Non-equilibrium Dynamics of O(N) Nonlinear Sigma models: a Large-N approach

We study the time evolution of the mass gap of the O(N) non-linear sigma model in 2+1 dimensions due to a time-dependent coupling in the large-$N$ limit. Using the Schwinger-Keldysh approach, we derive a set of equations at large $N$ which determine the time dependent gap in terms of the coupling. These equations lead to a criterion for the breakdown of adiabaticity for slow variation of the coupling leading to a Kibble-Zurek scaling law. We describe a self-consistent numerical procedure to solve these large-$N$ equations and provide explicit numerical solutions for a coupling which starts deep in the gapped phase at early times and approaches the zero temperature equilibrium critical point $g_c$ in a linear fashion. We demonstrate that for such a protocol there is a value of the coupling $g= g_c^{\rm dyn}> g_c$ where the gap function vanishes, possibly indicating a dynamical instability. We study the dependence of $g_c^{\rm dyn}$ on both the rate of change of the coupling and the initial temperature. We also verify, by studying the evolution of the mass gap subsequent to a sudden change in $g$, that the model does not display thermalization within a finite time interval $t_0$ and discuss the implications of this observation for its conjectured gravitational dual as a higher spin theory in $AdS_4$.Comment: 22 pages, 9 figures. Typos corrected, references rearranged and added.v3 : sections rearranged, abstract modified, comment about Kibble-Zurek scaling correcte

Meson Thermalization in Various Dimensions

In gauge/gravity duality framework the thermalization of mesons in strongly coupled (p+1)-dimensional gauge theories is studied for a general Dp-Dq system, q>=p, using the flavour Dq-brane as a probe. Thermalization corresponds to the horizon formation on the flavour Dq-brane. We calculate the thermalization time-scale due to a time-dependent change in the baryon number chemical potential, baryon injection in the field theory. We observe that for such a general system it has a universal behaviour depending only on the t'Hooft coupling constant and the two parameters which describe how we inject baryons into the system. We show that this universal behaviour is independent of the details of the theory whether it is conformal and/or supersymmetric.Comment: 26 pages, 2 figure

Pathophysiological Correlation between Cigarette Smoking and Amyotrophic Lateral Sclerosis

Cigarette smoke (CS) has been consistently demonstrated to be an environmental risk factor for amyotrophic lateral sclerosis (ALS), although the molecular pathogenic mechanisms involved are yet to be elucidated. Here, we propose different mechanisms by which CS exposure can cause sporadic ALS pathogenesis. Oxidative stress and neuroinflammation are widely implicated in ALS pathogenesis, with blood–spinal cord barrier disruption also recognised to be involved in the disease process. In addition, immunometabolic, epigenetic and microbiome alterations have been implicated in ALS recently. Identification of the underlying pathophysiological mechanisms that underpin CS-associated ALS will drive future research to be conducted into new targets for treatment

Measuring Black Hole Formations by Entanglement Entropy via Coarse-Graining

We argue that the entanglement entropy offers us a useful coarse-grained entropy in time-dependent AdS/CFT. We show that the total von-Neumann entropy remains vanishing even when a black hole is created in a gravity dual, being consistent with the fact that its corresponding CFT is described by a time-dependent pure state. We analytically calculate the time evolution of entanglement entropy for a free Dirac fermion on a circle following a quantum quench. This is interpreted as a toy holographic dual of black hole creations and annihilations. It is manifestly free from the black hole information problem.Comment: 25 pages, Latex, 8 figure

A frequentist framework of inductive reasoning

Reacting against the limitation of statistics to decision procedures, R. A. Fisher proposed for inductive reasoning the use of the fiducial distribution, a parameter-space distribution of epistemological probability transferred directly from limiting relative frequencies rather than computed according to the Bayes update rule. The proposal is developed as follows using the confidence measure of a scalar parameter of interest. (With the restriction to one-dimensional parameter space, a confidence measure is essentially a fiducial probability distribution free of complications involving ancillary statistics.) A betting game establishes a sense in which confidence measures are the only reliable inferential probability distributions. The equality between the probabilities encoded in a confidence measure and the coverage rates of the corresponding confidence intervals ensures that the measure's rule for assigning confidence levels to hypotheses is uniquely minimax in the game. Although a confidence measure can be computed without any prior distribution, previous knowledge can be incorporated into confidence-based reasoning. To adjust a p-value or confidence interval for prior information, the confidence measure from the observed data can be combined with one or more independent confidence measures representing previous agent opinion. (The former confidence measure may correspond to a posterior distribution with frequentist matching of coverage probabilities.) The representation of subjective knowledge in terms of confidence measures rather than prior probability distributions preserves approximate frequentist validity.Comment: major revisio

Silicon-based spin and charge quantum computation

Silicon-based quantum-computer architectures have attracted attention because of their promise for scalability and their potential for synergetically utilizing the available resources associated with the existing Si technology infrastructure. Electronic and nuclear spins of shallow donors (e.g. phosphorus) in Si are ideal candidates for qubits in such proposals due to the relatively long spin coherence times. For these spin qubits, donor electron charge manipulation by external gates is a key ingredient for control and read-out of single-qubit operations, while shallow donor exchange gates are frequently invoked to perform two-qubit operations. More recently, charge qubits based on tunnel coupling in P$_2^+$ substitutional molecular ions in Si have also been proposed. We discuss the feasibility of the building blocks involved in shallow donor quantum computation in silicon, taking into account the peculiarities of silicon electronic structure, in particular the six degenerate states at the conduction band edge. We show that quantum interference among these states does not significantly affect operations involving a single donor, but leads to fast oscillations in electron exchange coupling and on tunnel-coupling strength when the donor pair relative position is changed on a lattice-parameter scale. These studies illustrate the considerable potential as well as the tremendous challenges posed by donor spin and charge as candidates for qubits in silicon.Comment: Review paper (invited) - to appear in Annals of the Brazilian Academy of Science

Quasi-normal frequencies: Key analytic results

The study of exact quasi-normal modes [QNMs], and their associated quasi-normal frequencies [QNFs], has had a long and convoluted history - replete with many rediscoveries of previously known results. In this article we shall collect and survey a number of known analytic results, and develop several new analytic results - specifically we shall provide several new QNF results and estimates, in a form amenable for comparison with the extant literature. Apart from their intrinsic interest, these exact and approximate results serve as a backdrop and a consistency check on ongoing efforts to find general model-independent estimates for QNFs, and general model-independent bounds on transmission probabilities. Our calculations also provide yet another physics application of the Lambert W function. These ideas have relevance to fields as diverse as black hole physics, (where they are related to the damped oscillations of astrophysical black holes, to greybody factors for the Hawking radiation, and to more speculative state-counting models for the Bekenstein entropy), to quantum field theory (where they are related to Casimir energies in unbounded systems), through to condensed matter physics, (where one may literally be interested in an electron tunelling through a physical barrier).Comment: V1: 29 pages; V2: Reformatted, 31 pages. Title changed to reflect major additions and revisions. Now describes exact QNFs for the double-delta potential in terms of the Lambert W function. V3: Minor edits for clarity. Four references added. No physics changes. Still 31 page

Blood-Spinal Cord Barrier: Its Role in Spinal Disorders and Emerging Therapeutic Strategies

The blood-spinal cord barrier (BSCB) has been long thought of as a functional equivalent to the blood-brain barrier (BBB), restricting blood flow into the spinal cord. The spinal cord is supported by various disc tissues that provide agility and has different local immune responses compared to the brain. Though physiologically, structural components of the BSCB and BBB share many similarities, the clinical landscape significantly differs. Thus, it is crucial to understand the composition of BSCB and also to establish the cause–effect relationship with aberrations and spinal cord dysfunctions. Here, we provide a descriptive analysis of the anatomy, current techniques to assess the impairment of BSCB, associated risk factors and impact of spinal disorders such as spinal cord injury (SCI), amyotrophic lateral sclerosis (ALS), peripheral nerve injury (PNI), ischemia reperfusion injury (IRI), degenerative cervical myelopathy (DCM), multiple sclerosis (MS), spinal cavernous malformations (SCM) and cancer on BSCB dysfunction. Along with diagnostic and mechanistic analyses, we also provide an up-to-date account of available therapeutic options for BSCB repair. We emphasize the need to address BSCB as an individual entity and direct future research towards it.</jats:p

Holographic Evolution of Entanglement Entropy

We study the evolution of entanglement entropy in a 2-dimensional equilibration process that has a holographic description in terms of a Vaidya geometry. It models a unitary evolution in which the field theory starts in a pure state, its vacuum, and undergoes a perturbation that brings it far from equilibrium. The entanglement entropy in this set up provides a measurement of the quantum entanglement in the system. Using holographic techniques we recover the same result obtained before from the study of processes triggered by a sudden change in a parameter of the hamiltonian, known as quantum quenches. Namely, entanglement in 2-dimensional conformal field theories propagates with velocity v^2=1. Both in quantum quenches and in the Vaidya model equilibration is only achieved at the local level. Remarkably, the holographic derivation of this last fact requires information from behind the apparent horizon generated in the process of gravitational collapse described by the Vaidya geometry. In the early stages of the evolution the apparent horizon seems however to play no relevant role with regard to the entanglement entropy. We speculate on the possibility of deriving a thermalization time for occupation numbers from our analysis.Comment: 26 pages, 10 figure

Thermal quenches in N=2* plasmas

We exploit gauge/gravity duality to study `thermal quenches' in a plasma of the strongly coupled N=2* gauge theory. Specifically, we consider the response of an initial thermal equilibrium state of the theory under variations of the bosonic or fermionic mass, to leading order in m/T<<1. When the masses are made to vary in time, novel new counterterms must be introduced to renormalize the boundary theory. We consider transitions the conformal super-Yang-Mills theory to the mass deformed gauge theory and also the reverse transitions. By construction, these transitions are controlled by a characteristic time scale \calt and we show how the response of the system depends on the ratio of this time scale to the thermal time scale 1/T. The response shows interesting scaling behaviour both in the limit of fast quenches with T\calt<<1 and slow quenches with T\calt>>1. In the limit that T\calt\to\infty, we observe the expected adiabatic response. For fast quenches, the relaxation to the final equilibrium is controlled by the lowest quasinormal mode of the bulk scalar dual to the quenched operator. For slow quenches, the system relaxes with a (nearly) adiabatic response that is governed entirely by the late time profile of the mass. We describe new renormalization scheme ambiguities in defining gauge invariant observables for the theory with time dependant couplings.Comment: 78 pages, 17 figure