Quantum integrability of the Alday-Arutyunov-Frolov model

We investigate the quantum integrability of the Alday-Arutyunov-Frolov (AAF) model by calculating the three-particle scattering amplitude at the first non-trivial order and showing that the S-matrix is factorizable at this order. We consider a more general fermionic model and find a necessary constraint to ensure its integrability at quantum level. We then show that the quantum integrability of the AAF model follows from this constraint. In the process, we also correct some missed points in earlier works.Comment: 40 pages; Replaced with published version. Appendix and comments adde

Ictal and interictal MEG in pediatric patients with tuberous sclerosis and drug resistant epilepsy

Purpose: Drug resistant epilepsy (DRE) is common in patients with tuberous sclerosis (TS). Interictal MEG has been shown as a valuable instrument in the presurgical workup. The goal of our study was to evaluate the role of ictal MEG in epileptogenic tuber selection, especially in patients with multiple irritative zones. Methods: The clinical and MEG data of 23 patients with TS and DRE from two medical/research centers were reviewed. Seven pediatric patients, who had seizures during MEG recording and underwent resection or disconnection surgery, were included into the study. Cortical sources of ictal and interictal epileptiform MEG discharges were compared with epileptogenic zone location in six patients with favorable surgery outcome. Results: In patients who improved substantially after surgery all resected and several other tubers demonstrated epileptiform activity on interictal MEG. Ictal MEG provided crucial information about lobar location of the seizure onset zone (SOZ) in two cases, and in the other four it confirmed the SOZ location derived from the interictal data. In one case, ictal MEG findings were unreliable. In one patient, who did not benefit from surgical treatment, the resected tubers did not overlap with interictal and ictal MEG sources. Conclusion: The combination of interictal and ictal MEG is a valuable tool for identification of the epileptogenic tuber/tubers in presurgical work-up in patients with TS.Peer reviewe

Quantum oscillations from Fermi arcs

When a metal is subjected to strong magnetic field B nearly all measurable quantities exhibit oscillations periodic in 1/B. Such quantum oscillations represent a canonical probe of the defining aspect of a metal, its Fermi surface (FS). In this study we establish a new mechanism for quantum oscillations which requires only finite segments of a FS to exist. Oscillations periodic in 1/B occur if the FS segments are terminated by a pairing gap. Our results reconcile the recent breakthrough experiments showing quantum oscillations in a cuprate superconductor YBCO, with a well-established result of many angle resolved photoemission (ARPES) studies which consistently indicate "Fermi arcs" -- truncated segments of a Fermi surface -- in the normal state of the cuprates.Comment: 8 pages, 5 figure

The S-matrix of the Faddeev-Reshetikhin Model, Diagonalizability and PT Symmetry

We study the question of diagonalizability of the Hamiltonian for the Faddeev-Reshetikhin (FR) model in the two particle sector. Although the two particle S-matrix element for the FR model, which may be relevant for the quantization of strings on $AdS_{5}\times S^{5}$, has been calculated recently using field theoretic methods, we find that the Hamiltonian for the system in this sector is not diagonalizable. We trace the difficulty to the fact that the interaction term in the Hamiltonian violating Lorentz invariance leads to discontinuity conditions (matching conditions) that cannot be satisfied. We determine the most general quartic interaction Hamiltonian that can be diagonalized. This includes the bosonic Thirring model as well as the bosonic chiral Gross-Neveu model which we find share the same S-matrix. We explain this by showing, through a Fierz transformation, that these two models are in fact equivalent. In addition, we find a general quartic interaction Hamiltonian, violating Lorentz invariance, that can be diagonalized with the same two particle S-matrix element as calculated by Klose and Zarembo for the FR model. This family of generalized interaction Hamiltonians is not Hermitian, but is $PT$ symmetric. We show that the wave functions for this system are also $PT$ symmetric. Thus, the theory is in a $PT$ unbroken phase which guarantees the reality of the energy spectrum as well as the unitarity of the S-matrix.Comment: 32 pages, 1 figure; references added, version published in JHE

Quasiparticle Hall Transport of d-wave Superconductors in Vortex State

We present a theory of quasiparticle Hall transport in strongly type-II superconductors within their vortex state. We establish the existence of integer quantum spin Hall effect in clean unconventional $d_{x^2-y^2}$ superconductors in the vortex state from a general analysis of the Bogoliubov-de Gennes equation. The spin Hall conductivity $\sigma^s_{xy}$ is shown to be quantized in units of $\frac{\hbar}{8\pi}$. This result does not rest on linearization of the BdG equations around Dirac nodes and therefore includes inter-nodal physics in its entirety. In addition, this result holds for a generic inversion-symmetric lattice of vortices as long as the magnetic field $B$ satisfies $H_{c1} \ll B \ll H_{c2}$. We then derive the Wiedemann-Franz law for the spin and thermal Hall conductivity in the vortex state. In the limit of $T \to 0$, the thermal Hall conductivity satisfies $\kappa_{x y}=\frac{4\pi^2}{3}(\frac{k_B}{\hbar})^2 T \sigma^s_{xy}$. The transitions between different quantized values of $\sigma^s_{xy}$ as well as relation to conventional superconductors are discussed.Comment: 18 pages REVTex, 3 figures, references adde

Сравнительный анализ возбудимости корешковой и внутримышечной аксональной систем у здоровых добровольцев при периферической магнитной стимуляции

Background. Peripheral magnetic stimulation (PMS) is applied over spinal roots, peripheral nerves, terminal motor nerve branches. PMS has been used as a method of diagnosis and treatment for two decades. Despite the considerable amount of PMS studies, there is no consensus on the approach to determine the intensity of the magnetic stimulus in the treatment stimulation, the need for the differentiated activation of the different parts of the peripheral nervous system. This was the prerequisite for carrying out this study.  Objective: to investigate the PMS intensity required to activate spinal roots and terminal nerve branches, the second object was the comparison of the threshold values among volunteers. Materials and methods. Thirty four healthy subjects with no neuromuscular diseases were enrolled in the study (mean age 31.0 ± 8.6 years). PNS was applied by Magstim 200 magnetic stimulator (Great Britain). During the research the subjective threshold, the threshold of muscle contraction, the threshold of the root activation (according to motor evoked potential) were estimated. Stimulation-induced muscle activity was recorded via surface EMG system (Neurosoft, Russia) synchronized with the magnetic stimulator. Results. The analysis of data identified the significant differences (p <0.05) between the root activation and terminal nerve branches threshold values. There were no reports of gender differences between the threshold values of all investigated parameters within the group (p >0.05). There were no significant differences between right and left limbs (p >0.05) in the comparison of all parameters. Conclusion. The results of the present study can indicate the possibility of the individual approach of the determination the intensity of the magnetic stimulus for each patient. The findings of our study provide an opportunity for a better understanding of the action mechanism of PMS and can be used in order to develop the treatment algorithm for the use in the clinical settings.Введение. Периферическая магнитная стимуляция (ПМС) предполагает воздействие импульсного магнитного поля на структуры периферической нервной системы: корешки, спинномозговые и периферические нервы. В последние годы ПМС широко используется в качестве метода диагностики и лечения. Несмотря на большое количество исследований ПМС, не существует единого мнения о подходе к определению интенсивности магнитного стимула при лечебной стимуляции, необходимости дифференцированной стимуляции различных отделов периферической нервной системы, что явилось предпосылкой для проведения данной работы. Цель исследования – определение порогов возбуждения двигательной корешковой системы и терминальных ветвей аксона при ПМС. Было проведено сравнение полученных пороговых значений среди здоровых добровольцев. Материалы и методы. В исследовании приняли участие 34 здоровых добровольца (средний возраст 31,0 ± 8,6 года). ПМС проводили на магнитном стимуляторе фирмы Magstim 200 (Великобритания). В ходе исследования оценивали субъективный порог, порог сокращения мышцы и порог активации корешка (по данным вызванного моторного ответа). Электрофизиологическую регистрацию вызванного моторного ответа осуществляли на компьютерном электромиографе (Нейрософт, Россия), синхронизированном с магнитным стимулятором. Результаты. Были определены статистически достоверные различия (р <0,05) между пороговыми значениями активации ко-решковой системы и терминальных внутримышечных ветвей. Между пороговыми значениями всех исследуемых параметров внутри группы достоверных гендерных различий не зарегистрировано (р >0,05). Также не выявлено достоверных различий при сравнении всех параметров между правой и левой конечностями (p >0,05). Заключение. Полученные результаты позволяют предположить, что при формировании протокола ПМС следует использовать индивидуальный подход к определению интенсивности магнитного стимула для каждого пациента. Данные нашего исследования дают возможность лучшего понимания механизма действия ПМС и могут быть использованы для разработки лечебного алгоритма магнитной стимуляции в клинической практике.