Terms Of Bosons Research Articles

Landau functions for noninteracting bosons

We discuss the statistics of Bose-Einstein condensation (BEC) in a canonical ensemble of $N$ noninteracting bosons in terms of a Landau function ${\mathcal{L}}_{N}^{\mathrm{BEC}}(q)$ defined by the logarithm of the probability distribution of the order parameter $q$ for BEC. We also discuss the corresponding Landau function for spontaneous symmetry breaking (SSB), which for finite $N$ should be distinguished from ${\mathcal{L}}_{N}^{\mathrm{BEC}}(q)$. Only for $N\ensuremath{\rightarrow}\ensuremath{\infty}$ BEC and SSB can be described by the same Landau function which depends on the dimensionality and on the form of the external potential in a surprisingly complex manner. For bosons confined by a three-dimensional harmonic trap the Landau function exhibits the usual behavior expected for continuous phase transitions.

Checkerboard or stripes: Hard-core bosons on the checkerboard lattice as a model of charge ordering in planar cuprates

The formation of density modulations observed in cuprates by means of scanning tunneling microscopy is analyzed in the framework of an effective model for hole-doped short-range two-dimensional antiferromagnets. That model has been derived from the $t\text{\ensuremath{-}}J$ model on the square lattice. It is defined in terms of hard-core bosons. The latter objects represent tightly bound hole pairs. Long-range Coulomb repulsion between them is assumed. The nature of the ground state for the effective model is determined by analyzing the density correlation function and the density structure factor. The exact diagonalization for four hard-core bosons in the 128-site cluster, which corresponds to eight holes in the $8\ifmmode\times\else\texttimes\fi{}8$ cluster of sites in the initial square lattice, is performed to derive these quantities. Signatures of the density modulations with the periodicity 4 spacings between nearest-neighbor sites in the initial square lattice in horizontal and vertical directions and with the full symmetry of that lattice may be seen both in the density correlation function and in the density structure factor. On the other hand, a strong tendency to form smectic order may be noticed in the results of the calculation. It turns out that the ground state is a symmetric combination of states representing stripes running either in the vertical or in the horizontal directions. In a real system, the same effect may have the formation of regions with short-range fluctuating stripe order oriented either vertically or horizontally.

Boson structure of the low-lying states of 1p0f-shell nuclei

The boson structure of the low-lying states of A = 44 and A = 60 nuclei is investigated by studying the eigenvalue problem of the boson image of the shell-model Hamiltonian in spaces expanded in terms of bosons corresponding to the collective nuclear pairs allowed in the 1p0f shell.

CURRENT ALGEBRA BASED EFFECTIVE CHIRAL THEORY OF MESONS AND A NEW EW THEORY

A current algebra based effective chiral theory of pseudoscalar, vector, axial-vector mesons is reviewed. A new mechanism generating the masses and guage fixing terms of gauge boson is revealed from this effective theory. A EW theory without Higgs is proposed. The masses and gauge fixing terms of W and Z are dynamically generated. Three heavy scalar fields are dynamically generated too. They are ghosts.

Nonanticommutative deformation of Script N = 4 SYM theory: the Myers effect and vacuum states

We propose a deformation of ${\cal N}=4$ SYM theoery induced by nonanticommutative star product. The deformation introduces new bosonic terms which we identify with the corresponding Myers terms of a stack of D3-branes in the presence of a five-form RR flux. We take this as an indication that the deformed lagrangian describes D3-branes in such a background. The vacuum states of the theory are also examined. In a specific case where the U(1) part of the gauge field is nonvanishing the (anti)holomorphic transverse coordinates of the brane sit on a fuzzy two sphere. For a supersymmetric vacuum the antiholomorphic coordinates must necessarily commute. However, we also encounter non-supersymmetric vacua for which the antiholomorphic coordinates do not commute.

Bosonization approach to the edge reconstruction of two-dimensional electron systems in a quantum dot

We consider edge reconstruction of electrons in a two-dimensional harmonic trap under a strong magnetic field. In this system the edge reconstruction occurs as a result of competition between electron-electron interaction and confining potential. We develop a bosonization scheme for two-dimensional electron systems. With this method we obtain the excitation spectrum and demonstrate that the edge reconstruction occurs when magnetic field reaches a critical value. We also show that the edge reconstruction depends on the number of electrons. We calculate the third-order terms of bosons in Hamiltonian and examine the effect of those terms with a perturbation theory.

Anomalous gauge-boson couplings and the Higgs-boson mass

We study anomalous gauge-boson couplings induced by a locally SU(2) × U(1) invariant effective Lagrangian containing ten operators of dimension six built from boson fields of the standard model (SM) before spontaneous symmetry breaking (SSB). After SSB some operators lead to new three- and four-gauge-boson interactions, some contribute to the diagonal and off-diagonal kinetic terms of the gauge bosons, to the kinetic term of the Higgs boson and to the mass terms of the W and Z bosons. This requires a renormalisation of the gauge-boson fields, which, in turn, modifies the charged- and neutral-current interactions, although none of the additional operators contain fermion fields. Also the Higgs field must be renormalised. Bounds on the anomalous couplings from electroweak precision measurements at LEP and SLC are correlated with the Higgs-boson mass m H . Rather moderate values of anomalous couplings allow m H up to 500 GeV. At a future linear collider the triple-gauge-boson couplings $\gamma WW$ and ZWW can be measured in the reaction $e^ + e^- \rightarrow WW$ . We compare three approaches to anomalous gauge-boson couplings: the form-factor approach, the addition of anomalous-coupling terms to the SM Lagrangian after and, as outlined above, before SSB. The translation of the bounds on the couplings from one approach to another is not straightforward. We show that it can be done for the process $e^ + e^- \rightarrow WW$ by defining new effective $\gamma WW$ and ZWW couplings.

5-field terms in the open superstring effective action

Some time ago the bosonic and fermionic 4-field terms of the non-abelian low energy effective action of the open superstring were obtained, to all order in $\alpha'$. This was done at tree level by directly generalizing the abelian case, treated some time before, and considering the known expressions of all massless superstring 4-point amplitudes (at tree level). In the present work we obtain the bosonic 5-field terms of this effective action, to all order in $\alpha'$. This is done by considering the simplified expression of the superstring 5-point amplitude for massless bosons, obtained some time ago.

Stationary and dynamical descriptions of strong correlated systems

This work is mainly devoted to the description of processes that involve the interaction between an atom and a surface, in which a strong Coulomb repulsion on the atomic site $(U)$ limits the charge exchange to one electron (infinite-$U$ limit). In this limit, the Anderson Hamiltonian for a many-fold $(N)$ of states localized on the atomic site can be represented in terms of auxiliary bosons and physical operators in the mixed boson-electron space can be defined. In this work the Hamiltonian is solved by defining appropriate Green's functions for physical operators. Then we solved the equations of motion of these Green's functions, up to a second order in the atom-surface coupling, either for the stationary case or for a real time-dependent problem. We show that our approach reproduces the known exact results in the nondegenerate $(N=1)$ case, and for $N\ensuremath{\succ}1$ gives excellent agreement with exact calculations and approximations valid for large $N$ (the $1∕N$ expansion). Finally, the accurate description of dynamical processes is shown by the comparison with the exact results available for a small four-level system. In this case we also compare with results obtained by using the noncrossing approximation and with the usual spinless model calculation.

A unified and complete construction of all finite dimensional irreducible representations of gl(2∣2)

Representations of the non-semisimple superalgebra gl(2∣2) in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical representations and lowest weight (indecomposable) Kac modules of gl(2∣2) are constructed explicitly through the explicit construction of all gl(2)⊕gl(2) particle states (multiplets) in terms of boson and fermion creation operators in the super-Fock space. This gives a unified and complete treatment of finite-dimensional representations of gl(2∣2) in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.

The Ramond–Ramond sector of string theory beyond leading order

Present knowledge of higher-derivative terms in string effective actions is, with a few exceptions, restricted to the NS–NS sector, a situation which prevents the development of a variety of interesting applications for which the RR terms are relevant. We here provide the formalism as well as efficient techniques to determine the latter directly from string-amplitude calculations. As an illustration of these methods, we compute the dependence of the type-IIB action on the 3- and 5-form RR field strengths at four-point, genus-one, order-(α′)3 level. We explicitly verify that our results are in accord with the S-duality invariance of type-IIB string theory. Extensions of our method to other bosonic terms in the type-II effective actions are also discussed.

The supersymmetric extension of the Faddeev model

We study the supersymmetric extension of the Faddeev model in four dimensions. The Faddeev model contains three-dimensional soliton solutions and we are interested in how these solitons are affected by supersymmetry. We consider both the N=1 and N=2 extensions and find that in neither case it is possible to supersymmetrize the model without adding additional bosonic terms. There are essentially two ways of constructing the supersymmetric theory, one that will lead to a model which allows for solitons and another that gives a model where solitons are excluded. The N=2 model is studied since extending supersymmetry is the natural way of including topological charges in the algebra. A lower bound to the mass is obtained by computing the central charge. The result is that it is possible to have a nontrivial lower bound on the mass, this in principle allows for massive solitons.

Exact Reformulation of the Bosonic Many-Body Problem in Terms of Stochastic Wave Functions: an Elementary Derivation

Recently, a new method was developed to reformulate in an exact way the N-body problem of interacting bosons in terms of the stochastic evolution of single particle wavefunctions, see I. Carusotto, Y. Castin, and J. Dalibard, Phys. Rev. A 63, 023606 (2001). The original derivation is however often considered as rather involved. For the specific scheme called ‘simple Fock scheme’ we present here a very elementary derivation of such an approach.

Pseudogap state in superconductors: Extended Hartree approach to time-dependent Ginzburg-Landau theory

It is well known that conventional pairing fluctuation theory at the Hartree level leads to a normal state pseudogap in the fermionic spectrum. Our goal is to extend this Hartree approximated scheme to arrive at a generalized mean field theory of pseudogapped superconductors for all temperatures $T$. While an equivalent approach to the pseudogap has been derived elsewhere using a more formal Green's function decoupling scheme, in this paper we re-interpret this mean field theory and BCS theory as well, and demonstrate how they naturally relate to ideal Bose gas condensation. Here we recast the Hartree approximated Ginzburg-Landau self consistent equations in a T-matrix form. This recasting makes it possible to consider arbitrarily strong attractive coupling, where bosonic degrees of freedom appear at $ T^*$ considerably above $T_c$. The implications for transport both above and below $T_c$ are discussed. Below $T_c$ we find two types of contributions. Those associated with fermionic excitations have the usual BCS functional form. That they depend on the magnitude of the excitation gap, nevertheless, leads to rather atypical transport properties in the strong coupling limit, where this gap (as distinct from the order parameter) is virtually $T$-independent. In addition, there are bosonic terms arising from non-condensed pairs whose transport properties are shown here to be reasonably well described by an effective time-dependent Ginzburg-Landau theory.

4-point effective actions in open and closed superstring theory

Recently the effective action for the 4-point functions in abelian open superstring theory has been derived, giving an explicit construction of the bosonic and fermionic terms of this infinite $\alpha'$ series. In the present work we generalize this result to the nonabelian case. We test our result, at ${\alpha'}^3$ and ${\alpha'}^4$ order, with several existing versions for these terms, finding agreement in most of the cases. We also apply these ideas to derive the effective action for the 4-point functions of the NS-NS sector of closed superstring theory, to all order in $\alpha'$.

Observation of sharp collective excitations of the one-dimensional electron gas in cleaved-edge-overgrown semiconductor quantum wires

Coulomb interactions in a dilute one-dimensional (1D) electron system in high quality cleaved-edge overgrown GaAs quantum wires are probed by optics experiments. Intra-subband collective excitation modes are observed in resonant inelastic light-scattering spectra. A sharp intra-subband excitation occurs close to the single particle transition energy. It is narrower and weaker than the plasmon band, and its width is consistent with electron mean free paths in the micrometer range. Scattering intensities display large enhancements only for scattered photon energies in resonance with the optical gap of the wires. Preliminary analysis reveals impact of interactions in the 1D system. Possible interpretation in terms of Luttinger-liquid bosons is discussed.

String backgrounds and LCFT

We describe a large class of exact string backgrounds with a null Killing vector arising, via a limiting à la Penrose procedure, from string backgrounds corresponding to coset conformal field theories for compact groups G N / H N times a free time-like boson U(1) − N . In this way a class of novel logarithmic conformal field theories (LCFT) emerges, that includes the one constructed recently as an N→∞ limit of the SU(2) N / U(1)× U(1) − N theory. We explicitly give the exact operator algebra for the basic chiral fields as well as their representation in terms of free bosons, even though these are not known in general at finite N. We also compute four-point functions of various operators in the theory. For the cases of the four- and five-dimensional models, corresponding to a limit of the theory SO( D+1) N / SO( D) N × U(1) − N for D=3 and 4, we also present the explicit expressions for the background fields.

Testing the fermionic terms in the non-abelian D-brane effective action through order α′3

Recently the construction of the non-abelian effective D-brane action was performed through order $\alpha'{}^3$ including the terms quadratic in the gauginos. This result can be tested by calculating the spectrum in the presence of constant magnetic background fields and comparing it to the string theoretic predictions. This test was already performed for the purely bosonic terms. In this note we extend the test to the fermionic terms. We obtain perfect agreement.

One loop renormalizability of spontaneously broken gauge theory with a product of gauge groups on noncommutative spacetime: the U(1) × U(1) case

A generalization of the standard electroweak model to noncommutative spacetime would involve a product gauge group which is spontaneously broken. Gauge interactions in terms of physical gauge bosons are canonical with respect to massless gauge bosons as required by the exact gauge symmetry, but not so with respect to massive ones; and furthermore they are generally asymmetric in the two sets of gauge bosons. On noncommutative spacetime this already occurs for the simplest model of U(1) x U(1). We examine whether the above feature in gauge interactions can be perturbatively maintained in this model. We show by a complete one loop analysis that all ultraviolet divergences are removable with a few renormalization constants in a way consistent with the above structure.

Spontaneous magnetization of the O(3) ferromagnet at low temperatures

We investigate the low-temperature behavior of ferromagnets with a spontaneously broken symmetry $\mathrm{O}(3)\ensuremath{\rightarrow}\mathrm{O}(2).$ The analysis is performed within the perspective of nonrelativistic effective Lagrangians, where the dynamics of the system is formulated in terms of Goldstone bosons. Unlike in a Lorentz-invariant framework (chiral perturbation theory), where loop graphs are suppressed by two powers of momentum, loops involving ferromagnetic spin waves are suppressed by three momentum powers. The leading coefficients of the low-temperature expansion for the partition function are calculated up to order ${p}^{10}.$ In agreement with Dyson's pioneering microscopic analysis of the cubic ferromagnet, we find that, in the spontaneous magnetization, the magnon-magnon interaction starts manifesting itself only at order ${T}^{4}.$ The striking difference with respect to the low-temperature properties of the O(3) antiferromagnet is discussed from a unified point of view, relying on the effective Lagrangian technique.