Current-current Interaction Research Articles

Relativistic two-fluid hydrodynamics with quantized vorticity from the nonlinear Klein-Gordon equation

Abstract We consider a relativistic two-fluid model of superfluidity, in which the superfluid is described by an order parameter that is a complex scalar field satisfying the nonlinear Klein-Gordon equation (NLKG). The coupling to the normal fluid is introduced via a covariant current-current interaction, which results in the addition of an effective potential, whose imaginary part describes particle transfer between superfluid and normal fluid. Quantized vorticity arises in a class of singular solutions and the related vortex dynamics is incorporated in the modified NLKG, facilitating numerical analysis which is usually very complicated in the phenomenology of vortex filaments. The dual transformation to a string theory description (Kalb-Ramond) of quantum vorticity, the Magnus force and the mutual friction between quantized vortices and normal fluid are also studied.

About Non-relativistic Quantum Mechanics and Electromagnetism

We describe here the coherent formulation of electromagnetism in the non-relativistic quantum-mechanical many-body theory of interacting charged particles. We use the mathematical frame of the field theory and its quantization in the spirit of the quantum electrodynamics (QED). This is necessary because a manifold of misinterpretations emerged especially regarding the magnetic field and gauge invariance. The situation was determined by the historical development of quantum mechanics, starting from the Schrödinger equation of a single particle in the presence of given electromagnetic fields, followed by the many-body theories of many charged identical particles having just Coulomb interactions. Our approach to the non-relativistic QED emphasizes the role of the gauge-invariance and of the external fields. We develop further the approximation of this theory allowing a closed description of the interacting charged particles without photons. The resulting Hamiltonian coincides with the quantized version of the Darwin Hamiltonian containing besides the Coulomb also a current-current diamagnetic interaction. We show on some examples the importance of this extension of the many-body theory.

Inhomogeneous Phase of the Chiral Gross-Neveu Model.

There is substantial evidence that the ground state of the 2D chiral Gross-Neveu model, in the presence of a U(1) fermion number chemical potential μ and in the large N limit, is given by a "chiral spiral" phase, namely an inhomogeneous phase with a chiral condensate having a spatially periodic phase. We show that the chiral spiral configuration persists at finite N and T=0 for any μ>0. Our analysis is based on nonabelian bosonization, that relates the model to a U(N)_{1} Wess-Zumino-Witten model deformed by current-current interactions. In this description, the appearance of the inhomogeneous phase is surprisingly simple. We also rederive the phase diagram of the large N chiral Gross-Neveu model via a direct diagrammatic computation, finding agreement with previous results in the literature.

Chiral Sachdev-Ye model: Integrability and chaos of anyons in 1+1d

We construct and study a chiral Sachdev-Ye (SY) model consisting of $N$ chiral $\mathrm{SU}{(M)}_{1}$ Wess-Zumino-Witten (WZW) models with current-current interactions among each other, which generalizes the $0+1\mathrm{d}$ quantum chaotic SY spin model into $1+1\mathrm{d}$ chiral system with anyon excitations. Each WZW model hosts Abelian anyons as charge excitations, and may arise as the chiral edge theory of $2+1\mathrm{d}$ gapped topological phases. We solve the chiral SY model in two limits which show distinct quantum dynamics. The first limit is the case with uniform interactions at any integers $N$ and $M$, which is integrable and decomposes into a chiral $\mathrm{SU}{(M)}_{N}$ WZW model and its coset with a different speed of light. When $N=M=2$, the model maps to a free Majorana fermion model. The second limit is the large $N$ and $M$ limit with random interactions, which is solvable to the leading $\frac{1}{NM}$ order, and exhibits many-body quantum chaos in the out-of-time-ordered correlation of anyons. As the interaction strength approaches the upper limit preserving the chirality, the leading velocity-dependent Lyapunov exponent of the model saturates the maximal chaos bound $2\ensuremath{\pi}/\ensuremath{\beta}$ at temperature ${\ensuremath{\beta}}^{\ensuremath{-}1}$.

Semirelativistic (e,2e) study with a twisted electron beam on Cu and Ag

In this paper, we report our calculations of the triple-differential cross section (TDCS) for the relativistic $(e,2e)$ process with a twisted electron beam on Cu and Ag atomic targets in coplanar asymmetric geometry mode. The theoretical formalism has been developed in the first Born approximation, in which we use the Dirac plane wave as well as the twisted electron wave for the incident electron beam to study the effect of various parameters of the twisted electron beam on the $(e,2e)$ process. We use a Dirac plane-wave function, semirelativistic Coulomb wave function, and Darwin wave function for the scattered, ejected, and K-shell electron, respectively. We compare the angular profiles of the TDCS of the twisted electron impact $(e,2e)$ process with that of the plane wave. We segregate the TDCS for charge-charge interaction and current-current interaction with their interference term and study the effect of different parameters of the twisted electron beam on them. The study is also extended to the macroscopic Cu and Ag targets to further investigate the effect of the opening angle of the twisted electron beam on TDCS. The spin asymmetry in TDCS caused by the polarized incident electron beam is also studied to elucidate the effects of the twisted electron beam on the $(e,2e)$ process.

Electromagnetic quantum shifts in relativistic Bose-Einstein condensation

We compute deviations from ideal gas behavior of the pressure, density, and Bose-Einstein condensation temperature of a relativistic gas of charged scalar bosons caused by the current-current interaction induced by electromagnetic quantum fluctuations treated via scalar quantum electrodynamics. We obtain expressions for those quantities in the ultra-relativistic and nonrelativistic limits, and present numerical results for the relativistic case.

Reading the footprints of the B-meson flavor anomalies

Motivated by the recent LHCb announcement of a 3.1σ violation of lepton- flavor universality in the ratio RK = Γ(B → Kμ+μ−)/Γ(B → Ke+e−), we present an updated, comprehensive analysis of the flavor anomalies seen in both neutral-current (b → sℓ+ℓ−) and charged-current (b → ctau overline{nu} ) decays of B mesons. Our study starts from a model-independent effective field-theory approach and then considers both a simplified model and a UV-complete extension of the Standard Model featuring a vector leptoquark U1 as the main mediator of the anomalies. We show that the new LHCb data corroborate the emerging pattern of a new, predominantly left-handed, semileptonic current-current interaction with a flavor structure respecting a (minimally) broken U(2)5 flavor symmetry. New aspects of our analysis include a combined analysis of the semileptonic operators involving tau leptons, including in particular the important constraint from Bs- {overline{B}}_s mixing, a systematic study of the effects of right-handed leptoquark couplings and of deviations from minimal flavor-symmetry breaking, a detailed analysis of various rare B-decay modes which would provide smoking-gun signatures of this non-standard framework (LFV decays, di-tau modes, and B → K(*) nu overline{nu} ), and finally an updated analysis of collider bounds on the leptoquark mass and couplings.

The Non-Relativistic Many-Body Quantum-Mechanical Hamiltonian with Diamagnetic Current-Current Interaction

We extend the standard solid-state quantum mechanical Hamiltonian containing only Coulomb interactions between the charged particles by inclusion of the (transverse) current-current diamagnetic interaction starting from the non-relativistic QED restricted to the states without photons and neglecting the retardation in the photon propagator. This derivation is supplemented with a derivation of an analogous result along the non-rigorous old classical Darwin-Landau-Lifshitz argumentation within the physical Coulomb gauge.

Cross section of ultrahigh-energy neutrinos: Estimation of the uncertanties due to parton distribution functions

In this work we analyze the effect of uncertainties in parton distribution functions upon the calculation of cross sections for ultrahigh-energy neutrinos. As a detector we choose $^{12}\mathrm{C}$. The elementary diagrams for the neutrino-proton and neutron interactions have been calculated at quark level using nuclear parton distribution functions and their corresponding error bars, as given by the Jyvaskyla group. The leptonic sector of the current-current interactions includes active-sterile neutrino mixing. From the calculated cross section we have set limits on the values of the mixing parameters.

Cross sections of ultrahigh-energy neutrinos: Comparison with ICE-CUBE data

Ultrahigh energetic neutrino events have been recorded by ICE-CUBE. The detection of these events indicates the extragalactic origin of the neutrinos. In order to characterized the elementary mechanisms responsible for the emission of these neutrinos it is necessary to determine their energy distributions and flavor compositions. In this work we are presenting the results of neutrino-nucleon cross section for the interaction with nucleons of a detector. The elementary diagrams for the neutrino-proton (or neutron) interactions have been calculated at the quark level adding the corresponding form factors for quarks in nucleons, as well as nuclear parton distribution functions. The leptonic sector of the current-current interactions have been calculated including neutrino oscillations and the mixing with a sterile neutrino.

Mean-field study of the Amperean pairing state

Amperean pairing states, which represent a special case of pair-density-wave (PDW) states with members of the Cooper pair carrying equal momenta, offer a promising description of the pseudogap phase of the cuprates. It has been suggested that such states may develop in systems with current-current interactions; here we check this proposal by a fully self-consistent mean-field analysis. We find that previous non-self-consistent theories have correctly identified the essential physical properties of the Amperean states. However, we find that Amperean pairing states are not optimal within the class of PDW states and our lowest-energy solutions do not fit the pseudogap phenomenology. A model-independent interpretation of the Fermi arcs is presented as well.

Absence of chiral symmetry breaking in Thirring models in 1+2 dimensions

The Thirring model is an interacting fermion theory with current-current interaction. The model in $1+2$ dimensions has applications in condensed-matter physics to describe the electronic excitations of Dirac materials. Earlier investigations with Schwinger-Dyson equations, the functional renormalization group and lattice simulations with staggered fermions suggest that a critical number of (reducible) flavors $N^{\mathrm{c}}$ exists, below which chiral symmetry can be broken spontaneously. Values for $N^{\mathrm{c}}$ found in the literature vary between $2$ and $7$. Recent lattice studies with chirally invariant SLAC fermions have indicated that chiral symmetry is unbroken for all integer flavor numbers [Wellegehausen et al., 2017]. An independent simulation based on domain wall fermions seems to favor a critical flavor-number that satisfies $1<N^{\mathrm{c}}<2$ [Hands, 2018]. However, in the latter simulations difficulties in reaching the massless limit in the broken phase (at strong coupling and after the $L_s\to\infty$ limit has been taken) are encountered. To find an accurate value $N^{\mathrm{c}}$ we study the Thirring model (by using an analytic continuation of the parity even theory to arbitrary real $N$) for $N$ between $0.5$ and $1.1$. We investigate the chiral condensate, the spectral density of the Dirac operator, the spectrum of (would-be) Goldstone bosons and the variation of the filling-factor and conclude that the critical flavor number is $N^{\mathrm{c}}=0.80(4)$. Thus we see no chiral symmetry breaking in all Thirring models with $1$ or more flavors of ($4$-component) fermions. Besides the artifact transition to the unphysical lattice artifact phase we find strong evidence for a hitherto unknown phase transition that exists for $N>N^{\mathrm{c}}$ and should answer the question of where to construct a continuum limit.

From coupled wires to coupled layers: Model with three-dimensional fractional excitations

We propose a systematic approach to constructing microscopic models with fractional excitations in three-dimensional (3D) space. Building blocks are quantum wires described by the (1+1)-dimensional conformal field theory (CFT) associated with a current algebra $\mathfrak{g}$. The wires are coupled with each other to form a 3D network through the current-current interactions of $\mathfrak{g}_1$ and $\mathfrak{g}_2$ CFTs that are related to the $\mathfrak{g}$ CFT by a nontrivial conformal embedding $\mathfrak{g} \supset \mathfrak{g}_1 \times \mathfrak{g}_2$. The resulting model can be viewed as a layer construction of a 3D topologically ordered state, in which the conformal embedding in each wire implements the anyon condensation between adjacent layers. Local operators acting on the ground state create point-like or loop-like deconfined excitations depending on the branching rule. We demonstrate our construction for a simple solvable model based on the conformal embedding $SU(2)_1 \times SU(2)_1 \supset U(1)_4 \times U(1)_4$. We show that the model possesses extensively degenerate ground states on a torus with deconfined quasiparticles, and that appropriate local perturbations lift the degeneracy and yield a 3D $Z_2$ gauge theory with a fermionic $Z_2$ charge.

Model of spin liquids with and without time-reversal symmetry

We study a model in (2+1)-dimensional spacetime that is realized by an array of chains, each of which realizes relativistic Majorana fields in (1+1)-dimensional spacetime, coupled via current-current interactions. The model is shown to have a lattice realization in an array of two-leg quantum spin-1/2 ladders. We study the model both in the presence and absence of time-reversal symmetry, within a mean-field approximation. We find regimes in coupling space where Abelian and non-Abelian spin liquid phases are stable. In the case when the Hamiltonian is time-reversal symmetric, we find regimes where gapped Abelian and non-Abelian chiral phases appear as a result of spontaneous breaking of time-reversal symmetry. These gapped phases are separated by a discontinuous phase transition. More interestingly, we find a regime where a non-chiral gapless non-Abelian spin liquid is stable. The excitations in this regime are described by relativistic Majorana fields in (2+1)-dimensional spacetime, much as those appearing in the Kitaev honeycomb model, but here emerging in a model of coupled spin ladders that does not break SU(2) spin-rotation symmetry.

The experimental investigation of weak effects in the KLL Auger electron spectrum of Zr and Nb generated in radioactive decay

The KLL Auger electron spectra of Zr (Z = 40) and Nb (Z = 41) following respectively the electron capture (EC) decay of 90Nb and the de-excitation of the isomeric state of 91mNb were investigated in detail using a combined electrostatic electron spectrometer and radioactive sources prepared by surface sorption on a polycrystalline carbon substrate. For both elements, energies, relative intensities, and natural widths of all the nine well-resolved basic spectrum components were determined and compared with theoretical predictions and with results of previous measurement as well. Results of our ab initio multiconfiguration Dirac-Hartree-Fock calculations are discussed also in relation to the solid-state effect. Indications of an influence of the EC decay on the absolute energy of the KL2L3(1D2) transition (so-called atomic structure effect) in Zr were found. The effect of the retarded current-current interaction on the KL1L2(3P0) transition intensity was observed to be appreciable for the investigated elements in accordance with the prediction.

Spin Dynamics and Andreev-Bashkin Effect in Mixtures of One-Dimensional Bose Gases.

We investigate the propagation of spin waves in two-component mixtures of one-dimensional Bose gases interacting through repulsive contact potentials. By using quantum MonteCarlo methods we calculate static ground-state properties, such as the spin susceptibility and the spin structure factor, as a function of the coupling strengths and we determine the critical parameters for phase separation. In homogeneous mixtures, results of the velocity of spin waves and of its softening close to the critical point of phase separation are obtained by means of hydrodynamic theory and a sum-rule approach. We quantify the nondissipative drag effect, resulting from the Andreev-Bashkin current-current interaction between the two components of the gas, and we show that in the regime of strong coupling it causes a significant suppression of the spin-wave velocity.

Critical flavor number of the Thirring model in three dimensions

The Thirring model is a four-fermion theory with a current-current interaction and $U(2N)$ chiral symmetry. It is closely related to three-dimensional QED and other models used to describe properties of graphene. In addition it serves as a toy model to study chiral symmetry breaking. In the limit of flavour number $N \to 1/2$ it is equivalent to the Gross-Neveu model, which shows a parity-breaking discrete phase transition. The model was already studied with different methods, including Dyson-Schwinger equations, functional renormalisation group methods and lattice simulations. Most studies agree that there is a phase transition from a symmetric phase to a spontaneously broken phase for a small number of fermion flavours, but no symmetry breaking for large $N$. But there is no consensus on the critical flavour number $N^\text{cr}$ above which there is no phase transition anymore and on further details of the critical behaviour. Values of $N$ found in the literature vary between $2$ and $7$. All earlier lattice studies were performed with staggered fermions. Thus it is questionable if in the continuum limit the lattice model recovers the internal symmetries of the continuum model. We present new results from lattice Monte Carlo simulations of the Thirring model with SLAC fermions which exactly implement all internal symmetries of the continuum model even at finite lattice spacing. If we reformulate the model in an irreducible representation of the Clifford algebra, we find, in contradiction to earlier results, that the behaviour for even and odd flavour numbers is very different: For even flavour numbers, chiral and parity symmetry are always unbroken. For odd flavour numbers parity symmetry is spontaneously broken below the critical flavour number $N_\text{ir}^\text{cr}=9$ while chiral symmetry is still unbroken.

Optical absorption and conductivity in quasi-two-dimensional crystals from first principles: Application to graphene

This paper gives a theoretical formulation of the electromagnetic response of the quasi-two-dimensional (Q2D) crystals suitable for investigation of optical activity and polariton modes. The response to external electromagnetic field is described by current-current response tensor $\Pi_{\mu\nu}$ calculated by solving the Dyson equation in the random phase approximation (RPA), where current-current interaction is mediated by the photon propagator $D_{\mu\nu}$. The irreducible current-current response tensor $\Pi^0_{\mu\nu}$ is calculated from the {\em ab initio} Kohn-Sham (KS) orbitals. The accuracy of $\Pi^0_{\mu\nu}$ is tested in the long wavelength limit where it gives correct Drude dielectric function and conductivity. The theory is applied to the calculation of optical absorption and conductivity in pristine and doped single layer graphene and successfully compared with previous calculations and measurements.

Spontaneous baryogenesis from asymmetric inflaton

We propose a variant scenario of spontaneous baryogenesis from asymmetric inflaton based on current-current interactions between the inflaton and matter fields with a non-zero B-L charge. When the inflaton starts to oscillate around the minimum after inflation, it may lead to excitation of a CP-odd component, which induces an effective chemical potential for the B-L number through the current-current interactions. We study concrete inflation models and show that the spontaneous baryogenesis scenario can be naturally implemented in the chaotic inflation in supergravity.

Numerical Analysis of Thirring Model under White Noise

Today, the effects of noise on dynamical systems are an attractive area of research. The noise acts as a driving term in the equations of motion in nonlinear systems. In this work, we present conformally invariant pure spinor nonlinear Thirring model. Thirring model describes Dirac fermions in (1+1) space-time dimensions with local current-current interaction. This model has rich dynamic of the quantization of relativistic quantum field theories. We investigate the response of Thirring oscillator to white noise by constructing phase space displays.