Generalized Uncertainty Principle, Modified Dispersion Relation and Barrier penetration by a Dirac particle

We have studied the energy band structure of a Dirac particle in presence of a generalised uncertainty principle (GUP). We start from defining a modified momentum operator and derive corresponding modified dispersion relation (MDR) and GUP. Apart from the forbidden band within the range $\pm m$, $m$ being the mass of the particle, we find the existence of additional forbidden bands at the both ends of the spectrum. Such band structure forbids a Dirac particle to penetrate a potential step of sufficient height ($\sim E_P$, $E_P$ being Planck energy). This is also true for massless particle. Unlike the relativistic case, a massless particle also can reflect from a barrier of sufficient height. Finally we discuss about the Klein's paradox in presence of the GUP.Comment: 10 pages, 7 figures, LaTe

Accurate energy spectrum for double-well potential: periodic basis

We present a variational study of employing the trigonometric basis functions satisfying periodic boundary condition for the accurate calculation of eigenvalues and eigenfunctions of quartic double-well oscillators. Contrary to usual Dirichlet boundary condition, imposing periodic boundary condition on the basis functions results in the existence of an inflection point with vanishing curvature in the graph of the energy versus the domain of the variable. We show that this boundary condition results in a higher accuracy in comparison to Dirichlet boundary condition. This is due to the fact that the periodic basis functions are not necessarily forced to vanish at the boundaries and can properly fit themselves to the exact solutions.Comment: 15 pages, 5 figures, to appear in Molecular Physic

Saddle point localization of molecular wavefunctions

The quantum mechanical description of isomerization is based on bound eigenstates of the molecular potential energy surface. For the near-minimum regions there is a textbook-based relationship between the potential and eigenenergies. Here we show how the saddle point region that connects the two minima is encoded in the eigenstates of the model quartic potential and in the energy levels of the [H, C, N] potential energy surface. We model the spacing of the eigenenergies with the energy dependent classical oscillation frequency decreasing to zero at the saddle point. The eigenstates with the smallest spacing are localized at the saddle point. The analysis of the HCN???HNC isomerization states shows that the eigenstates with small energy spacing relative to the effective (v1, v3, l) bending potentials are highly localized in the bending coordinate at the transition state. These spectroscopically detectable states represent a chemical marker of the transition state in the eigenenergy spectrum. The method developed here provides a basis for modeling characteristic patterns in the eigenenergy spectrum of bound states

Topological Surface States Protected From Backscattering by Chiral Spin Texture

Topological insulators are a new class of insulators in which a bulk gap for electronic excitations is generated by strong spin orbit coupling. These novel materials are distinguished from ordinary insulators by the presence of gapless metallic boundary states, akin to the chiral edge modes in quantum Hall systems, but with unconventional spin textures. Recently, experiments and theoretical efforts have provided strong evidence for both two- and three-dimensional topological insulators and their novel edge and surface states in semiconductor quantum well structures and several Bi-based compounds. A key characteristic of these spin-textured boundary states is their insensitivity to spin-independent scattering, which protects them from backscattering and localization. These chiral states are potentially useful for spin-based electronics, in which long spin coherence is critical, and also for quantum computing applications, where topological protection can enable fault-tolerant information processing. Here we use a scanning tunneling microscope (STM) to visualize the gapless surface states of the three-dimensional topological insulator BiSb and to examine their scattering behavior from disorder caused by random alloying in this compound. Combining STM and angle-resolved photoemission spectroscopy, we show that despite strong atomic scale disorder, backscattering between states of opposite momentum and opposite spin is absent. Our observation of spin-selective scattering demonstrates that the chiral nature of these states protects the spin of the carriers; they therefore have the potential to be used for coherent spin transport in spintronic devices.Comment: to be appear in Nature on August 9, 200

Fully gapped topological surface states in Bi2_2Se3_3 films induced by a d-wave high-temperature superconductor

Topological insulators are a new class of materials, that exhibit robust gapless surface states protected by time-reversal symmetry. The interplay between such symmetry-protected topological surface states and symmetry-broken states (e.g. superconductivity) provides a platform for exploring novel quantum phenomena and new functionalities, such as 1D chiral or helical gapless Majorana fermions, and Majorana zero modes which may find application in fault-tolerant quantum computation. Inducing superconductivity on topological surface states is a prerequisite for their experimental realization. Here by growing high quality topological insulator Bi$_2$Se$_3$ films on a d-wave superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ using molecular beam epitaxy, we are able to induce high temperature superconductivity on the surface states of Bi$_2$Se$_3$ films with a large pairing gap up to 15 meV. Interestingly, distinct from the d-wave pairing of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, the proximity-induced gap on the surface states is nearly isotropic and consistent with predominant s-wave pairing as revealed by angle-resolved photoemission spectroscopy. Our work could provide a critical step toward the realization of the long sought-after Majorana zero modes.Comment: Nature Physics, DOI:10.1038/nphys274

Is food addiction a predictor of treatment outcome among patients with eating disorder?

ObjectivesThe study aimed to examine whether food addiction (FA) was associated with greater severity in both binge eating disorders (BED) and bulimia nervosa and, therefore, to determine if FA was predictive of treatment outcome.MethodSeventy-one adult patients with bulimia nervosa and BED (42 and 29, respectively) participated in the study. FA was assessed by means of the Yale Food Addiction Scale.ResultsThe results confirmed a high prevalence of FA in patients with binge disorders (around 87%) and also its association with a greater severity of the disorder (i.e., related to an increased eating psychopathology and greater frequency of binge eating episodes). Although FA did not appear as a predictor of treatment outcome in general terms, when the diagnostic subtypes were considered separately, FA was associated with poor prognosis in the BED group. In this vein, FA appeared as a mediator in the relationship between ED severity and treatment outcome.DiscussionsOur findings suggest that FA may act as an indicator of ED severity, and it would be a predictor of treatment outcome in BED but not in BN.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/152018/1/erv2705.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/152018/2/erv2705_am.pd

Stochastic and Regulatory Role of Chromatin Silencing in Genomic Response to Environmental Changes

Phenotypic diversity and fidelity can be balanced by controlling stochastic molecular mechanisms. Epigenetic silencing is one that has a critical role in stress response. Here we show that in yeast, incomplete silencing increases stochastic noise in gene expression, probably owing to unstable chromatin structure. Telomere position effect is suggested as one mechanism. Expression diversity in a population achieved in this way may render a subset of cells to readily respond to various acute stresses. By contrast, strong silencing tends to suppress noisy expression of genes, in particular those involved in life cycle control. In this regime, chromatin may act as a noise filter for precisely regulated responses to environmental signals that induce huge phenotypic changes such as a cell fate transition. These results propose modulation of chromatin stability as an important determinant of environmental adaptation and cellular differentiation

Advances in nanomaterial-based immunosensors for prostate cancer screening

Prostate cancer is one of the most common health hazards for men worldwide, specifically in Western countries. Rapid prostate cancer screening by analyzing the prostate-specific antigen present in male serum has brought about a sharp decline in the mortality index of this disease. Immunoassay technology quantifies the target analyte in the sample using the antigen-antibody reaction. Immunoassays are now pivotal in disease diagnostics, drug monitoring, and pharmacokinetics. Recently, immunosensors have gained momentum in delivering better results with high specificity and lower limit of detection (LOD). Nanomaterials like gold, silver, and copper exhibit numerous exceptional features and their use in developing immunosensors have garnered excellent results in the diagnostic field. This review highlights the recent and different immunoassay techniques used to detect prostate-specific antigens and discusses the advances in nanomaterial-based immunosensors to detect prostate cancer efficiently. The review also explores the importance of specific biomarkers and nanomaterials-based biosensors with good selectivity and sensitivity to prostate cancer