Current-current Interaction Research Articles

Possibility of flux expulsion and flux trapping in thick mesoscopic cylinders

Persistent currents in mesoscopic nonsuperconducting rings and cylinders are a manifestation of quantum coherence. In this paper the possibility of self-sustaining persistent currents in thick mesoscopic cylinders is disscussed. The long-range magnetostatic (current-current) interactions are taken into account by the method of self-consistent field. Axially symmetric solutions of the differential equations for the self-consistent flux are found for geometry of a long hollow cylinder made of a set of a large number of cylindrical layers. The conditions under which the system exhibits flux expulsion and quantization of trapped flux are formulated.

Chiral stabilization of the renormalization group for flavor and color anisotropic current interactions

We propose an all-orders beta function for current-current interactions in 2d with flavor anisotropy. When the number of left-moving and right-moving flavors are unequal, the beta function has a non-trivial fixed point at finite values of the couplings. We also extend the computation to simple cases with both flavor and color anisotropy.

Strong-coupling fixed points of current interactions and disordered fermions in two dimensions

The all-orders beta function is used to study disordered Dirac fermions in 2D. The generic strong coupling fixed `points' of anisotropic current-current interactions at large distances are actually isotropic manifolds corresponding to subalgebras of the maximal current algebra at short distances. The IR theories are argued to be current algebra cosets. We illustrate this with the simple example of anisotropic su(2), which is the physics of Kosterlitz-Thouless transitions. We work out the phase diagram for the Chalker-Coddington network model which is in the universality class of the integer Quantum Hall transition. One massless phase is in the universality class of dense polymers.

On the dual equivalence of the Born–Infeld–Chern–Simons model coupled to dynamical U(1) charged matter

We study the equivalence between a nonlinear self-dual model (NSD) with the Born-Infeld-Chern-Simons (BICS) models using an iterative gauge embedding procedure that produces the duality mapping, including the case where the NSD model is minimally coupled to dynamical, U(1) charged fermionic matter. The duality mapping introduces a current-current interaction term while at the same time the minimal coupling of the original nonlinear self-dual model is replaced by a non-minimal magnetic like coupling in the BICS side.

Beta function for anisotropic current interactions in 2D.

By making use of current-algebra Ward identities we study renormalization of general anisotropic current-current interactions in 2D. In this prescription we propose a compact expression for the beta function to all orders.

QED out of matter

The Wilsonian renormalization group implies that an arbitrary four dimensional field theory with an ultraviolet cutoff is equivalent to a theory which is renormalizable by power counting at energy scales much below the cutoff. This applies to any theory including those with non-renormalizable interactions as long as we fine-tune the mass parameters. We analyze two simple models with current-current interactions but without elementary gauge fields from this viewpoint. We show how to tune the parameters of the models so that they become equivalent to QED at energies much below the cutoff.

Hawking radiation from Feynman diagrams

The aim of this letter is to clarify the relationships between Hawking radiation and the scattering of light by matter falling into a black hole. To this end we analyze the S-matrix elements of a model composed of a massive infalling particle (described by a quantized field) and the radiation field. These fields are coupled by current-current interactions and propagate in the Schwarzschild geometry. As long as the photons energy is much smaller than the mass of the infalling particle, one recovers Hawking radiation since our S-matrix elements identically reproduce the Bogoliubov coefficients obtained by treating the trajectory of the infalling particle classically. But after a brief period, the energy of the `partners' of Hawking photons reaches this mass and the production of thermal photons through these interactions stops. The implications of this result are discussed.

Graviton-graviton scattering, Bel-Robinson and energy (pseudo)-tensors

Motivated by recent work involving the graviton-graviton tree scattering amplitude, and its twin descriptions as the square of the Bel-Robinson tensor, Bµ, and as the `current-current interaction' square of gravitational energy pseudo-tensors t, we find an exact tensor-square root equality , for a combination of Einstein and Landau-Lifschitz in Riemann normal coordinates. In the process, we relate, on-shell, the usual superpotential basis for classifying pseudo-tensors with one spanned by polynomials in the curvature.

Model for stars of interacting bosons and fermions

In this paper we introduce a current-current type interaction term in the Lagrangian density of gravity coupled to complex scalar fields, in the presence of a degenerated Fermi gas. For low transferred momenta, such a term, which might account for the interaction among boson and fermion constituents of compact stellar objects, is subsequently reduced to a quadratic one in the scalar sector. This procedure enforces the use of a complex radial field counterpart in the equations of motion. The real and the imaginary components of the scalar field exhibit different behavior as the interaction increases. The results also suggest that the Bose-Fermi system undergoes a phase transition for a suitable choice of the coupling constant.

Four-point current-current interactions for nonmesonic weak decay of hypernuclei Λ4He, Λ5He and Λ12C

Four-point current-current interactions for nonmesonic weak decay of hypernuclei Λ4He, Λ5He and Λ12C

The Electrodynamics of Current-Current Interaction in a Double Helix

General expressions for the tangential and radial forces for two current elements moving contra-wise to each other in a helical manner are derived. The two repulsive forces are calculated as a function of velocity, with explicit values given for parameters, appropriate to DNA. The calculated electrodynamic respulsive forces oppose the stabilizing standard radial and tangential forces in the helix and, if large enough, can result in strand separation. The currents required are of the same order of magnitude as observed intra-cellular currents and as passed recently through short segments of duplex DNA. A speculative mechanism involving a resistance-capacitance membrane network in series with a resistance DNA network is formulated. Strand separation in DNA may well originate in such an electrodynamic system.

Constraints on the universal contact interaction

Forces beyond those of the standard model may manifest themselves at low energies as four-fermion contact interactions. If these new forces are independent of colour and flavour quantum numbers including baryon and lepton number, then all low energy constraints, arising from quark-lepton universality, flavour-changing neutral currents and atomic parity violation are evaded. This is due to the global U(45) symmetry which the standard model exhibits in the limit of vanishing gauge and Yukawa couplings. The corresponding contact interaction is a unique current-current interaction. Constraints from LEP2 imply that this universal contact interaction cannot be the origin of the recently observed high-$Q^2$ events at HERA.

Bosonization of Fermi liquids

We consider systems of nonrelativistic, interacting electrons at finite density and zero temperature in d=2,3,ldots dimensions. Our main concern is to characterize those systems that, under the renormalization flow, are driven away from the Landau Fermi-liquid (LFL) renormalization-group fixed point. We are especially interested in understanding under what circumstances such a system is a marginal Fermi-liquid (MFL) when the dimension of space is d\ensuremath{\geqslant}2. The interacting electron system is analyzed by combining renormalization-group (RG) methods with so called 'Luther-Haldane' bosonization techniques. The RG calculations are organized as a double expansion in the inverse scale parameter ${\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}1}$ , which is proportional to the width of the effective momentum space around the Fermi surface and in the running coupling constant ${\mathrm{g}}_{\ensuremath{\lambda}}$ , which measures the strength of electron interactions at energy scales \ensuremath{\sim}${\mathrm{v}}_{\mathrm{F}}$ ${\mathrm{k}}_{\mathrm{F}}$ /\ensuremath{\lambda}. For systems with a strictly convex Fermi surface, superconductivity is the only symmetry-breaking instability. Excluding such an instability, the system can be analyzed by means of bosonization. The RG and the underlying perturbation expansion in powers of ${\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}1}$ serve to characterize the approximations involved by bosonizing the system. We argue that systems with short-range interactions flow to the LFL fixed point. Within the approximations involved by bosonization, the same holds for systems with long-range, longitudinal, density-density interactions. For electron systems interacting via long-range, transverse, current-current interactions, a deviation from LFL behavior is possible: if the exponent \ensuremath{\alpha} parametrizing the singularity of the interaction potential in momentum space by V-hat(|p|)\ensuremath{\sim}1/|p${\mathrm{|}}^{\mathrm{\ensuremath{\alpha}}}$ is greater than or equal to d-1, the results of the bosonization calculation are consistent with a MFL.

Current-carrying ground states in mesoscopic and macroscopic systems.

We extend a theorem of Bloch, which concerns the net orbital current carried by an interacting electron system in equilibrium, to include mesoscopic effects. We obtain a rigorous upper bound to the allowed ground-state current in a ring or disc, for an interacting electron system in the presence of static but otherwise arbitrary electric and magnetic fields. We also investigate the effects of spin-orbit and current-current interactions on the upper bound. Current-current interactions, caused by the magnetic field produced at a point r by a moving electron at r, are found to reduce the upper bound by an amount that is determined by the self-inductance of the system. A solvable model of an electron system that includes current-current interactions is shown to realize our upper bound, and the upper bound is compared with measurements of the persistent current in a single ring.

Conformal points and duality of non-abelian thirring models and interacting WZNW models

We show that the strong coupling phase of the non-Abelian Thirring model is dual to the weakcoupling phase of a system of two WZNW models coupled to each other through a current-current interaction. This latter system is integrable and is related to a perturbed conformal field theory which, in the large | k| limit, has a non-trivial zero of the perturbation-parameter beta function. The non-Abelian Thirring model reduces to a free fermion theory plus a topological field theory at this critical point, which should therefore be identified with the isoscalar Dashen-Frishman conformal point. The relationship with the Gross-Neveu model is discussed.

Non-Abelian soliton operators.

We construct soliton operators for the Wess-Zumino-Witten (WZW) model with a chiral O(N)\ifmmode\times\else\texttimes\fi{}O(N) invariance, and use them to derive non-Abelian bosonization properties directly. The soliton operators express the fermion fields as nonlocal functions of the boson currents and provide a direct map from the boson to the fermion fields. With them we determine the fermion equivalent Lagrangian for level k=N together with the fermion bilinears equivalent to the boson fields. We generalize this construction to arbitrary values of the coupling constant and find the equivalent fermion model, which has current-current interactions.

Quantum disordered phase in a doped antiferromagnet

A quantitative description of the transition to a quantum disordered phase in a doped antiferromagnet is obtained for the long-wavelength limit of the spin-fermion model, which is given by the O(3)non-linear a model, a free fermionic part and current-current interactions. By choosing local spin quantization axes for the fermionic spinor we show that the low-energy limit of the model is equivalent to a U(1)gauge theory, where both the bosonic and fermionic degrees of freedom are minimally coupled to a vector gauge field. Within a large-N expansion, the strength of the gauge fields is found to be determined by the gap in the spin-wave spectrum, which is dynamically generated. The explicit doping dependence of the spin-gap is determined as a function of the parameters of the original model. As a consequence of the above, the gauge-fields mediate a long-range interaction among dopant holes and S-1/2magnetic excitations only in the quantum disordered phase. The possible bound-states in this regime correspond to charge-spin separation and pairing.

Quantum disordered phase in an antiferromagnet via doping

A quantitative description of the transition to a quantum disordered phase in a doped antiferromagnet is obtained for the long-wavelength limit of the spin-fermion model, which is given by the O(3) nonlinear σ model, a free fermionic part and current-current interactions as obtained by Shraiman and Siggia for the t − J model. By choosing local spin quantization axes for the fermions we show that the low-energy limit of the model is equivalent to a U(1) gauge theory, where both the bosonic and fermionic degrees of freedom are coupled minimally to a vector gauge field. Within a large- N expansion, the strength of the gauge fields is found to be determined by the gap in the spin-wave spectrum, which is dynamically generated. The explicit doping dependence of the spin-gap is determined as a function of the parameters of the original model. As a consequence of the above, the gauge-fields mediate a confining interaction among dopant holes and S- 1 2 magnetic excitations only in the quantum disordered phase. The possible bound-states in this regime correspond to charge-spin separation and pairing.

Fermion current-current interactions and orthogonality in two dimensions

Abstract The wavefunction renormalization Z of a two-dimensional Fermi gas with current-current interaction mediated by an unscreened transverse gauge field is discussed within a simple Hartree approximation for self-field effects. In the case of a three-dimensional gauge field, a critical coupling strength is required before level crossing and strict orthogonality occur. In the case of a two-dimensional gauge field, any finite coupling guarantees orthogonality beyond a critical system size.

Bosonization of current-current interactions

We discuss a generalization of the conventional bosonization procedure to the case of current-current interactions which get their natural representation in terms of current instead of fermion number density operators. A consistent bosonization procedure requires a geometrical quantization of the hamiltonian action of $W_\infty$ on its coadjoint orbits. An integrable example of a nontrivial realization of this symmetry is presented by the Calogero-Sutherland model. For an illustrative nonintegrable example we consider transverse gauge interactions and calculate the fermion Green function.