Transport in the XX chain at zero temperature: Emergence of flat magnetization profiles

We study the connection between magnetization transport and magnetization profiles in zero-temperature XX chains. The time evolution of the transverse magnetization, m(x,t), is calculated using an inhomogeneous initial state that is the ground state at fixed magnetization but with m reversed from -m_0 for x0. In the long-time limit, the magnetization evolves into a scaling form m(x,t)=P(x/t) and the profile develops a flat part (m=P=0) in the |x/t|1/2 while it expands with the maximum velocity, c_0=1, for m_0->0. The states emerging in the scaling limit are compared to those of a homogeneous system where the same magnetization current is driven by a bulk field, and we find that the expectation values of various quantities (energy, occupation number in the fermionic representation) agree in the two systems.Comment: RevTex, 8 pages, 3 ps figure

Schizophrenia: Redox Regulation and Volume Neurotransmission

Here, we show that volume neurotransmission and the redox property of dopamine, as well as redox-regulated processes at glutamate receptors, can contribute significantly to our understanding of schizophrenia. Namely, volume neurotransmission may play a key role in the development of dysconnectivity between brain regions in schizophrenic patients, which can cause abnormal modulation of NMDA-dependent synaptic plasticity and produce local paroxysms in deafferented neural areas. During synaptic transmission, neuroredox regulations have fundamental functions, which involve the excellent antioxidant properties and nonsynaptic neurotransmission of dopamine. It is possible that the effect of redox-linked volume neurotransmission (diffusion) of dopamine is not as exact as communication by the classical synaptic mechanism, so approaching the study of complex schizophrenic mechanisms from this perspective may be beneficial. However, knowledge of redox signal processes, including the sources and molecular targets of reactive species, is essential for understanding the physiological and pathophysiological signal pathways in cells and the brain, as well as for pharmacological design of various types of new drugs

Detection of transcranial alternating current stimulation aftereffects is improved by considering the individual electric field strength and self-rated sleepiness

Non-invasive electrical stimulation methods, such as transcranial alternating current stimulation (tACS), are increasingly used in human neuroscience research and offer potential new avenues to treat neurological and psychiatric disorders. However, their often variable effects have also raised concerns in the scientific and clinical communities. This study aims to investigate the influence of subject-specific factors on the alpha tACS-induced aftereffect on the alpha amplitude (measured with electroencephalography, EEG) as well as on the connectivity strength between nodes of the default mode network (DMN) [measured with functional magnetic resonance imaging (fMRI)]. As subject-specific factors we considered the individual electrical field (EFIELD) strength at target regions in the brain, the frequency mismatch between applied stimulation and individual alpha frequency (IAF) and as a covariate, subject's changes in mental state, i.e., sleepiness. Eighteen subjects participated in a tACS and a sham session conducted on different days. Each session consisted of three runs (pre/stimulation/). tACS was applied during the second run at each subject's individual alpha frequency (IAF), applying 1 mA peak-to-peak intensity for 7 min, using an occipital bihemispheric montage. In every run, subjects watched a video designed to increase in-scanner compliance. To investigate the aftereffect of tACS on EEG alpha amplitude and on DMN connectivity strength, EEG data were recorded simultaneously with fMRI data. Self-rated sleepiness was documented using a questionnaire. Conventional statistics (ANOVA) did not show a significant aftereffect of tACS on the alpha amplitude compared to sham stimulation. Including individual EFIELD strengths and self-rated sleepiness scores in a multiple linear regression model, significant tACS-induced aftereffects were observed. However, the subject-wise mismatch between tACS frequency and IAF had no contribution to our model. Neither standard nor extended statistical methods confirmed a tACS-induced aftereffect on DMN functional connectivity. Our results show that it is possible and necessary to disentangle alpha amplitude changes due to intrinsic mechanisms and to external manipulation using tACS on the alpha amplitude that might otherwise be overlooked. Our results suggest that EFIELD is really the most significant factor that explains the alpha amplitude modulation during a tACS session. This knowledge helps to understand the variability of the tACS-induced aftereffects

Poisson Structures of Calogero-Moser and Ruijsenaars-Schneider Models

We examine the Hamiltonian structures of some Calogero-Moser and Ruijsenaars-Schneider N-body integrable models. We propose explicit formulations of the bihamiltonian structures for the discrete models, and field-theoretical realizations of these structures. We discuss the relevance of these realizations as collective-field theory for the discrete models.Comment: 15 pages, no figures; v2 references added, typos correcte

Quantum Metamorphosis of Conformal Transformation in D3-Brane Yang-Mills Theory

We show how the linear special conformal transformation in four-dimensional N=4 super Yang-Mills theory is metamorphosed into the nonlinear and field-dependent transformation for the collective coordinates of Dirichlet 3-branes, which agrees with the transformation law for the space-time coordinates in the anti-de Sitter (AdS) space-time. Our result provides a new and strong support for the conjectured relation between AdS supergravity and super conformal Yang-Mills theory (SYM). Furthermore, our work sheds elucidating light on the nature of the AdS/SYM correspondence.Comment: 8 pages, no figure

Exact solution of a two-type branching process: Clone size distribution in cell division kinetics

We study a two-type branching process which provides excellent description of experimental data on cell dynamics in skin tissue (Clayton et al., 2007). The model involves only a single type of progenitor cell, and does not require support from a self-renewed population of stem cells. The progenitor cells divide and may differentiate into post-mitotic cells. We derive an exact solution of this model in terms of generating functions for the total number of cells, and for the number of cells of different types. We also deduce large time asymptotic behaviors drawing on our exact results, and on an independent diffusion approximation.Comment: 16 page

Excited Random Walk in One Dimension

We study the excited random walk, in which a walk that is at a site that contains cookies eats one cookie and then hops to the right with probability p and to the left with probability q=1-p. If the walk hops onto an empty site, there is no bias. For the 1-excited walk on the half-line (one cookie initially at each site), the probability of first returning to the starting point at time t scales as t^{-(2-p)}. Although the average return time to the origin is infinite for all p, the walk eats, on average, only a finite number of cookies until this first return when p<1/2. For the infinite line, the probability distribution for the 1-excited walk has an unusual anomaly at the origin. The positions of the leftmost and rightmost uneaten cookies can be accurately estimated by probabilistic arguments and their corresponding distributions have power-law singularities near the origin. The 2-excited walk on the infinite line exhibits peculiar features in the regime p>3/4, where the walk is transient, including a mean displacement that grows as t^{nu}, with nu>1/2 dependent on p, and a breakdown of scaling for the probability distribution of the walk.Comment: 14 pages, 13 figures, 2-column revtex4 format, for submission to J. Phys.