The quantized Hall conductance of a single atomic wire: A proposal based on synthetic dimensions

We propose a method by which the quantization of the Hall conductance can be directly measured in the transport of a one-dimensional atomic gas. Our approach builds on two main ingredients: (1) a constriction optical potential, which generates a mesoscopic channel connected to two reservoirs, and (2) a time-periodic modulation of the channel, specifically designed to generate motion along an additional synthetic dimension. This fictitious dimension is spanned by the harmonic-oscillator modes associated with the tightly-confined channel, and hence, the corresponding "lattice sites" are intimately related to the energy of the system. We analyze the quantum transport properties of this hybrid two-dimensional system, highlighting the appealing features offered by the synthetic dimension. In particular, we demonstrate how the energetic nature of the synthetic dimension, combined with the quasi-energy spectrum of the periodically-driven channel, allows for the direct and unambiguous observation of the quantized Hall effect in a two-reservoir geometry. Our work illustrates how topological properties of matter can be accessed in a minimal one-dimensional setup, with direct and practical experimental consequences.

Bosonization of strongly interacting electrons

Strong repulsive interactions in a one-dimensional electron system suppress the exchange coupling J of electron spins to a value much smaller than the Fermi energy E_F. The conventional theoretical description of such systems based on the bosonization approach and the concept of Tomonaga-Luttinger liquid is applicable only at energies below J. In this paper we develop a theoretical approach valid at all energies below the Fermi energy, including a broad range of energies between J and E_F. The method involves bosonization of the charge degrees of freedom, while the spin excitations are treated exactly. We use this technique to calculate the spectral functions of strongly interacting electron systems at energies in the range J<<epsilon<< E_F$. We show that in addition to the expected features at the wavevector k near the Fermi point k_F, the spectral function has a strong peak centered at k=0. Our theory also provides analytical description of the spectral function singularities near 3k_F (the "shadow band" features).Comment: 21 pages, 4 figure

Wigner Molecules in Nanostructures

The one-- and two-- particle densities of up to four interacting electrons with spin, confined within a quasi one--dimensional ``quantum dot'' are calculated by numerical diagonalization. The transition from a dense homogeneous charge distribution to a dilute localized Wigner--type electron arrangement is investigated. The influence of the long range part of the Coulomb interaction is studied. When the interaction is exponentially cut off the ``crystallized'' Wigner molecule is destroyed in favor of an inhomogeneous charge distribution similar to a charge density wave .Comment: 10 pages (excl. Figures), Figures available on request LaTe

Бухгалтерский учет основных средств

Inflammatory pseudotumors (IPs), mostly benign lesions characterized by fibrotic ground tissue and polyclonal mononuclear infiltrate, may affect all organ systems. IPs originating in the central nervous system (IP-CNS) are very rare, and their distinct histopathologic features are poorly characterized. Three otherwise healthy patients (age 8, 15, and 17 years) presented with focal neurologic symptoms (seizures, n = 2; headaches, n = 1), corresponding to a left temporal, left occipital, and left frontal IP, respectively, extending from meningeal structures into brain tissue. After resection, no recurrence was observed in patient 1 during 5 years of follow-up, whereas patient 2 developed a rapidly progressive local recurrence and a second intracerebral lesion despite antiviral, immunosuppressive, antibiotic, and radiation therapy. In patient 3, who also showed local recurrences, sequential histopathologic investigations revealed transformation to a semimalignant fibrohistiocytic tumor. In this patient, anaplastic lymphoma kinase (ALK) expression was also positive, whereas it was negative in patient 1. A detailed literature analysis confirmed that most IP-CNS arise from dural/meningeal structures (n = 34). Intraparenchymatous (n = 7), mixed intraparenchymatous/meningeal (n = 4), and intraventricular lesions (n = 7) or IP extending per continuitatem from intracerebral to extracerebral sites (n = 5) were rare. The recurrence rate was 40% within 2 years in general. It was increased after incomplete resection and in female patients (multivariate Cox regression model, P < 0.02). Although rare, IP-CNS are important differential diagnoses among tumor-like intracranial lesions. Their potential risk of malignant transformation and high risk of recurrence necessitate close follow-up, especially when resection is incomplete. Prospective multicenter trials are needed to optimize classification and treatment of this rare inflammatory lesion. Copyright 2003, Elsevier Inc. All rights reserved

Effective charge-spin models for quantum dots

It is shown that at low densities, quantum dots with few electrons may be mapped onto effective charge-spin models for the low-energy eigenstates. This is justified by defining a lattice model based on a many-electron pocket-state basis in which electrons are localised near their classical ground-state positions. The equivalence to a single-band Hubbard model is then established leading to a charge-spin ($t-J-V$) model which for most geometries reduces to a spin (Heisenberg) model. The method is refined to include processes which involve cyclic rotations of a ``ring'' of neighboring electrons. This is achieved by introducing intermediate lattice points and the importance of ring processes relative to pair-exchange processes is investigated using high-order degenerate perturbation theory and the WKB approximation. The energy spectra are computed from the effective models for specific cases and compared with exact results and other approximation methods.Comment: RevTex, 24 pages, 7 figures submitted as compressed and PostScript file

Gender-based Restrictions in Tourism: An Example of the Phenomenon of Avaton in the Modern Socio-cultural Expanse

The article deals with the problems of the impact of tourism, including pilgrimage, on the socio-cultural environment of modern society, changes and reformatting of the gender restrictions of religious content. Investigated the access restrictions based on gender to objects of tourist interest as an example of socio-religious phenomenon “avaton” monastic republic of Athos in Northern Greece. Avaton regarded as a characteristic example of the alignment and sustained physical boundaries of the gender division, which for centuries allows preserving the unique closed social system. The paper focuses on the very concept of gender segregation, signs of it in the archaic and modern religions and on the relationship between the sexual divisions of the principles of Orthodox monasticism. The authors considered conflict of values of modern Western society and conservative traditions of Eastern Christianity. Gender discrimination is contrasted with the need to preserve the unique social phenomenon as part of the socio-cultural heritage of humanity

Coulombically Interacting Electrons in a One-dimensional Quantum Dot

The spectral properties of up to four interacting electrons confined within a quasi one--dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground state energy is investigated as a function of the electron number and of the system length. The limitations of a description in terms of a capacitance are demonstrated. The energetically lowest lying excitations are physically explained as vibrational and tunneling modes. The limits of a dilute, Wigner-type arrangement of the electrons, and a dense, more homogeneous charge distribution are discussed.Comment: 10 pages (excl. Figures), Figures added in POSTSCRIPT, LaTe

Tomonaga-Luttinger parameters for quantum wires

The low-energy properties of a homogeneous one-dimensional electron system are completely specified by two Tomonaga-Luttinger parameters $K_{\rho}$ and $v_{\sigma}$. In this paper we discuss microscopic estimates of the values of these parameters in semiconductor quantum wires that exploit their relationship to thermodynamic properties. Motivated by the recognized similarity between correlations in the ground state of a one-dimensional electron liquid and correlations in a Wigner crystal, we evaluate these thermodynamic quantities in a self-consistent Hartree-Fock approximation. According to our calculations, the Hartree-Fock approximation ground state is a Wigner crystal at all electron densities and has antiferromagnetic order that gradually evolves from spin-density-wave to localized in character as the density is lowered. Our results for $K_{\rho}$ are in good agreement with weak-coupling perturbative estimates $K_{\rho}^{pert}$ at high densities, but deviate strongly at low densities, especially when the electron-electron interaction is screened at long distances. $K_{\rho}^{pert}\sim n^{1/2}$ vanishes at small carrier density $n$ whereas we conjecture that $K_{\rho}\to 1/2$ when $n\to 0$, implying that $K_{\rho}$ should pass through a minimum at an intermediate density. Observation of such a non-monotonic dependence on particle density would allow to measure the range of the microscopic interaction. In the spin sector we find that the spin velocity decreases with increasing interaction strength or decreasing $n$. Strong correlation effects make it difficult to obtain fully consistent estimates of $v_{\sigma}$ from Hartree-Fock calculations. We conjecture that v_{\sigma}/\vf\propto n/V_0 in the limit $n\to 0$ where $V_0$ is the interaction strength.Comment: RevTeX, 23 pages, 8 figures include

Crossover from Fermi liquid to Wigner molecule behavior in quantum dots

The crossover from weak to strong correlations in parabolic quantum dots at zero magnetic field is studied by numerically exact path-integral Monte Carlo simulations for up to eight electrons. By the use of a multilevel blocking algorithm, the simulations are carried out free of the fermion sign problem. We obtain a universal crossover only governed by the density parameter $r_s$. For $r_s>r_c$, the data are consistent with a Wigner molecule description, while for $r_s<r_c$, Fermi liquid behavior is recovered. The crossover value $r_c \approx 4$ is surprisingly small.Comment: 4 pages RevTeX, 3 figures, corrected Tabl

Сверточная нейронная сеть для классификации без использования дополнительных библиотек

В работе представляется сверточная нейронная сеть для классификации цифр на изображениях реализованная без использования дополнительных библиотек машинного обучения. Для оценки качества сегментации применяются различные метрики, такие как: ошибка по модулю и процентная точность. Проведено сравнение различных топологий нейронной сети, на выборке данных, находящейся в библиотеке машинного обучения "Scikit-learn" [1]. По полученным результатам тестирования сделан вывод о наилучшей из рассматриваемых топологий нейронной сети