Exact Spectrum Research Articles

Long- and short-range interaction footprints in entanglement entropies of two-particle Wigner molecules in 2D quantum traps

The occupancies and entropic entanglement measures for the ground state of two particles in a two-dimensional harmonic anisotropic trap are studied. We implement a method to study the large interaction strength limit for different short- and long-range interaction potentials that allows to obtain the exact entanglement spectrum and several entropies. We show that for long-range interactions, the von Neumann, min-entropy and the family of Rényi entropies remain finite for the anisotropic traps and diverge logarithmically for the isotropic traps. In the short-range interaction case the entanglement measures diverge for any anisotropic parameter due to the divergence of uncertainty in the momentum since for short-range interactions the relative position width vanishes. We also show that when the reduced density matrix has finite support the Rényi entropies present a non-analytical behavior.

Analytic solutions in the acoustic black hole analogue of the conical Kerr metric**Supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (140612/2014-9)

We study the sound perturbation of a rotating acoustic black hole in the presence of a disclination. The radial part of the massless Klein-Gordon equation is written into a Heun form, and its analytical solution is obtained. These solutions have an explicit dependence on the parameter of the disclination. We obtain the exact Hawking-Unruh radiation spectrum.

Median floor acceleration spectra of linear structures with uncertain properties

SummaryResponse parameters used to estimate nonstructural damage differ depending on whether deformation‐sensitive or acceleration‐sensitive components are considered. In the latter case, seismic demand is usually represented through floor spectra, that is response spectra in terms of pseudo‐acceleration, which are calculated at the floor levels of the structure where the nonstructural components are attached to. Objective of this paper is to present a new spectrum‐to‐spectrum method for calculating floor acceleration spectra, which is able to explicitly account for epistemic uncertainties in the modal properties of the supporting structure. By using this method, effects on the spectra of possible variations from nominal values of the periods of vibration of the structure can be estimated. The method derives from the extension of closed‐form equations recently proposed by the authors to predict uniform hazard floor acceleration spectra. These equations are built to rigorously account for the input ground motion uncertainty, that is the record‐to‐record variability of the nonstructural response. In order to evaluate the proposed method, comparisons with exact spectra obtained from a standard probabilistic seismic demand analysis, as well as spectra calculated using the Eurocode 8 equation, are finally shown. Copyright © 2017 John Wiley & Sons, Ltd.

Worldline as a spin chain

The general theoretical ground for models based on compact angle coordinates is presented. It is observed that the proper dependence on compact coordinates has to be through the group elements and is achieved most naturally in a discrete-time formulation of the theory. By the construction, the discrete worldline inlaid by compact coordinates resembles the spin chains of magnetic systems. As examples, the models based on the groups U(1), {mathbb {Z}}_N and SU(2) are explicitly constructed and their exact energy spectra are obtained. As the consequence of the minima in the spectra, the models exhibit a phase transition of first order. We attempt to fit the dynamics by the U(1) group to the proposed role for monopoles in the dual Meissner effect of the confinement mechanism.

Exact solution of the relativistic quantum Toda chain

The relativistic quantum Toda chain model is studied with the generalized algebraic Bethe Ansatz method. By employing a set of local gauge transformations, proper local vacuum states can be obtained for this model. The exact spectrum and eigenstates of the model are thus constructed simultaneously.

Spectrum of Congenital Heart Diseases in Eastern Nepal: A tertiary care hospital experience

Background & Objectives: Congenital heart diseases are neglected especially in world’s poorest nations and appear to be ignored and unexplored dimension of health. The exact prevalence and spectrum of congenital heart diseases in Nepal is largely unknown. The aim of this study was to describe the local experience on the magnitude and the pattern of congenital heart disease in order to increase the awareness of the public and health policy makers on its burden in Nepal.Materials & Methods: This is an observational hospital based study carried out in a tertiary care hospital in Eastern Nepal. The duration of this study was from April 2015 to July 2016. The echocardiography reports of all patients clinically suspected of having congenital heart disease were retrieved, and their diagnostic details were extracted. Only patients of day one of life to 14 years of age were included. Congenital heart diseases like bicuspid aortic valve, mitral valve prolapse and various inherited cardiomyopathies were excluded.Results: A total of 330 echocardiograms were performed for clinically suspected congenital heart disease. The mean age of study population was 22.31±34.08 months with male to female ratio of 1.2:1. 23% of clinically suspected congenital heart disease cases turned out to have normal echocardiography. Acyanotic congenital heart disease was most common (81.5%) followed by cyanotic congenital heart disease (14.2%) and obstructive congenital heart disease (4.3%). Atrial septal defect was found to be the most common form of acyanotic congenital heart disease (52%) which was followed by ventricular septal defect (28.8%) and patent ductus arteriosus (14.8%). Tetralogy of Fallot and double outlet right ventricle were the most common form of cyanotic CHD representing 44.4% of all cyanotic patients. Pulmonary stenosis was the most common obstructive congenital heart disease observed in this study population (63.6%). Rarer entities, like d-transposition of great arteries, congenitally corrected transposition of great arteries, various types of total anomalous pulmonary venous drainage, double inlet left ventricle, interrupted aortic arch, Shone complex, etc. were also observed, however represented only the minority of the study population.Conclusion: The spectrum of congenital heart disease seen in this study very likely and only represents the tip of the iceberg. Public awareness programmes and training of health care personnel needs to be emphasized in order to facilitate its early diagnosis and improve its outcome.

Relativistic quantum dynamics on a double cone

In this paper, we study the relativistic quantum problem of a particle constrained to a double cone surface. For this purpose, we build the Dirac equation in a curved space using the tetrads formalism. Two cases are analysed. First, we consider a free particle on the conical surface, and then we add an uniform magnetic field. In the first case, the exact energy spectrum is obtained and its non-relativistic limit compared to previously published results. In the second case, the spectrum is also exactly obtained and a detailed analysis considering all possible combinations of signs of the quantum numbers reveals the occurrence of highly degenerate zero energy modes. The results obtained here can be applied, for instance, in the investigation of the electronic and transport properties of condensed matter systems that can be described by an effective Dirac equation, such as graphene and topological insulators.

Spectrum-to-spectrum methods for the generation of elastic floor acceleration spectra

In seismic codes, the acceleration demand of nonstructural components is commonly expressed in terms of floor response spectra and estimated by means of simple predictive equations. By using the latter, response-history analysis of the structure is not required, being floor spectra calculated directly from the peak ground acceleration expected at the site. The price for this simplicity in the method used for the estimation of floor spectra is the generally poor approximation of the obtained predictions. Codes’ equations, in fact, do not explicitly account for important factors influencing floor spectra, such as the contribution of the higher modes of vibration of the structure and the actual value of the nonstructural components’ damping ratio. Alternative spectrum-to-spectrum methods for direct generation of floor spectra have been proposed, which include these factors and improve the accuracy of the predictions. Different approaches have been used and several methods developed. Despite large research effort, however, a comparative evaluation of the currently available proposals is still lacking. The objective of this paper is to fill this gap, by reviewing selected proposals representative of practice-oriented spectrum-to-spectrum methods. A case study consisting in a six-story frame is analyzed and predictions obtained with the investigated methods are compared with exact floor spectra derived from time-history analyses of the structure, as well as spectra calculated using the Eurocode 8 equation.

Strain-Induced Landau Levels in Arbitrary Dimensions with an Exact Spectrum.

Certain nonuniform strain applied to graphene flakes has been shown to induce pseudo-Landau levels in the single-particle spectrum, which can be rationalized in terms of a pseudomagnetic field for electrons near the Dirac points. However, this Landau level structure is, in general, approximate and restricted to low energies. Here, we introduce a family of strained bipartite tight-binding models in arbitrary spatial dimension d and analytically prove that their entire spectrum consists of perfectly degenerate pseudo-Landau levels. This construction generalizes the case of triaxial strain on graphene's honeycomb lattice to arbitrary d; in d=3, our model corresponds to tetraxial strain on the diamond lattice. We discuss general aspects of pseudo-Landau levels in arbitrary d.

Determination of phenolic compounds and diterpenes in roots of Salvia miltiorrhiza and Salvia przewalskii by two LC–MS tools: Multi-stage and high resolution tandem mass spectrometry with assessment of antioxidant capacity

Comparative phytochemical analyses of hydroalcoholic (50% EtOH) extracts from roots of S. miltiorrhiza (SM) and S. przewalskii (SP) were performed using two complementary LC–MS systems: the first system HPLC-DAD-MSn an ion trap mass spectrometer and the second system consisted high resolution MS/MS Orbitrap mass spectrometer. The individual compounds were identified using a previously published approach via comparison of the exact molecular masses, mass spectra and retention times to those of standard compounds, online available databases and literature data. Moreover, the determination of antioxidative activities of extracts by DPPH and FRAP methods was carried out. Analysis allowed to identify 39 chemical compounds in extracts from both species. Extract from root of SP differs from SM in the presence of several metabolites such as: przewalskinic acid and their derivatives, przewaquinone C, przewaquinonate A, glycosides of rosmarinic acid, methyltanshinonate, whereas tanshinones, salvianolic acids and lithospermic acids occurred in both species. Moreover, it was shown that hydroalcoholic extract from roots of SM exerted stronger antioxidant properties in a FRAP test (max. 323.92μMFe2+/L) and in DPPH test (max. 78.64nM TE) in comparison with SP extract.

T-system on T-hook: Grassmannian solution and twisted Quantum Spectral Curve

We propose an efficient grassmannian formalism for solution of bi-linear finite-difference Hirota equation (T-system) on T-shaped lattices related to the space of highest weight representations of $gl(K_1,K_2|M)$ superalgebra. The formalism is inspired by the quantum fusion procedure known from the integrable spin chains and is based on exterior forms of Baxter-like Q-functions. We find a few new interesting relations among the exterior forms of Q-functions and reproduce, using our new formalism, the Wronskian determinant solutions of Hirota equations known in the literature. Then we generalize this construction to the twisted Q-functions and demonstrate the subtleties of untwisting procedure on the examples of rational quantum spin chains with twisted boundary conditions. Using these observations, we generalize the recently discovered, in our paper with N. Gromov, AdS/CFT Quantum Spectral Curve for exact planar spectrum of AdS/CFT duality to the case of arbitrary Cartan twisting of AdS$_5\times$S$^5$ string sigma model. Finally, we successfully probe this formalism by reproducing the energy of gamma-twisted BMN vacuum at single-wrapping orders of weak coupling expansion.

Exact Electronic Bands for a Periodic Pöschl—Teller Potential

We show that supersymmetry is a simple but powerful tool to exactly solve quantum mechanics problems. Here, the supersymmetric approach is used to analyse a quantum system with periodic Pöschl—Teller potential, and to find out the exact energy spectra and the corresponding band structure.

Primitive groups, graph endomorphisms and synchronization

Let $\Omega$ be a set of cardinality $n$, $G$ a permutation group on $\Omega$, and $f:\Omega\to\Omega$ a map which is not a permutation. We say that $G$ \emph{synchronizes} $f$ if the transformation semigroup $\langle G,f\rangle$ contains a constant map, and that $G$ is a \emph{synchronizing group} if $G$ synchronizes \emph{every} non-permutation. A synchronizing group is necessarily primitive, but there are primitive groups that are not synchronizing. Every non-synchronizing primitive group fails to synchronize at least one uniform transformation (that is, transformation whose kernel has parts of equal size), and it has previously been conjectured that a primitive group synchronizes every non-uniform transformation. The first goal of this paper is to prove that this conjecture is false, by exhibiting primitive groups that fail to synchronize specific non-uniform transformations of ranks $5$ and $6$. In addition we produce graphs whose automorphism groups have approximately $\sqrt{n}$ \emph{non-synchronizing ranks}, thus refuting another conjecture on the number of non-synchronizing ranks of a primitive group. The second goal of this paper is to extend the spectrum of ranks for which it is known that primitive groups synchronize every non-uniform transformation of that rank. It has previously been shown that a primitive group of degree $n$ synchronizes every non-uniform transformation of rank $n-1$ and $n-2$, and here this is extended to $n-3$ and $n-4$. Determining the exact spectrum of ranks for which there exist non-uniform transformations not synchronized by some primitive group is just one of several natural, but possibly difficult, problems on automata, primitive groups, graphs and computational algebra arising from this work; these are outlined in the final section.

A class of solutions under GUP for a harmonic oscillator and a particle in a box

The existence of a minimal observable length is the common prediction of different theories of quantum gravity such as string theory, loop quantum gravity and black hole physics. The ordinary Heisenberg uncertainty principle (HUP) is not compatible with this prediction, so the HUP was generalized to the Generalized Uncertainty Principle (GUP) in literature. The consequences of this generalization are the generalized commutation relations between operators and so the generalized Hamiltonian for systems. In this paper, we represent the solutions of a harmonic oscillator and a particle in a box in the sense of a generalized commutation relation. We show that using of the Hellmann-Feynman (HF) theorem leads to the approximate energy spectrum of a harmonic oscillator and the exact energy spectrum of a particle in a box. In these cases, we do not solve the corresponding generalized Schro¨ dinger equation directly, but the HF theorem exhibit the effect of GUP on the energy spectrum. Also we obtain the uncertainties in both position and momentum for a harmonic oscillator and derive the GUP.

Truncatable bootstrap equations in algebraic form and critical surface exponents

We describe examples of drastic truncations of conformal bootstrap equations encoding much more information than that obtained by a direct numerical approach. A three-term truncation of the four point function of a free scalar in any space dimensions provides algebraic identities among conformal block derivatives which generate the exact spectrum of the infinitely many primary operators contributing to it. In boundary conformal field theories, we point out that the appearance of free parameters in the solutions of bootstrap equations is not an artifact of truncations, rather it reflects a physical property of permeable conformal interfaces which are described by the same equations. Surface transitions correspond to isolated points in the parameter space. We are able to locate them in the case of 3d Ising model, thanks to a useful algebraic form of 3d boundary bootstrap equations. It turns out that the low-lying spectra of the surface operators in the ordinary and the special transitions of 3d Ising model form two different solutions of the same polynomial equation. Their interplay yields an estimate of the surface renormalization group exponents, y h = 0.72558(18) for the ordinary universality class and y h = 1.646(2) for the special universality class, which compare well with the most recent Monte Carlo calculations. Estimates of other surface exponents as well as OPE coefficients are also obtained.

Exact Bethe Ansatz Spectrum of a Tight-Binding Chain with Dephasing Noise.

We construct an exact map between a tight-binding model on any bipartite lattice in the presence of dephasing noise and a Hubbard model with imaginary interaction strength. In one dimension, the exact many-body Liouvillian spectrum can be obtained by application of the Bethe ansatz method. We find that both the nonequilibrium steady state and the leading decay modes describing the relaxation at late times are related to the η-pairing symmetry of the Hubbard model. We show that there is a remarkable relation between the time evolution of an arbitrary k-point correlation function in the dissipative system and k-particle states of the corresponding Hubbard model.

Nonperturbative emergence of non-Fermi-liquid behavior ind=2quantum critical metals

We consider the planar local patch approximation of $d=2$ fermions at finite density coupled to a critical boson. In the quenched or Bloch-Nordsieck approximation, where one takes the limit of fermion flavors $N_f\rightarrow 0$, the fermion spectral function can be determined {exactly}. We show that one can obtain this non-perturbative answer thanks to a specific identity of fermionic two-point functions in the planar local patch approximation. The resulting spectrum is that of a non-Fermi liquid: quasiparticles are not part of the exact fermionic excitation spectrum of the theory. Instead one finds continuous spectral weight with power law scaling excitations as in a $d=1$ dimensional critical state. Moreover, at low energies there are three such excitations at three different Fermi surfaces, two with a low energy Green's function $G \sim (\omega-v_*k)^{-1/2}$ and one with $G \sim |\omega+k|^{-1/3}$.

A photon counting and a squeezing measurement method by the exact absorption and dispersion spectrum of Λ-type Atoms.

Recently, the master equations for the interaction of two-mode photons with a three-level Λ-type atom are exactly solved for the coherence terms. In this paper the exact absorption spectrum is applied for the presentation of a non-demolition photon counting method, for a few number of coupling photons, and its benefits are discussed. The exact scheme is also applied where the coupling photons are squeezed and the photon counting method is also developed for the measurement of the squeezing parameter of the coupling photons.

Exact spectra of strong coulomb correlations of 3-D 2-e harmonic dots in magnetic field

Applications of 3-D 2-e systems have proliferated very fast due to technological advancements in wide range of phenomena from atomic landscape to mesoscopic scale. The unusual properties of atomic/mesoscopic systems are the results of interplaying charge interactions among different bound states. The non-trivial e–e correlations in electrically and/or magnetically confined systems improvise wealth of intriguing challenges at fundamental level due to lack of exact solution of Schrödinger equations. For the first time, a novel methodology of exactly finite summed coulomb correlations invented by us is so handy that even usual programmable calculator can be used to examine the electronic structures of 3-D 2-e harmonic dots in perpendicular magnetic field (symmetric gauge). Statistics of electronic levels, heat capacity measurements and magnetization (T∼1K) are also investigated in brief to probe the degree of disorderedness.

The Expression of Human Cytomegalovirus MicroRNA MiR-UL148D during Latent Infection in Primary Myeloid Cells Inhibits Activin A-triggered Secretion of IL-6.

The successful establishment and maintenance of human cytomegalovirus (HCMV) latency is dependent on the expression of a subset of viral genes. Whilst the exact spectrum and functions of these genes are far from clear, inroads have been made for protein-coding genes. In contrast, little is known about the expression of non-coding RNAs. Here we show that HCMV encoded miRNAs are expressed de novo during latent infection of primary myeloid cells. Furthermore, we demonstrate that miR-UL148D, one of the most highly expressed viral miRNAs during latent infection, directly targets the cellular receptor ACVR1B of the activin signalling axis. Consistent with this, we observed upregulation of ACVR1B expression during latent infection with a miR-UL148D deletion virus (ΔmiR-UL148D). Importantly, we observed that monocytes latently infected with ΔmiR-UL148D are more responsive to activin A stimulation, as demonstrated by their increased secretion of IL-6. Collectively, our data indicates miR-UL148D inhibits ACVR1B expression in latently infected cells to limit proinflammatory cytokine secretion, perhaps as an immune evasion strategy or to postpone cytokine-induced reactivation until conditions are more favourable. This is the first demonstration of an HCMV miRNA function during latency in primary myeloid cells, implicating that small RNA species may contribute significantly to latent infection.