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We consider a toy model for the study of monitored dynamics in many-body quantum systems. We study the stochastic Schrödinger equation resulting from continuous monitoring with a rate Γ of a random Hermitian operator, drawn from the Gaussian unitary ensemble (GUE) at every time t. Due to invariance by unitary transformations, the dynamics of the eigenvalues {λα}α=1n of the density matrix decouples from that of the eigenvectors, and is exactly described by stochastic equations that we derive. We consider two regimes: in the presence of an extra dephasing term, which can be generated by imperfect quantum measurements, the density matrix has a stationary distribution, and we show that in the limit of large size n→∞ it matches with the inverse-Marchenko–Pastur distribution. In the case of perfect measurements, instead, purification eventually occurs and we focus on finite-time dynamics. In this case, remarkably, we find an exact solution for the joint probability distribution of λ’s at each time t and for each size n. Two relevant regimes emerge: at short times tΓ=O(1), the spectrum is in a Coulomb gas regime, with a well-defined continuous spectral distribution in the n→∞ limit. In that case, all moments of the density matrix become self-averaging and it is possible to exactly characterize the entanglement spectrum. In the limit of large times tΓ=O(n), one enters instead a regime in which the eigenvalues are exponentially separated log(λα/λβ)=O(Γt/n), but fluctuations ∼O(Γt/n) play an essential role. We are still able to characterize the asymptotic behaviors of the entanglement entropy in this regime.

We consider a system of $N$ spinless fermions, interacting with each other via a power-law interaction $\epsilon/r^n$, and trapped in an external harmonic potential $V(r) = r^2/2$, in $d=1,2,3$ dimensions. For any $0 < n < d+2$, we obtain the ground-state energy $E_N$ of the system perturbatively in $\epsilon$, $E_{N}=E_{N}^{≤ft(0)}+\epsilon E_{N}^{≤ft(1)}+O≤ft(\epsilon^{2})$. We calculate $E_{N}^{≤ft(1)}$ exactly, assuming that $N$ is such that the "outer shell" is filled. For the case of $n=1$ (corresponding to a Coulomb interaction for $d=3$), we extract the $N \gg 1$ behavior of $E_{N}^{≤ft(1)}$, focusing on the corrections to the exchange term with respect to the leading-order term that is predicted from the local density approximation applied to the Thomas-Fermi approximate density distribution. The leading correction contains a logarithmic divergence, and is of particular importance in the context of density functional theory. We also study the effect of the interactions on the fermions' spatial density. Finally, we find that our result for $E_{N}^{≤ft(1)}$ significantly simplifies in the case where $n$ is even.

We consider critical one-dimensional quantum systems initially prepared in their ground state and perturbed by a smooth noise coupled to the energy density. By using conformal field theory, we deduce a universal description of the out-of-equilibrium dynamics. In particular, the full time-dependent distribution of any two-point chiral correlation function can be obtained from solving two coupled ordinary stochastic differential equations. In contrast to the general expectation of heating, we demonstrate that, over the noise realizations, the system reaches a nontrivial and universal stationary distribution of states characterized by broad tails of physical quantities. As an example, we analyze the entanglement entropy production associated to a given interval of size ℓ. The corresponding stationary distribution has a 3/2 right tail for all ℓ and converges to a one-sided Levy stable for large ℓ. We obtain a similar result for the local energy density: While its first moment diverges exponentially fast in time, the stationary distribution, which we derive analytically, is symmetric around a negative median and exhibits a fat tail with 3/2 decay exponent. We show that this stationary distribution for the energy density emerges even if the initial state is prepared at finite temperature. Our results are benchmarked via analytical and numerical calculations for a chain of noninteracting spinless fermions with excellent agreement.

We present a systematic short time expansion for the generating function of the one point height probability distribution for the KPZ equation with droplet initial condition, which goes much beyond previous studies. The expansion is checked against a numerical evaluation of the known exact Fredholm determinant expression. We also obtain the next order term for the Brownian initial condition. Although initially devised for short time, a resummation of the series allows to obtain also the long time large deviation function, found to agree with previous works using completely different techniques. Unexpected similarities with stationary large deviations of TASEP with periodic and open boundaries are discussed. Two additional applications are given. (i) Our method is generalized to study the linear statistics of the Airy point process, i.e. of the GUE edge eigenvalues. We obtain the generating function of the cumulants of the empirical measure to a high order. The second cumulant is found to match the result in the bulk obtained from the Gaussian free field by Borodin and Ferrari [1,2], but we obtain systematic corrections to the Gaussian free field (higher cumulants, expansion towards the edge). This also extends a result of Basor and Widom [3] to a much higher order. We obtain large deviation functions for the Airy point process for a variety of linear statistics test functions. (ii) We obtain results for the counting statistics of trapped fermions at the edge of the Fermi gas in both the high and the low temperature limits.

We calculate the effective action for disordered elastic manifolds in the ground state (equilibrium) up to 3-loop order. This yields the renormalization-group β-function to third order in ε=4−d, in an expansion in the dimension d around the upper critical dimension d=4. The calculations are performed using exact RG, and several other techniques, which allow us to resolve consistently the problems associated with the cusp of the renormalized disorder.

We study $N$ spinless fermions in their ground state confined by an external potential in one dimension with long range interactions of the general Calogero-Sutherland type. For some choices of the potential this system maps to standard random matrix ensembles for general values of the Dyson index $\beta$. In the fermion model $\beta$ controls the strength of the interaction, $\beta=2$ corresponding to the noninteracting case. We study the quantum fluctuations of the number of fermions ${\cal N}_{\cal D}$ in a domain $\cal{D}$ of macroscopic size in the bulk of the Fermi gas. We predict that for general $\beta$ the variance of ${\cal N}_{\cal D}$ grows as $A_{\beta} \log N + B_{\beta}$ for $N \gg 1$ and we obtain a formula for $A_\beta$ and $B_\beta$. This is based on an explicit calculation for $\beta\in\left\{ 1,2,4\right\} $ and on a conjecture that we formulate for general $\beta$. This conjecture further allows us to obtain a universal formula for the higher cumulants of ${\cal N}_{\cal D}$. Our results for the variance in the microscopic regime are found to be consistent with the predictions of the Luttinger liquid theory with parameter $K = 2/\beta$, and allow to go beyond. In addition we present families of interacting fermion models in one dimension which, in their ground states, can be mapped onto random matrix models. We obtain the mean fermion density for these models for general interaction parameter $\beta$. In some cases the fermion density exhibits interesting transitions, for example we obtain a noninteracting fermion formulation of the Gross-Witten-Wadia model.

The O-acetylated form of GD2, almost exclusively expressed in cancerous tissues, is considered to be a promising therapeutic target for neuroectoderm-derived tumors, especially for breast cancer. Our recent data have shown that 9-O-acetylated GD2 (9-OAcGD2) is the major O-acetylated ganglioside species in breast cancer cells. In 2015, Baumann et al. proposed that Cas 1 domain containing 1 (CASD1), which is the only known human sialyl-O-acetyltransferase, plays a role in GD3 O-acetylation. However, the mechanisms of ganglioside O-acetylation remain poorly understood. The aim of this study was to determine the involvement of CASD1 in GD2 O-acetylation in breast cancer. The role of CASD1 in OAcGD2 synthesis was first demonstrated using wild type CHO and CHOΔCasd1 cells as cellular models. Overexpression using plasmid transfection and siRNA strategies was used to modulate CASD1 expression in SUM159PT breast cancer cell line. Our results showed that OAcGD2 expression was reduced in SUM159PT that was transiently depleted for CASD1 expression. Additionally, OAcGD2 expression was increased in SUM159PT cells transiently overexpressing CASD1. The modulation of CASD1 expression using transient transfection strategies provided interesting insights into the role of CASD1 in OAcGD2 and OAcGD3 biosynthesis, and it highlights the importance of further studies on O-acetylation mechanisms.

Abstract Background Magnesium sulphate (MgSO4) is the only treatment approved for fetal neuroprotection. No information on its use is available in the absence of a national registry of neonatal practices. The objective of our study was to evaluate the use of MgSO4 for fetal neuroprotection in French tertiary maternity hospitals (FTMH). Methods Online and phone survey of all FTMH between August 2014 and May 2015. A participation was expected from one senior obstetrician, one senior anaesthetist and one senior neonatologist from each FTMH. Information was obtained from 63/63 (100%) FTMH and 138/189 (73%) physicians. Use of MgSO4 for fetal neuroprotection, regimen and injection protocols, reasons for non-use were the main outcome measures. Results 60.3% of FTMH used MgSO4 for fetal neuroprotection. No significant difference was observed between university and non-university hospitals or according to the annual number of births. Protocols differed especially in terms of the maximum gestational age (3%

We study the properties of spin-less non-interacting fermions trapped in a confining potential in one dimension but in the presence of one or more impurities which are modelled by delta function potentials. We use a method based on the single particle Green's function. For a single impurity placed in the bulk, we compute the density of the Fermi gas near the impurity. Our results, in addition to recovering the Friedel oscillations at large distance from the impurity, allow the exact computation of the density at short distances. We also show how the density of the Fermi gas is modified when the impurity is placed near the edge of the trap in the region where the unperturbed system is described by the Airy gas. Our method also allows us to compute the effective potential felt by the impurity both in the bulk and at the edge. In the bulk this effective potential is shown to be a universal function only of the local Fermi wave vector, or equivalently of the local fermion density. When the impurity is placed near the edge of the Fermi gas, the effective potential can be expressed in terms of Airy functions. For an attractive impurity placed far outside the support of the fermion density, we show that an interesting transition occurs where a single fermion is pulled out of the Fermi sea and forms a bound state with the impurity. This is a quantum analogue of the well-known Baik-Ben Arous-P\'ech\'e (BBP) transition, known in the theory of spiked random matrices. The density at the location of the impurity plays the role of an order parameter. We also consider the case of two impurities in the bulk and compute exactly the effective force between them mediated by the background Fermi gas.

We consider the Kardar-Parisi-Zhang (KPZ) equation for the stochastic growth of an interface of height $h(x,t)$ on the positive half line with boundary condition $\partial_x h(x,t)|_{x=0}=A$. It is equivalent to a continuum directed polymer (DP) in a random potential in half-space with a wall at $x=0$ either repulsive $A>0$, or attractive $A - \frac{1}{2}$ the large time PDF is the GSE Tracy-Widom distribution. For $A= \frac{1}{2}$, the critical point at which the DP binds to the wall, we obtain the GOE Tracy-Widom distribution. In the critical region, $A+\frac{1}{2} = \epsilon t^{-1/3} \to 0$ with fixed $\epsilon = \mathcal{O}(1)$, we obtain a transition kernel continuously depending on $\epsilon$. Our work extends the results obtained previously for $A=+\infty$, $A=0$ and $A=- \frac{1}{2}$.

The expression and biological functions of oncofetal markers GD2 and GD3 were extensively studied in neuroectoderm-derived cancers in order to characterize their potential as therapeutic targets. Using immunological approaches, we previously identified GD3, GD2, and OAcGD2 expression in breast cancer (BC) cell lines. However, antibodies specific for O-acetylated gangliosides are not exempt of limitations, as they only provide information on the expression of a limited set of O-acetylated ganglioside species. Consequently, the aim of the present study was to use structural approaches in order to apprehend ganglioside diversity in melanoma, neuroblastoma, and breast cancer cells, focusing on O-acetylated species that are usually lost under alkaline conditions and require specific analytical procedures. We used purification and extraction methods that preserve the O-acetyl modification for the analysis of native gangliosides by MALDI-TOF. We identified the expression of GM1, GM2, GM3, GD2, GD3, GT2, and GT3 in SK-Mel28 (melanoma), LAN-1 (neuroblastoma), Hs 578T, SUM 159PT, MDA-MB-231, MCF-7 (BC), and BC cell lines over-expressing GD3 synthase. Among O-acetylated gangliosides, we characterized the expression of OAcGM1, OAcGD3, OAcGD2, OAcGT2, and OAcGT3. Furthermore, the experimental procedure allowed us to clearly identify the position of the sialic acid residue that carries the O-acetyl group on b- and c-series gangliosides by MS/MS fragmentation. These results show that ganglioside O-acetylation occurs on both inner and terminal sialic acid residue in a cell type-dependent manner, suggesting different O-acetylation pathways for gangliosides. They also highlight the limitation of immuno-detection for the complete identification of O-acetylated ganglioside profiles in cancer cells.

We investigate the short-time regime of the KPZ equation in $1+1$ dimensions and develop a unifying method to obtain the height distribution in this regime, valid whenever an exact solution exists in the form of a Fredholm Pfaffian or determinant. These include the droplet and stationary initial conditions in full space, previously obtained by a different method. The novel results concern the droplet initial condition in a half space for several Neumann boundary conditions: hard wall, symmetric, and critical. In all cases, the height probability distribution takes the large deviation form $P(H,t) \sim \exp( - \Phi(H)/\sqrt{t})$ for small time. We obtain the rate function $\Phi(H)$ analytically for the above cases. It has a Gaussian form in the center with asymmetric tails, $|H|^{5/2}$ on the negative side, and $H^{3/2}$ on the positive side. The amplitude of the left tail for the half-space is found to be half the one of the full space. As in the full space case, we find that these left tails remain valid at all times. In addition, we present here (i) a new Fredholm Pfaffian formula for the solution of the hard wall boundary condition and (ii) two Fredholm determinant representations for the solutions of the hard wall and the symmetric boundary respectively.

Riders to the Sea: An opera in one act based on the play by John Millington Synge, Ralph Vaughan Williams’s fifth opera, composed between 1925 and 1932, after The Poisoned Kiss (A Romantic Extravaganza), was first performed at London’s Royal College of Music on December 1st, 1937, with Malcolm Sargent conducting. A masterpiece of poetic intensity and a compendium of pain and quiet, resigned courage, worthy of a Greek tragedy, the Irish dramatist’s play was faithfully adapted by the composer-librettist in a work whose originality and universal message cannot fail to impress. Originating in his wide-ranging imagination―humanistic, brotherly, idealistic, universal―it speaks of a voyage of initiation to the Aran Islands, off the west coast of Ireland. The composer, inspired by folk wisdom and the world of the Spirit, open to worldly solicitations as well as to meditation, saw the play as a vehicle to highlight some aspects of his own musical heritage. In a few pages of dialogue, the score conveys a whole range of different emotions arising from the confrontation with Nature, and more particularly, from the forlorn struggle of the islanders against the sea and God, their ruler.

Building upon the one-step replica symmetry breaking formalism, duly understood and ramified, we show that the sequence of ordered extreme values of a general class of Euclidean-space logarithmically correlated random energy models (logREMs) behave in the thermodynamic limit as a randomly shifted decorated exponential Poisson point process. The distribution of the random shift is determined solely by the large-distance ("infra-red", IR) limit of the model, and is equal to the free energy distribution at the critical temperature up to a translation. the decoration process is determined solely by the small-distance ("ultraviolet", UV) limit, in terms of the biased minimal process. Our approach provides connections of the replica framework to results in the probability literature and sheds further light on the freezing/duality conjecture which was the source of many previous results for log-REMs. In this way we derive the general and explicit formulae for the joint probability density of depths of the first and second minima (as well its higher-order generalizations) in terms of model-specific contributions from UV as well as IR limits. In particular, we show that the second min statistics is largely independent of details of UV data, whose influence is seen only through the mean value of the gap. For a given log-correlated field this parameter can be evaluated numerically, and we provide several numerical tests of our theory using the circular model of $1/f$-noise.