An experimental investigation of the transition from Fowler–Nordheim (FN) field emission to space-charge-limited (SCL) flows in a nanogap is presented. Electrodes with gap size D∼30–70 nm corresponding to D/λo up to a maximum of ∼2×103, where λo is the de Broglie wavelength of the space-charge-electrons, are experimented. The transition from the FN field emission to the classical SCL flow is a function of the applied bias and lies in the range 5–15 V. The equilibrium transmitted current density for the 50 nm sample indicates a transition from the FN to the quantum SCL flow at ∼0.4 V with D/λo of ∼35 and then gradually to the classical SCL behavior as the voltage is increased beyond ∼9 V. The experiments indicate no sharp demarcation between the different regimes.

We use the poor man's scaling approach to study the phase boundaries of a pair of quantum impurity models featuring a power-law density of states ρ(ε) ∝ |ε| r , either vanishing (for r > 0) or diverging (for r < 0) at the Fermi energy ε = 0, that gives rise to quantum phase transitions between local-moment and Kondo-screened phases. For the Anderson model with a pseudogap (i.e., r > 0), we find the phase boundary for (a) 0 < r < 1/2, a range over which the model exhibits interacting quantum critical points both at and away from particle-hole (p-h) symmetry, and (b) r > 1, where the phases are separated by first-order quantum phase transitions that are accessible only for broken p-h symmetry. For the p-h-symmetric Kondo model with easy-axis or easy-plane anisotropy of the impurity-band spin exchange, the phase boundary and scaling trajectories are obtained for both r > 0 and r < 0. Throughout the regime of weak-to-moderate impurity-band coupling in which poor man's scaling is expected to be valid, the approach predicts phase boundaries in excellent qualitative and good quantitative agreement with the nonperturbative numerical renormalization group, while also establishing the functional relations between model parameters along these boundaries.

The Anderson impurity model with a density of states ρ(ε) ∝ |ε| r containing a power-law pseudogap centered on the Fermi energy (ε = 0) features for 0 < r < 1 a Kondo-destruction quantum critical point (QCP) separating Kondo-screened and local-moment phases. The observation of mixed valency in quantum critical β-YbAlB4 has prompted study of this model away from particle-hole symmetry. The critical spin response associated with all Kondo destruction QCPs has been shown to be accompanied, for r = 0.6 and noninteger occupation of the impurity site, by a divergence of the local charge susceptibility on both sides of the QCP. In this work, we use the numerical renormalization-group method to characterize the Kondo-destruction charge response using five critical exponents, which are found to assume nontrivial values only for 0.55 r < 1. For 0 < r 0.55, by contrast, the local charge susceptibility shows no divergence at the QCP, but rather exhibits nonanalytic corrections to a regular leading behavior. Both the charge critical exponents and the previously obtained spin critical exponents satisfy a set of scaling relations derived from an ansatz for the free energy near the QCP. These critical exponents can all be expressed in terms of just two underlying exponents: the correlation-length exponent ν(r) and the gap exponent ∆(r). The ansatz predicts a divergent local charge susceptibility for ν < 2, which coincides closely with the observed range 0.55 r < 1. Many of these results are argued to generalize to interacting QCPs that have been found in other quantum impurity models.

We study the impurity entanglement entropy Se in quantum impurity models that feature a Kondo-destruction quantum critical point (QCP) arising from a pseudogap in the conduction-band density of states or from coupling to a bosonic bath. On the local-moment (Kondo-destroyed) side of the QCP, the entanglement entropy contains a critical component that can be related to the order parameter characterizing the quantum phase transition. In Kondo models describing a spinSimp, Se assumes its maximal value of ln(2Simp + 1) at the QCP and throughout the Kondo phase, independent of features such as particle-hole symmetry and under-or over-screening. In Anderson models, Se is nonuniversal at the QCP, and at particle-hole symmetry, rises monotonically on passage from the local-moment phase to the Kondo phase; breaking this symmetry can lead to a cusp peak in Se due to a divergent charge susceptibility at the QCP. Implications of these results for quantum critical systems and quantum dots are discussed.

We investigate the dynamical properties of the two-channel Anderson model using the non-crossing approximation (NCA) supplemented by numerical renormalization group (NRG) calculations. We provide evidence supporting the conventional wisdom that the NCA gives reliable results for the standard two-channel Anderson model of a magnetic impurity in a metal. We extend the analysis to the pseudogap two-channel model describing a semi-metallic host with a density of states that vanishes in power-law fashion at the Fermi energy. This model exhibits continuous quantum phase transitions between weak- and strong-coupling phases. The NCA is shown to reproduce the correct qualitative features of the pseudogap model, including the phase diagram, and to yield critical exponents in excellent agreement with the NRG and exact results. The forms of the dynamical magnetic susceptibility and impurity Green's function at the fixed points are suggestive of frequency-over-temperature scaling

e takes its maximal value, a signature of strong entanglement associated with the QCP. In the Kondo phase, S imp e decreases for R ≫ R * , but (in contrast to the conventional metallic case) remains nonzero even for R → ∞ due to the incomplete screening of the

Geometrically frustrated quantum impurities coupled to metallic leads have been shown to exhibit rich behavior with a quantum phase transition separating Kondo screened and local moment phases. Frustration in the quantum impurity can alternatively be introduced via Kitaev-couplings between different spins of the impurity cluster. We use the Numerical Renormalization Group (NRG) to study a range of systems where the quantum impurity comprising a Kitaev cluster is coupled to a bath of non-interacting fermions. The models exhibits a competition between Kitaev and Kondo dominated physics depending on whether the Kitaev couplings are greater or less than the Kondo temperature. We characterize the ground state properties of the system and determine the temperature dependence of the crossover scale for the emergence of fractionalized degrees of freedom in the model. We also demonstrate qualitatively as well as quantitatively that in the Kondo limit, the complex impurity can be mapped to an effective two-impurity system, where the emergent spin 1/2 comprises of both Majorana and flux degrees of freedom. For a tetrahedral-shaped Kitaev cluster, an extra orbital degree of freedom closely related to a flux degree of freedom remains unscreened even in the presence of both Heisenberg and Kondo interactions.

Herbal gargles have gained significant attention as potential alternatives to conventional oral care products due to their perceived natural composition and reported therapeutic benefits. This review aims to provide a comprehensive overview of the efficacy of herbal gargles in promoting oral health and preventing various oral ailments. Our oral cavity is a sweet able place to grow different types of bacterial species either harmless or harmful for human. From ancient age medicinal plants are considered as a store room of different types of biological activity in Ayurveda, Unani and Siddha, and have important role to cleanse tooth and prevent different human pathogens are responsible for unpleasant odour, inflammation of teeth root, dental plaque. The study evaluates a wide range of herbal ingredients commonly found in mouth gargles, including essential oils, plant extracts, and traditional herbal remedies. It explores their antimicrobial properties, antioxidant activity, and potential for reducing plaque formation, gingivitis, and bad breath. Aqueous extract of Tulsi, Turmeric, Clove, Fennel, Betel leaves, Pudina, Ginger, Liquorice shows effective antimicrobial, antifungal activity, anti-inflammatory and anti-plaque properties. In this research work herbal gargle was evaluated depends on various parameter like color, pH, Phase separation , Homogeneity and antibacterial properties. Herbal gargles show potential as adjuncts to conventional oral care, Herbal gargle is suitable for any age group due to less side effect. Healthcare professionals and consumers should approach herbal gargles with caution, taking into consideration individual oral health needs and consulting oral healthcare providers for personalized recommendations.