SU(1) × U(1) — invariance of the theory in this representation is independent of whether fermions possess mass or not, and, consequently, it is not necessary to introduce interactions between Higgs bosons and fermions. The study discusses a possible relation between spontaneous breaking of parity in the isotopic Foldy-Wouthuysen representation and the composition of elementary particles of “dark matter”.     

Contribution to the theory of spin relaxation at finite temperatures in the odd-filling quantum Hall effect regime

Spin relaxation in a two-dimensional electron gas (2D EG) is treated as the establishment of equilibrium in a gas of spin excitons as a result of processes that change the number of spin excitons. Coalescence is the dominant channel above a temperature of the order of 1 K. The coalescence of excitons can occurr as a result of spin-orbit and Coulomb interactions in the 2D EG. The rate of coalescence falls exponentially at low temperatures. The relaxation time is calculated, and the critical temperature below which the main annihilation process becomes that due to the exciton-phonon interaction is determined. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 8, 531–536 (25 October 1999)     

Energy transfer by singlet and triplet excitons in carbazole-containing polymers

Quantum yields of pyrene fluorescence and bis[2-(2′-benzothienyl)-pyridinato-N,C^3′](acetylacetonate)iridium [Btp₂Ir(acac)] phosphorescence upon excitation via a matrix of poly-N-epoxypropylcarbazole (PEPC) or poly-N-epoxypropyl-3,6-dibromocarbazole (DBrPEPC), respectively, were found to be lower than those for the compounds directly excited in a polystyrene (PS) matrix. It was established that the energy in PEPC was transferred to an acceptor by both singlet excitons (by migration and long-range dipole–dipole interaction) and triplet excitons (through migration and short-range exchange electron interaction); however, only by triplet excitons in DBrPEPC, which did not show any fluorescence. The energy-transfer efficiency in PEPC by singlet excitons was higher than by triplet excitons. The observed effects were explained by the fact that energy transfer to the acceptor competed with such processes as localization of the excitons in the “tail” energy states, dissociation of singlet excitons into geminal electron–hole pairs (EHP), and capture of triplet excitons by polymer oxidation products.     

Pair production of charged Higgs bosons in the left–right twin Higgs model at the ILC and LHC

The left–right twin Higgs (LRTH) model predicts the existence of a pair of charged Higgs bosons φ^±. In this paper, we study the production of the charged Higgs boson pair φ^± at the international linear collider (ILC) and the CERN large hadron collider (LHC). The numerical results show that the production rates are at the level of several tens fb at the ILC, and the process e⁺e^-→φ⁺φ^- can produce adequately distinct multi-jet final states. We also discuss the charged Higgs boson pair production via the process qq̄→φ⁺φ^- at the LHC and estimate in this case the production rates. We find that, as long as the charged Higgs bosons are not too heavy, they can be abundantly produced at the LHC. The possible signatures of these new particles might be detected at the ILC and LHC experiments. PACS 12.60.Fr; 14.80.Mz; 14.65.Ha; 12.15.Lk