Boundedness of Pseudodifferential Operators on Banach Function Spaces

We show that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space $X(\mathbb{R}^n)$ and on its associate space $X'(\mathbb{R}^n)$, then a pseudodifferential operator $\operatorname{Op}(a)$ is bounded on $X(\mathbb{R}^n)$ whenever the symbol $a$ belongs to the H\"ormander class $S_{\rho,\delta}^{n(\rho-1)}$ with $0<\rho\le 1$, $0\le\delta<1$ or to the the Miyachi class $S_{\rho,\delta}^{n(\rho-1)}(\varkappa,n)$ with $0\le\delta\le\rho\le 1$, $0\le\delta0$. This result is applied to the case of variable Lebesgue spaces $L^{p(\cdot)}(\mathbb{R}^n)$.Comment: To appear in a special volume of Operator Theory: Advances and Applications dedicated to Ant\'onio Ferreira dos Santo

Splitting of Long-Wavelength Modes of the Fractional Quantum Hall Liquid at ν=1/3\nu=1/3

Resonant inelastic light scattering experiments at $\nu=1/3$ reveal a novel splitting of the long wavelength modes in the low energy spectrum of quasiparticle excitations in the charge degree of freedom. We find a single peak at small wavevectors that splits into two distinct modes at larger wavevectors. The evidence of well-defined dispersive behavior at small wavevectors indicates a coherence of the quantum fluid in the micron length scale. We evaluate interpretations of long wavelength modes of the electron liquid.Comment: 4 pages, 4 figure

Localization Length in Anderson Insulator with Kondo Impurities

The localization length, $\xi$, in a 2--dimensional Anderson insulator depends on the electron spin scattering rate by magnetic impurities, $\tau_s^{-1}$. For antiferromagnetic sign of the exchange, %constant, the time $\tau_s$ is {\em itself a function of $\xi$}, due to the Kondo correlations. We demonstrate that the unitary regime of localization is impossible when the concentration of magnetic impurities, $n_{\tiny M}$, is smaller than a critical value, $n_c$. For $n_{\tiny M}>n_c$, the dependence of $\xi$ on the dimensionless conductance, $g$, is {\em reentrant}, crossing over to unitary, and back to orthogonal behavior upon increasing $g$. Sensitivity of Kondo correlations to a weak {\em parallel} magnetic field results in a giant parallel magnetoresistance.Comment: 5 pages, 1 figur

Quantum transport thermometry for electrons in graphene

We propose a method of measuring the electron temperature $T_e$ in mesoscopic conductors and demonstrate experimentally its applicability to micron-size graphene devices in the linear-response regime ($T_e\approx T$, the bath temperature). The method can be {especially useful} in case of overheating, $T_e>T$. It is based on analysis of the correlation function of mesoscopic conductance fluctuations. Although the fluctuation amplitude strongly depends on the details of electron scattering in graphene, we show that $T_e$ extracted from the correlation function is insensitive to these details.Comment: 4 pages, 4 figures; final version, as publishe

Mesoscopic conductance fluctuations in dirty quantum dots with single channel leads

We consider a distribution of conductance fluctuations in quantum dots with single channel leads and continuous level spectra and we demonstrate that it has a distinctly non-Gaussian shape and strong dependence on time-reversal symmetry, in contrast to an almost Gaussian distribution of conductances in a disordered metallic sample connected to a reservoir by broad multi-channel leads. In the absence of time-reversal symmetry, our results obtained within the diagrammatic approach coincide with those derived within non-perturbative techniques. In addition, we show that the distribution has lognormal tails for weak disorder, similar to the case of broad leads, and that it becomes almost lognormal as the amount of disorder is increased towards the Anderson transition.Comment: 14 pages in the ReVTeX preprint format, including 5 postscript figures; to be published in J.Phys.:Cond.Mat., 199

Asymptotically exact probability distribution for the Sinai model with finite drift

We obtain the exact asymptotic result for the disorder-averaged probability distribution function for a random walk in a biased Sinai model and show that it is characterized by a creeping behavior of the displacement moments with time, ~ t^{\mu n} where \mu is dimensionless mean drift. We employ a method originated in quantum diffusion which is based on the exact mapping of the problem to an imaginary-time Schr\"{odinger} equation. For nonzero drift such an equation has an isolated lowest eigenvalue separated by a gap from quasi-continuous excited states, and the eigenstate corresponding to the former governs the long-time asymptotic behavior.Comment: 4 pages, 2 figure

Theory of the Half-Polarized Quantum Hall States

We report a theoretical analysis of the half-polarized quantum Hall states observed in a recent experiment. Our numerical results indicate that the ground state energy of the quantum Hall $\nu= 2/3$ and $\nu= 2/5$ states versus spin polarization has a downward cusp at half the maximal spin polarization. We map the two-component fermion system onto a system of excitons and describe the ground state as a liquid state of excitons with non-zero values of exciton angular momentum.Comment: 4 pages (RevTeX), 3 figures (PostScript), added reference