Specificity in the regulation of eukaryotic gene transcription

The regulation of eukaryotic gene transcription poses major challenges in terms of the innumerable protein factors required to ensure tissue or cell-type specificity. While this specificity is sought to be explained by the interaction of cis-acting DNA elements and thetrans-acting protein factor(s), considerable amount of degeneracy has been observed in this interaction. Immunoglobulin heavy chain gene expression in B cells and liver-specific gene expression are discussed as examples of this complexity in this article. Heterodimerization and post-translational modification of transcription factors and the organization of composite promoter elements are strategies by which diverse sets of genes can be regulated in a specific manner using a finite number of protein factors

New La2CuO4 derivatives La(2-2x)Sr(2x)Cu(1-x)M(x)O(4) (M=Ti, Mn, Fe, or Ru): A study of linear Cu-O-M electronic interaction in two dimensions

Oxides of the general formula La2-2xSr2xCu1-xII,M(x)(IV)O(4) (M = Ti, Mn, Fe, or Ru), crystallizing in the tetragonal K,NIF, structure, have been synthesized. For M=Ti, only the x=0,5 member could be prepared, while for M=Mn and Fe, the composition range is 0 Cu(III)-O-Fe(III) valence degeneracy. Increasing the strontium content at the expense of lanthanum in La2-2xSr2xCu1-xFexO4 for x less than or equal to 0.20 renders the samples metallic but not superconducting. (C) 1997 Academic Press.

Investigation of valence states in the perovskite oxides, LaAFeNbO(6) (A = Ca, Sr)

Compounds of the type, LaAFeNbO(6) (A = Ca Sr) have been synthesized to study the electrical and magnetic properties and to examine valence degeneracy. The results show that valence degeneracy is not operative and the compounds are insulating. Magnetic susceptibility data show that part of the Fe is in Fs(2+) state, thus oxidizing part of Nb4+ to Nb5+ by an internal redox mechanism. The presence of mixed valent Fe is confirmed by Mossbauer spectra. (C) 1999 Elsevier Science B.V. All rights reserved.

Metal-insulator transition in a degenerate Hubbard model

We have studied the metal-insulator transition at integer fillings in a triply degenerate Hubbard model using the Lanczos method. The critical Coulomb interaction strength U-c, is found to depend strongly on the band filling, with U-c similar to root 3 W (W is the bandwidth) at half filling for this case with threefold degeneracy. We discuss the implications of our results on metal-insulator transitions in strongly correlated systems in general, and on the unusual electronic ground state of the alkali-metal-doped fullerenes, in particular. [S0163-1829(99)11003-8].

Zero-point entropy in 'spin ice'

Common water ice (ice I-h) is an unusual solid-the oxygen atoms form a periodic structure but the hydrogen atoms are highly disordered due to there being two inequivalent O-H bond lengths'. Pauling showed that the presence of these two bond lengths leads to a macroscopic degeneracy of possible ground states(2,3), such that the system has finite entropy as the temperature tends towards zero. The dynamics associated with this degeneracy are experimentally inaccessible, however, as ice melts and the hydrogen dynamics cannot be studied independently of oxygen motion(4). An analogous system(5) in which this degeneracy can be studied is a magnet with the pyrochlore structure-termed 'spin ice'-where spin orientation plays a similar role to that of the hydrogen position in ice I-h. Here we present specific-heat data for one such system, Dy2Ti2O7, from which we infer a total spin entropy of 0.67Rln2. This is similar to the value, 0.71Rln2, determined for ice I-h, SO confirming the validity of the correspondence. We also find, through application of a magnetic field, behaviour not accessible in water ice-restoration of much of the ground-state entropy and new transitions involving transverse spin degrees of freedom.

Semiconductor-metal transition in semiconducting bilayer sheets of transition-metal dichalcogenides

Using first-principles calculations we show that the band gap of bilayer sheets of semiconducting transition-metal dichalcogenides (TMDs) can be reduced smoothly by applying vertical compressive pressure. These materials undergo a universal reversible semiconductor-to-metal (S-M) transition at a critical pressure. The S-M transition is attributed to lifting of the degeneracy of the bands at the Fermi level caused by interlayer interactions via charge transfer from the metal to the chalcogen. The S-M transition can be reproduced even after incorporating the band gap corrections using hybrid functionals and the GW method. The ability to tune the band gap of TMDs in a controlled fashion over a wide range of energy opens up the possibility for its usage in a range of applications.

Entropy of quantum states: Ambiguities

The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. As pointed out to us by Sorkin, this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This non-unique entropy can occur at zero temperature. We will argue elsewhere in detail that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. Finally, we establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix.

Universal Conductance Fluctuations as a direct probe to valley coherence and universality class of disordered graphene

We demonstrate that the universal conductance fluctuations (UCF) can be used as a direct probe to study the valley quantum states in disordered graphene. The UCF magnitude in graphene is suppressed by a factor of four at high carrier densities where the short-range disorder essentially breaks the valley degeneracy of the K and K' valleys, leading to a density dependent crossover of symmetry class from symplectic near the Dirac point to orthogonal at high densities.

Unusual eigenvalue spectrum and relaxation in the Levy-Ornstein-Uhlenbeck process

We consider the rates of relaxation of a particle in a harmonic well, subject to Levy noise characterized by its Levy index mu. Using the propagator for this Levy-Ornstein-Uhlenbeck process (LOUP), we show that the eigenvalue spectrum of the associated Fokker-Planck operator has the form (n + m mu)nu where nu is the force constant characterizing the well, and n, m is an element of N. If mu is irrational, the eigenvalues are all nondegenerate, but rational mu can lead to degeneracy. The maximum degeneracy is shown to be 2. The left eigenfunctions of the fractional Fokker-Planck operator are very simple while the right eigenfunctions may be obtained from the lowest eigenfunction by a combination of two different step-up operators. Further, we find that the acceptable eigenfunctions should have the asymptotic behavior vertical bar x vertical bar(-n1-n2 mu) as vertical bar x vertical bar -> infinity, with n(1) and n(2) being positive integers, though this condition alone is not enough to identify them uniquely. We also assert that the rates of relaxation of LOUP are determined by the eigenvalues of the associated fractional Fokker-Planck operator and do not depend on the initial state if the moments of the initial distribution are all finite. If the initial distribution has fat tails, for which the higher moments diverge, one can have nonspectral relaxation, as pointed out by Toenjes et al. Phys. Rev. Lett. 110, 150602 (2013)].

Quantum entropy for the fuzzy sphere and its monopoles

Using generalized bosons, we construct the fuzzy sphere S-F(2) and monopoles on S-F(2) in a reducible representation of SU(2). The corresponding quantum states are naturally obtained using the GNS-construction. We show that there is an emergent nonabelian unitary gauge symmetry which is in the commutant of the algebra of observables. The quantum states are necessarily mixed and have non-vanishing von Neumann entropy, which increases monotonically under a bistochastic Markov map. The maximum value of the entropy has a simple relation to the degeneracy of the irreps that constitute the reducible representation that underlies the fuzzy sphere.

Cross-correlation-aided transport in stochastically driven accretion flows

The origin of linear instability resulting in rotating sheared accretion flows has remained a controversial subject for a long time. While some explanations of such non-normal transient growth of disturbances in the Rayleigh stable limit were available for magnetized accretion flows, similar instabilities in the absence of magnetic perturbations remained unexplained. This dichotomy was resolved in two recent publications by Chattopadhyay and co-workers Mukhopadhyay and Chattopadhyay, J. Phys. A 46, 035501 (2013); Nath et al., Phys. Rev. E 88, 013010 (2013)] where it was shown that such instabilities, especially for nonmagnetized accretion flows, were introduced through interaction of the inherent stochastic noise in the system (even a ``cold'' accretion flow at 3000Kis too ``hot'' in the statistical parlance and is capable of inducing strong thermal modes) with the underlying Taylor-Couette flow profiles. Both studies, however, excluded the additional energy influx (or efflux) that could result from nonzero cross correlation of a noise perturbing the velocity flow, say, with the noise that is driving the vorticity flow (or equivalently the magnetic field and magnetic vorticity flow dynamics). Through the introduction of such a time symmetry violating effect, in this article we show that nonzero noise cross correlations essentially renormalize the strength of temporal correlations. Apart from an overall boost in the energy rate (both for spatial and temporal correlations, and hence in the ensemble averaged energy spectra), this results in mutual competition in growth rates of affected variables often resulting in suppression of oscillating Alfven waves at small times while leading to faster saturations at relatively longer time scales. The effects are seen to be more pronounced with magnetic field fluxes where the noise cross correlation magnifies the strength of the field concerned. Another remarkable feature noted specifically for the autocorrelation functions is the removal of energy degeneracy in the temporal profiles of fast growing non-normal modes leading to faster saturation with minimum oscillations. These results, including those presented in the previous two publications, now convincingly explain subcritical transition to turbulence in the linear limit for all possible situations that could now serve as the benchmark for nonlinear stability studies in Keplerian accretion disks.

Observation of coherent population trapping in a V-type two-electron system

We observe coherent population trapping (CPT) in a two-electron atom-Yb-174-using the S-1(0), F= 0 -> P-3(1), F `= 1 transition. CPT is not possible for such a transition according to one-electron theory because the magnetic sublevels form a V-type system, but in a two-electron atom like Yb, the interaction of the electrons transforms the level structure into a V-type system, which allows the formation of a dark state and hence the observation of CPT. Since the two levels involved are degenerate, we use a magnetic field to lift the degeneracy. The single fluorescence dip then splits into five dips-the central unshifted one corresponds to coherent population oscillation, while the outer four are due to CPT. The linewidth of the CPT resonance is about 300 kHz and is limited by the natural linewidth of the excited state, which is to be expected because the excited state is involved in the formation of the dark state.

Non-Abelian gauge redundancy and entropic ambiguities

The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. Therefore one reaches the remarkable possibility that there may be many entropies for a given state. We show that this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This ambiguity in entropy, which can occur at zero temperature, can often be traced to a gauge symmetry emergent from the non-trivial topological character of the configuration space of the underlying system. We also establish the analogue of an H-theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix. After demonstrating this entropy ambiguity for the simple example of the algebra of 2 x 2 matrices, we argue that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. We work out the simplest situation with such non-Abelian symmetry, that of an ethylene molecule.