Gauge-invariant Density Research Articles

Lightwave terahertz quantum manipulation of nonequilibrium superconductor phases and their collective modes

We present a gauge-invariant density matrix description of non-equilibrium superconductor (SC) states with spatial and temporal correlations driven by intense terahertz (THz) lightwaves. We derive superconductor Bloch--Maxwell equations of motion that extend Anderson pseudo-spin models to include the Cooper pair center-of-mass motion and electromagnetic propagation effects. We thus describe quantum control of dynamical phases, collective modes, quasi-particle coherence, and high nonlinearities during cycles of carrier wave oscillations, which relate to our recent experiments. Coherent photogeneration of a nonlinear supercurrent with dc component via condensate acceleration by an effective lightwave field dynamically breaks the equilibrium inversion symmetry. Experimental signatures include high harmonic light emission at equilibrium-symmetry-forbidden frequencies, Rabi--Higgs collective modes and quasi-particle coherence, and non-equilibrium moving condensate states tuned by few-cycle THz fields. We use such lightwaves as an oscillating accelerating force that drives strong nonlinearities and anisotropic quasi-particle populations to control and amplify different classes of collective modes, e.g., damped oscillations, persistent oscillations, and overdamped dynamics via Rabi flopping. Recent phase-coherent nonlinear spectroscopy experiments can be modeled by solving the full nonlinear quantum dynamics including self-consistent light--matter coupling.

Dark sector evolution in Horndeski models

We use the Equation of State (EoS) approach to study the evolution of the dark sector in Horndeski models, the most general scalar-tensor theories with second order equations of motion. By including the effects of the dark sector into our code EoS_class, we demonstrate the numerical stability of the formalism and excellent agreement with results from other publicly available codes for a range of parameters describing the evolution of the function characterising the perturbations for Horndeski models, αx, with x = K, B, M, T. After demonstrating that on sub-horizon scales (k≳ 10−3 Mpc−1 at z=0) velocity perturbations in both the matter and the dark sector are typically subdominant with respect to density perturbations in the equation of state for perturbations, we find an attractor solution for the dark sector gauge-invariant density perturbation Δds by neglecting its time derivatives in the equation describing its time evolution, as commonly done in the well-known quasi-static approximation. Using this result, we provide simplified expressions for the equation-of-state functions: the dark sector entropy perturbations wdsΓds and anisotropic stress wdsΠds. From this we derive a growth factor-like equation for both matter and dark sector and are able to capture the relevant physics for several observables with great accuracy. We finally present new analytical expressions for the well-known modified gravity phenomenological functions μ, η and Σ for a generic Horndeski model as functions of αx. We show that on small scales they reproduce expressions presented in previous works, but on large scales, we find differences with respect to other works.

Hohenberg-Kohn theorem including electron spin

The Hohenberg-Kohn theorem is generalized to the case of a finite system of $N$ electrons in external electrostatic $\mathcal{E}(\mathbf{r})=\ensuremath{-}\ensuremath{\nabla}v(\mathbf{r})$ and magnetostatic $\mathbf{B}(\mathbf{r})=\ensuremath{\nabla}\ifmmode\times\else\texttimes\fi{}\mathbf{A}(\mathbf{r})$ fields in which the interaction of the latter with both the orbital and spin angular momentum is considered. For a nondegenerate ground state a bijective relationship is proved between the gauge invariant density $\ensuremath{\rho}(\mathbf{r})$ and physical current density $\mathbf{j}(\mathbf{r})$ and the potentials ${v(\mathbf{r}),\mathbf{A}(\mathbf{r})}$. The possible many-to-one relationship between the potentials ${v(\mathbf{r}),\mathbf{A}(\mathbf{r})}$ and the wave function is explicitly accounted for in the proof. With the knowledge that the basic variables are ${\ensuremath{\rho}(\mathbf{r}),\mathbf{j}(\mathbf{r})}$, and explicitly employing the bijectivity between ${\ensuremath{\rho}(\mathbf{r}),\mathbf{j}(\mathbf{r})}$ and ${v(\mathbf{r}),\mathbf{A}(\mathbf{r})}$, the further extension to $N$-representable densities and degenerate states is achieved via a Percus-Levy-Lieb constrained-search proof. A ${\ensuremath{\rho}(\mathbf{r}),\mathbf{j}(\mathbf{r})}$-functional theory is developed. Finally, a Slater determinant of equidensity orbitals which reproduces a given ${\ensuremath{\rho}(\mathbf{r}),\mathbf{j}(\mathbf{r})}$ is constructed.

New gauge anomalies and topological invariants in various dimensions

In the model of extended non-Abelian tensor gauge fields we have found new metric-independent densities: the exact (2n+3)-forms and their secondary characteristics, the (2n+2)-forms as well as the exact 6n-forms and the corresponding secondary (6n−1)-forms. These forms are the analogs of the Pontryagin densities: the exact 2n-forms and Chern–Simons secondary characteristics, the (2n−1)-forms. The (2n+3)- and 6n-forms are gauge invariant densities, while the (2n+2)- and (6n−1)-forms transform non-trivially under gauge transformations, which we compare with the corresponding transformations of the Chern–Simons secondary characteristics. This construction allows to identify new potential gauge anomalies in various dimensions.

Non-Abelian tensor gauge fields

Recently proposed extension of Yang-Mills theory contains non-Abelian tensor gauge fields. The Lagrangian has quadratic kinetic terms, as well as cubic and quartic terms describing non-linear interaction of tensor gauge fields with the dimensionless coupling constant. We analyze particle content of non-Abelian tensor gauge fields. In four-dimensional space-time the rank-2 gauge field describes propagating modes of helicity 2 and 0. We introduce interaction of the non-Abelian tensor gauge field with fermions and demonstrate that the free equation of motion for the spin-vector field correctly describes the propagation of massless modes of helicity 3/2. We have found a new metric-independent gauge invariant density which is a four-dimensional analog of the Chern-Simons density. The Lagrangian augmented by this Chern-Simons-like invariant describes massive Yang-Mills boson, providing a gauge-invariant mass gap for a four-dimensional gauge field theory.

Topological mass generation four-dimensional gauge theory

The Lagrangian of non-Abelian tensor gauge fields describes the interaction of the Yang–Mills and massless tensor bosons of increasing helicities. We have found a metric-independent gauge invariant density which is a four-dimensional analog of the Chern–Simons density. The Lagrangian augmented by this Chern–Simons-like invariant describes massive Yang–Mills boson, providing a gauge-invariant mass gap for a four-dimensional gauge field theory. We present invariant densities which can provide masses to the high-rank tensor bosons.

Gauge-invariant Density and Temperature Perturbations in the Quasi-Newtonian Formulation

We give an improved formalism for calculating the evolution of density fluctuations and temperature perturbations in flat universes. Our equations are general enough to treat the perturbations in collisionless relics like massive neutrinos. We find this formulation to be simpler to use than gauge dependent and other gauge-invariant formalisms. We show how to calculate temperature fluctuations (including multipole moments) and transfer functions, including the case of collisionless relics like massive neutrinos. We call this formalism "quasi-Newtonian" because the equations for the potential and cold matter fluctuation evolution have the same form as the Newtonian gravitational equations in an expanding space. The density fluctuation variable also has the same form inside and outside of the horizon which allows the initial conditions to be specified in a simple intuitive way. Our sample calculations demonstrate how to use these equations in cosmological models which have hot, cold, and mixed dark matter and adiabatic (isentropic) or isocurvature modes. We also give an approximation which may be used to get transfer functions quickly.

Theory of fermion liquids.

We develop a general theory of fermion liquids in spatial dimensions greater than one. The principal method, bosonization, is applied to the cases of short and long range longitudinal interactions, and to transverse gauge interactions. All the correlation functions of the system may be obtained with the use of a generating functional. Short-range and Coulomb interactions do not destroy the Landau Fermi fixed point. Novel fixed points are found, however, in the cases of a super-long range longitudinal interaction in two dimensions and transverse gauge interactions in two and three spatial dimensions. We consider in some detail the 2+1-dimensional problem of a Chern-Simons gauge action combined with a longitudinal two-body interaction $V({\bf q}) \propto |{\bf q}|^{y-1}$ which controls the density, and hence gauge, fluctuations. For $y < 0$ we find that the gauge interaction is irrelevant and the Landau fixed point is stable, while for $y > 0$ the interaction is relevant and the fixed point cannot be accessed by bosonization. Of special importance is the case $y = 0$ (Coulomb interaction) which describes the Halperin-Lee-Read theory of the half-filled Landau level. We obtain the full quasiparticle propagator which is of a marginal Fermi liquid form. Using Ward Identities, we show that neither the inclusion of nonlinear terms in the fermion dispersion, nor vertex corrections, alters our results: the fixed point is accessible by bosonization. As the two-point fermion Green's function is not gauge invariant, we also investigate the gauge-invariant density response function. Near momentum $Q = 2 k_F$, in addition to the Kohn anomaly we find singular behavior. In Appendices we present a numerical calculation of the spectral function for a Fermi liquid with Landau parameter $f_0 \neq 0$. We also show how Kohn's theorem is

EXACT SOLUTION OF INDUCED LATTICE GAUGE THEORY AT LARGE-N

We find the exact solution of a recently proposed model of the lattice gauge theory induced by heavy scalar field in adjoint representation at N=∞ for arbitrary dimension D. The nonlinear integral equation for the gauge invariant density of eigenvalues of the vacuum average of the scalar field is derived. In the continuum limit, the density grows as ɸα where [Formula: see text] arccos [Formula: see text].

Narrow electronic bands in high electric fields: Static properties.

We present a gauge-invariant formalism for studying the motion of electrons in uniform electric and magnetic fields. This paper treats static properties, mainly the spectral function and density of states. These results will be exploited in a second paper devoted to transport, with the aim of extending the results of Khan, Davies, and Wilkins [Phys. Rev. B 36, 2578 (1987)] to include periodic bands as well as parabolic bands. In particular, we define a gauge-invariant density of states that can be used in the presence of applied electric and magnetic fields. This density of states can be interpreted as a function of kinetic energy in the case of parabolic bands. It reduces smoothly to the usual results in the absence of applied fields and gains a tail into negative kinetic energies when an electric field is applied---a result well known from the theory of electroabsorption. Structure due to Landau levels is seen when a magnetic field is applied. The results are more striking in the case of a periodic energy band. Here the continuous density of states is split into a discrete ``Stark ladder'' when an electric field is applied, with the levels separated by the energy of Bloch oscillations. It is not necessary to introduce the Stark levels explicitly through the use of a scalar potential; they emerge naturally within the gauge-invariant formalism. Again the density of states shows no unphysical discontinuous behavior as the field goes to zero. The implications of these results for transport are briefly discussed.

Gauge-invariant density fluctuations in a cold dark matter universe

Adiabatic density fluctuations of a cold collisionless gas in a radiation background are examined using a gauge-invariant formalism. Particular attention is paid to fluctuations which cross the horizon during the radiation-dominated era. The resulting density spectrum invalidates previous arguments that a Zel'dovich primordial fluctuation spectrum is not consistent with an axion-dominated universe.

Behavior of higher modes of gravitational waves and gauge-invariant density perturbations in Bianchi IX cosmological models

Behavior of higher modes of gravitational waves and gauge-invariant density perturbations in Bianchi IX cosmological models