FQHE interferometers in strong tunneling regime. The role of compactness of edge fields

We consider multiple-point tunneling in the interferometers formed between edges of electron liquids with in general different filling factors in the regime of the Fractional Quantum Hall effect (FQHE). We derive an effective matrix Caldeira-Leggett models for the multiple tunneling contacts connected by the chiral single-mode FQHE edges. It is shown that the compactness of the Wen- Fr\"ohlich chiral boson fields describing the FQHE edge modes plays a crucial role in eliminating the spurious non-locality of the electron transport properties of the FQHE interferometers arising in the regime of strong tunneling.Comment: 5 page

Double Well Potential: Perturbation Theory, Tunneling, WKB (beyond instantons)

A simple approximate solution for the quantum-mechanical quartic oscillator $V= m^2 x^2+g x^4$ in the double-well regime $m^2<0$ at arbitrary $g \geq 0$ is presented. It is based on a combining of perturbation theory near true minima of the potential, semi-classical approximation at large distances and a description of tunneling under the barrier. It provides 9-10 significant digits in energies and gives for wavefunctions the relative deviation in real $x$-space less than $\lesssim 10^{-3}$.Comment: 13 pages, invited talk at "Crossing the boundaries: Gauge dynamics at strong coupling (Shifmania)", Minneapolis, May 14-17, 200

Generalized quantum measurements with matrix product states: Entanglement phase transition and clusterization

We propose a method, based on matrix product states, for studying the time evolution of many-body quantum lattice systems under continuous and site-resolved measurement. Both the frequency and the strength of generalized measurements can be varied within our scheme, thus allowing us to explore the corresponding two-dimensional phase diagram. The method is applied to one-dimensional chains of nearest-neighbor interacting hard-core bosons. A transition from an entangling to a disentangling (area-law) phase is found. However, by resolving time-dependent density correlations in the monitored system, we find important differences between different regions at the phase boundary. In particular, we observe a peculiar phenomenon of measurement-induced particle clusterization that takes place only for frequent moderately strong measurements, but not for strong infrequent measurements.Comment: 13 pages, 11 figures, plus an appendix (13 pp., 1 figure). Comments welcom

Evolution of many-body systems under ancilla quantum measurements

Measurement-induced phase transitions are the subject of intense current research, both from an experimental and a theoretical perspective. We explore the concept of implementing quantum measurements by coupling a many-body lattice system to an ancillary degree of freedom (implemented using two additional sites), on which projective measurements are performed. We analyze the effect of repeated (``stroboscopic'') measurements on the dynamical correlations of interacting hard-core bosons in a one-dimensional chain. An important distinctive ingredient of the protocol is the fact that the detector ancillas are not re-initialized after each measurement step. The detector thus maintains memory of the accumulated influence by the measured correlated system. Initially, we consider a model in which the ancilla is coupled to a single lattice site. This setup allows obtaining information about the system through Rabi oscillations in the ancillary degrees of freedom, modulated by the ancilla-system interaction. The statistics of quantum trajectories exhibits a ``quantum-Zeno-valve effect'' that occurs when the measurement becomes strong, with sharp branching between low and high entanglement. We proceed by extending numerical simulations to the case of two ancillas and, then, to measurements on all sites. With this realistic measurement apparatus, we find evidence of a disentangling-entangling measurement-induced transition as was previously observed in more abstract models. The dynamics features a broad distribution of the entanglement entropy.Comment: 23 pages, 17 figure

Case study of ozone anomalies over northern Russia in the 2015/2016 winter: measurements and numerical modelling

Episodes of extremely low ozone columns were observed over the territory of Russia in the Arctic winter of 2015/2016 and the beginning of spring 2016. We compare total ozone columns (TOCs) from different remote sensing techniques (satellite and ground-based observations) with results of numerical modelling over the territory of the Urals and Siberia for this period. We demonstrate that the provided monitoring systems (including the new Russian Infrared Fourier Spectrometer IKFS-2) and modern three-dimensional atmospheric models can capture the observed TOC anomalies. However, the results of observations and modelling show differences of up to 20&thinsp;%–30&thinsp;% in TOC measurements. Analysis of the role of chemical and dynamical processes demonstrates that the observed short-term TOC variability is not a result of local photochemical loss initiated by heterogeneous halogen activation on particles of polar stratospheric clouds that formed under low temperatures in the mid-winter.</p

Many-body localization and delocalization in large quantum chains

We theoretically study the quench dynamics for an isolated Heisenberg spin chain with a random on-site magnetic field, which is one of the paradigmatic models of a many-body localization transition. We use the time-dependent variational principle as applied to matrix product states, which allows us to controllably study chains of a length up to $L=100$ spins, i.e., much larger than $L \simeq 20$ that can be treated via exact diagonalization. For the analysis of the data, three complementary approaches are used: (i) determination of the exponent $\beta$ which characterizes the power-law decay of the antiferromagnetic imbalance with time; (ii) similar determination of the exponent $\beta_\Lambda$ which characterizes the decay of a Schmidt gap in the entanglement spectrum, (iii) machine learning with the use, as an input, of the time dependence of the spin densities in the whole chain. We find that the consideration of the larger system sizes substantially increases the estimate for the critical disorder $W_c$ that separates the ergodic and many-body localized regimes, compared to the values of $W_c$ in the literature. On the ergodic side of the transition, there is a broad interval of the strength of disorder with slow subdiffusive transport. In this regime, the exponents $\beta$ and $\beta_\Lambda$ increase, with increasing $L$, for relatively small $L$ but saturate for $L \simeq 50$, indicating that these slow power laws survive in the thermodynamic limit. From a technical perspective, we develop an adaptation of the "learning by confusion" machine learning approach that can determine $W_c$.Comment: 14 pages, 11 figures. Title changed compared to earlier arXiv versions. Comments welcom