Non-conformal asymptotic behavior of the time-dependent field-field correlators of 1D anyons

The exact large time and distance behavior of the field-field correlators has been computed for one-dimensional impenetrable anyons at finite temperatures. The result reproduces known asymptotics for impenetrable bosons and free fermions in the appropriate limits of the statistics parameter. The obtained asymptotic behavior of the correlators is dominated by the singularity in the spectral density of the quasiparticle states at the bottom of the band, and differs from the predictions of the conformal field theory. One can argue, however, that the anyonic response to the low-energy probes is still determined by the conformal terms in the asymptotic expansion.Comment: 5 pages, RevTeX

Modelling the unfolding pathway of biomolecules: theoretical approach and experimental prospect

We analyse the unfolding pathway of biomolecules comprising several independent modules in pulling experiments. In a recently proposed model, a critical velocity $v_{c}$ has been predicted, such that for pulling speeds $v>v_{c}$ it is the module at the pulled end that opens first, whereas for $v<v_{c}$ it is the weakest. Here, we introduce a variant of the model that is closer to the experimental setup, and discuss the robustness of the emergence of the critical velocity and of its dependence on the model parameters. We also propose a possible experiment to test the theoretical predictions of the model, which seems feasible with state-of-art molecular engineering techniques.Comment: Accepted contribution for the Springer Book "Coupled Mathematical Models for Physical and Biological Nanoscale Systems and Their Applications" (proceedings of the BIRS CMM16 Workshop held in Banff, Canada, August 2016), 16 pages, 6 figure

Singular responses of spin-incoherent Luttinger liquids

When a local potential changes abruptly in time, an electron gas shifts to a new state which at long times is orthogonal to the one in the absence of the local potential. This is known as Anderson's orthogonality catastrophe and it is relevant for the so-called X-ray edge or Fermi edge singularity, and for tunneling into an interacting one dimensional system of fermions. It often happens that the finite frequency response of the photon absorption or the tunneling density of states exhibits a singular behavior as a function of frequency: $(\frac{\omega_{\rm th}}{\omega-\omega_{\rm th}})^\alpha\Theta(\omega-\omega_{\rm th})$ where $\omega_{\rm th}$ is a threshold frequency and $\alpha$ is an exponent characterizing the singular response. In this paper singular responses of spin-incoherent Luttinger liquids are reviewed. Such responses most often do not fall into the familiar form above, but instead typically exhibit logarithmic corrections and display a much higher universality in terms of the microscopic interactions in the theory. Specific predictions are made, the current experimental situation is summarized, and key outstanding theoretical issues related to spin-incoherent Luttinger liquids are highlighted.Comment: 21 pages, 3 figures. Invited Topical Review Articl

Gravitomagnetic Jets

We present a family of dynamic rotating cylindrically symmetric Ricci-flat gravitational fields whose geodesic motions have the structure of gravitomagnetic jets. These correspond to helical motions of free test particles up and down parallel to the axis of cylindrical symmetry and are reminiscent of the motion of test charges in a magnetic field. The speed of a test particle in a gravitomagnetic jet asymptotically approaches the speed of light. Moreover, numerical evidence suggests that jets are attractors. The possible implications of our results for the role of gravitomagnetism in the formation of astrophysical jets are briefly discussed.Comment: 47 pages, 8 figures; v2: minor improvements; v3: paragraph added at the end of Sec. V and other minor improvements; v4: reference added, typos corrected, sentence added on p. 24; v5: a few minor improvement

Theorie de Lubin-Tate non-abelienne et representations elliptiques

Harris and Taylor proved that the supercuspidal part of the cohomology of the Lubin-Tate tower realizes both the local Langlands and Jacquet-Langlands correspondences, as conjectured by Carayol. Recently, Boyer computed the remaining part of the cohomology and exhibited two defects : first, the representations of GL\_d which appear are of a very particular and restrictive form ; second, the Langlands correspondence is not realized anymore. In this paper, we study the cohomology complex in a suitable equivariant derived category, and show how it encodes Langlands correspondance for all elliptic representations. Then we transfer this result to the Drinfeld tower via an enhancement of a theorem of Faltings due to Fargues. We deduce that Deligne's weight-monodromy conjecture is true for varieties uniformized by Drinfeld's coverings of his symmetric spaces.Comment: 54 page

Correlation Functions of One-Dimensional Lieb-Liniger Anyons

We have investigated the properties of a model of 1D anyons interacting through a $\delta$-function repulsive potential. The structure of the quasi-periodic boundary conditions for the anyonic field operators and the many-anyon wavefunctions is clarified. The spectrum of the low-lying excitations including the particle-hole excitations is calculated for periodic and twisted boundary conditions. Using the ideas of the conformal field theory we obtain the large-distance asymptotics of the density and field correlation function at the critical temperature T=0 and at small finite temperatures. Our expression for the field correlation function extends the results in the literature obtained for harmonic quantum anyonic fluids.Comment: 19 pages, RevTeX

Fermionic representations for characters of M(3,t), M(4,5), M(5,6) and M(6,7) minimal models and related Rogers-Ramanujan type and dilogarithm identities

Characters and linear combinations of characters that admit a fermionic sum representation as well as a factorized form are considered for some minimal Virasoro models. As a consequence, various Rogers-Ramanujan type identities are obtained. Dilogarithm identities producing corresponding effective central charges and secondary effective central charges are derived. Several ways of constructing more general fermionic representations are discussed.Comment: 14 pages, LaTex; minor correction

Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models

We present fermionic sum representations of the characters $\chi^{(p,p')}_{r,s}$ of the minimal $M(p,p')$ models for all relatively prime integers $p'>p$ for some allowed values of $r$ and $s$. Our starting point is binomial (q-binomial) identities derived from a truncation of the state counting equations of the XXZ spin ${1\over 2}$ chain of anisotropy $-\Delta=-\cos(\pi{p\over p'})$. We use the Takahashi-Suzuki method to express the allowed values of $r$ (and $s$) in terms of the continued fraction decomposition of $\{{p'\over p}\}$ (and ${p\over p'}$) where $\{x\}$ stands for the fractional part of $x.$ These values are, in fact, the dimensions of the hermitian irreducible representations of $SU_{q_{-}}(2)$ (and $SU_{q_{+}}(2)$) with $q_{-}=\exp (i \pi \{{p'\over p}\})$ (and $q_{+}=\exp ( i \pi {p\over p'})).$ We also establish the duality relation $M(p,p')\leftrightarrow M(p'-p,p')$ and discuss the action of the Andrews-Bailey transformation in the space of minimal models. Many new identities of the Rogers-Ramanujan type are presented.Comment: Several references, one further explicit result and several discussion remarks adde

The key neuroendocrine regulators of the onset of puberty in the Atlantic bluefin tuna (Thunnus thynnus)

Recently, significant progress on spawning induction in captive bluefin tuna (BFT, Thunnus thynnus), has been achieved providing the basis for the species' domestication. To further promote the development of a self- sustained BFT aquaculture, we investigated first sexual maturity in BFT reared from an immature stage in captivity. Accordingly, our major objectives were to evaluate: (i) maturational status of the brain-pituitary-gonadal (BPG) axis, and (ii) responsiveness of the BPG to exogenous hormones. Special emphasis was given to characterize the gonadotropins follicle stimulating hormone (FSH) and luteinizing hormone (LH) that act as central regulators of gonadal development and gamete maturation. The growth parameters recorded for the captive BFT juveniles are consistent with the length-weight relationship established for wild Mediterranean BFT stocks. The histological analyses of the gonads indicate advanced sexual maturation in BFT males compared to females, yet it is not yet clear whether this phenomenon typifies wild stocks or is induced due to the culture conditions. The hormone measurements show expression and accumulation of both gonadotropins in the pituitaries of immature and mature BFT. The pituitary LH content increased concomitantly with the age of the fish, exhibiting sex dimorphic patterns (i.e. 3-fold higher levels in females) in adult but not in juvenile BFT. The pituitary FSH levels, however, were elevated in 2Y immature males and in fully mature adults. Comparable to mammals, the intra-pituitary FSH/LH ratio was found to be higher (>1) in sexually immature than in maturing or pubertal BFT. Nevertheless, in the 3Y BFT females, which were all immature, the onset of puberty appears to require some other prerequisites, such as a rise in the LH storage above a minimal threshold. Our in vitro trials further demonstrated the capacity of rFSH and to a lesser extent that of rLH to stimulate cell proliferation in the immature ovarian and testicular fragments. Both rFSH and rLH have failed to stimulate steroidogenesis, yet pre-treatment with KiSS containing EVAc implants appeared to potentiate FSH-stimulated steroidogenesis in the immature testes. On the other hand, the expression levels of both the GtH-R and IGF I genes in the testicular fragments, derived from BFT juveniles and further exposed to the rLH treatment, showed dose-dependent pattern. Future studies testing the effects of captivity and hormone-based treatments on precocious maturity at relatively small body size are expected to facilitate the handling in confined environments, and to greatly improve the cost-efficiency of BFT farming.Postprin