Iso-spectral deformations of general matrix and their reductions on Lie algebras

We study an iso-spectral deformation of general matrix which is a natural generalization of the Toda lattice equation. We prove the integrability of the deformation, and give an explicit formula for the solution to the initial value problem. The formula is obtained by generalizing the orthogonalization procedure of Szeg\"{o}. Based on the root spaces for simple Lie algebras, we consider several reductions of the hierarchy. These include not only the integrable systems studied by Bogoyavlensky and Kostant, but also their generalizations which were not known to be integrable before. The behaviors of the solutions are also studied. Generically, there are two types of solutions, having either sorting property or blowing up to infinity in finite time.Comment: 25 pages, AMSLaTe

Undetermined states: how to find them and their applications

We investigate the undetermined sets consisting of two-level, multi-partite pure quantum states, whose reduced density matrices give absolutely no information of their original states. Two approached of finding these quantum states are proposed. One is to establish the relation between codewords of the stabilizer quantum error correction codes (SQECCs) and the undetermined states. The other is to study the local complementation rules of the graph states. As an application, the undetermined states can be exploited in the quantum secret sharing scheme. The security is guaranteed by their undetermineness.Comment: 6 pages, no figur

Dynamics of interacting fermions under spin-orbit coupling in an optical lattice clock

Quantum statistics and symmetrization dictate that identical fermions do not interact via s-wave collisions. However, in the presence of spin-orbit coupling (SOC), fermions prepared in identical internal states with distinct momenta become distinguishable. The resulting strongly interacting system can exhibit exotic topological and pairing behaviours, many of which are yet to be observed in condensed matter systems. Ultracold atomic gases offer a promising pathway for simulating these rich phenomena, but until recently have been hindered by heating and losses. Here we enter a new regime of many-body interacting SOC in a fermionic optical lattice clock (OLC), where the long-lived electronic clock states mitigate unwanted dissipation. Using clock spectroscopy, we observe the precession of the collective magnetization and the emergence of spin-locking effects arising from an interplay between p-wave and SOC-induced exchange interactions. The many-body dynamics are well captured by a collective XXZ spin model, which describes a broad class of condensed matter systems ranging from superconductors to quantum magnets. Furthermore, our work will aid in the design of next-generation OLCs by offering a route for avoiding the observed large density shifts caused by SOC-induced exchange interactions

Phase diagram of the ferroelectric-relaxor (1-x)PbMg(1/3)Nb(2/3)O3-xPbTiO3

Synchrotron x-ray powder diffraction measurements have been performed on unpoled ceramic samples of (1-x)PbMg(1/3)Nb(2/3)O3-xPbTiO3 (PMN-xPT) with 30%<= x<= 39% as a function of temperature around the morphotropic phase boundary (MPB), which is the line separating the rhombohedral and tetragonal phases in the phase diagram. The experiments have revealed very interesting features previously unknown in this or related systems. The sharp and well-defined diffraction profiles observed at high and intermediate temperatures in the cubic and tetragonal phases, respectively, are in contrast to the broad features encountered at low temperatures. These peculiar characteristics, which are associated with the monoclinic phase of MC-type previously reported by Kiat et al and Singh et al., can only be interpreted as multiple coexisting structures with MC as the major component. An analysis of the diffraction profiles has allowed us to properly characterize the PMN-xPT phase diagram and to determine the stability region of the monoclinic phase, which extends from x= 31% to x= 37% at 20 K. The complex lansdcape of observed phases points to an energy balance between the different PMN-xPT phases which is intrinsically much more delicate than that of related systems such as PbZr(1-x)TixO3 or (1-x)PbZn(1/3)Nb(1/3)O3-xPbTiO3. These observations are in good accord with an optical study of x= 33% by Xu et al., who observed monoclinic domains with several different polar directions coexisting with rhombohedral domains, in the same single crystal.Comment: REVTeX4, 11 pages, 10 figures embedde

Kondo effect in crossed Luttinger liquids

We study the Kondo effect in two crossed Luttinger liquids, using Boundary Conformal Field Theory. We predict two types of critical behaviors: either a two-channel Kondo fixed point with a nonuniversal Wilson ratio, or a new theory with an anomalous response identical to that found by Furusaki and Nagaosa (for the Kondo effect in a single Luttinger liquid). Moreover, we discuss the relevance of perturbations like channel anisotropy, and we make links with the Kondo effect in a two-band Hubbard system modeled by a channel-dependent Luttinger Hamiltonian. The suppression of backscattering off the impurity produces a model similar to the four-channel Kondo theory.Comment: 7 pages, RevteX, to be published in Physical Review

Edge reconstruction in the fractional quantum Hall regime

The interplay of electron-electron interaction and confining potential can lead to the reconstruction of fractional quantum Hall edges. We have performed exact diagonalization studies on microscopic models of fractional quantum Hall liquids, in finite size systems with disk geometry, and found numerical evidence of edge reconstruction under rather general conditions. In the present work we have taken into account effects like layer thickness and Landau level mixing, which are found to be of quantitative importance in edge physics. Due to edge reconstruction, additional nonchiral edge modes arise for both incompressible and compressible states. These additional modes couple to electromagnetic fields and thus can be detected in microwave conductivity measurements. They are also expected to affect the exponent of electron Green's function, which has been measured in tunneling experiments. We have studied in this work the electric dipole spectral function that is directly related to the microwave conductivity measurement. Our results are consistent with the enhanced microwave conductivity observed in experiments performed on samples with an array of antidots at low temperatures, and its suppression at higher temperatures. We also discuss the effects of the edge reconstruction on the single electron spectral function at the edge.Comment: 19 pages, 12 figure

Determination of the Argon Spectral Function From (e, e\u27p) Data

The E12-14-012 experiment, performed in Jefferson Lab Hall A, has measured the (e,e′p) cross section in parallel kinematics using a natural argon target. Here, we report the full results of the analysis of the data set corresponding to beam energy 2.222 GeV, and spanning the missing momentum and missing energy range 15 ≲ pm ≲ 300  MeV /c and 12 ≲ Em ≲ 80  MeV. The reduced cross section, determined as a function of pm and Em with ≈ 4% accuracy, has been fitted using the results of Monte Carlo simulations involving a model spectral function and including the effects of final state interactions. The overall agreement between data and simulations turns out to be quite satisfactory (χ2/d. o. f. =1.9). The resulting spectral function will provide valuable new information, needed for the interpretation of neutrino interactions in liquid argon detectors

Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling

Small lattices of $N$ nearest neighbor coupled excitable FitzHugh-Nagumo systems, with time-delayed coupling are studied, and compared with systems of FitzHugh-Nagumo oscillators with the same delayed coupling. Bifurcations of equilibria in N=2 case are studied analytically, and it is then numerically confirmed that the same bifurcations are relevant for the dynamics in the case $N>2$. Bifurcations found include inverse and direct Hopf and fold limit cycle bifurcations. Typical dynamics for different small time-lags and coupling intensities could be excitable with a single globally stable equilibrium, asymptotic oscillatory with symmetric limit cycle, bi-stable with stable equilibrium and a symmetric limit cycle, and again coherent oscillatory but non-symmetric and phase-shifted. For an intermediate range of time-lags inverse sub-critical Hopf and fold limit cycle bifurcations lead to the phenomenon of oscillator death. The phenomenon does not occur in the case of FitzHugh-Nagumo oscillators with the same type of coupling.Comment: accepted by Phys.Rev.

Collective atomic scattering and motional effects in a dense coherent medium

We investigate collective emission from coherently driven ultracold 88Sr atoms. We perform two sets of experiments using a strong and weak transition that are insensitive and sensitive, respectively, to atomic motion at 1 μK. We observe highly directional forward emission with a peak intensity that is enhanced, for the strong transition, by >103 compared with that in the transverse direction. This is accompanied by substantial broadening of spectral lines. For the weak transition, the forward enhancement is substantially reduced due to motion. Meanwhile, a density-dependent frequency shift of the weak transition (∼10% of the natural linewidth) is observed. In contrast, this shift is suppressed to <1% of the natural linewidth for the strong transition. Along the transverse direction, we observe strong polarization dependences of the fluorescence intensity and line broadening for both transitions. The measurements are reproduced with a theoretical model treating the atoms as coherent, interacting radiating dipoles

Reducing alcohol use through alcohol control policies in the general population and population subgroups: a systematic review and meta-analysis.

We estimate the effects of alcohol taxation, minimum unit pricing (MUP), and restricted temporal availability on overall alcohol consumption and review their differential impact across sociodemographic groups. Web of Science, Medline, PsycInfo, Embase, and EconLit were searched on 08/12/2022 and 09/26/2022 for studies on newly introduced or changed alcohol policies published between 2000 and 2022 (Prospero registration: CRD42022339791). We combined data using random-effects meta-analyses. Risk of bias was assessed using the Newcastle-Ottawa Scale. Of 1887 reports, 36 were eligible. Doubling alcohol taxes or introducing MUP (Int$ 0.90/10 g of pure alcohol) reduced consumption by 10% (for taxation: 95% prediction intervals [PI]: -18.5%, -1.2%; for MUP: 95% PI: -28.2%, 5.8%), restricting alcohol sales by one day a week reduced consumption by 3.6% (95% PI: -7.2%, -0.1%). Substantial between-study heterogeneity contributes to high levels of uncertainty and must be considered in interpretation. Pricing policies resulted in greater consumption changes among low-income alcohol users, while results were inconclusive for other socioeconomic indicators, gender, and racial and ethnic groups. Research is needed on the differential impact of alcohol policies, particularly for groups bearing a disproportionate alcohol-attributable health burden. Research reported in this publication was supported by the National Institute on Alcohol Abuse and Alcoholism of the National Institutes of Health under Award Number R01AA028009