Quantum dynamics and entanglement of a 1D Fermi gas released from a trap

We investigate the entanglement properties of the nonequilibrium dynamics of one-dimensional noninteracting Fermi gases released from a trap. The gas of N particles is initially in the ground state within hard-wall or harmonic traps, then it expands after dropping the trap. We compute the time dependence of the von Neumann and Renyi entanglement entropies and the particle fluctuations of spatial intervals around the original trap, in the limit of a large number N of particles. The results for these observables apply to one-dimensional gases of impenetrable bosons as well. We identify different dynamical regimes at small and large times, depending also on the initial condition, whether it is that of a hard-wall or harmonic trap. In particular, we analytically show that the expansion from hard-wall traps is characterized by the asymptotic small-time behavior $S \approx (1/3)\ln(1/t)$ of the von Neumann entanglement entropy, and the relation $S\approx \pi^2 V/3$ where V is the particle variance, which are analogous to the equilibrium behaviors whose leading logarithms are essentially determined by the corresponding conformal field theory with central charge $c=1$. The time dependence of the entanglement entropy of extended regions during the expansion from harmonic traps shows the remarkable property that it can be expressed as a global time-dependent rescaling of the space dependence of the initial equilibrium entanglement entropy.Comment: 19 pages, 18 fig

Power-law random walks

We present some new results about the distribution of a random walk whose independent steps follow a $q-$Gaussian distribution with exponent $\frac{1}{1-q}; q \in \mathbb{R}$. In the case $q>1$ we show that a stochastic representation of the point reached after $n$ steps of the walk can be expressed explicitly for all $n$. In the case $q<1,$ we show that the random walk can be interpreted as a projection of an isotropic random walk, i.e. a random walk with fixed length steps and uniformly distributed directions.Comment: 5 pages, 4 figure

BLUF Domain Function Does Not Require a Metastable Radical Intermediate State

BLUF (blue light using flavin) domain proteins are an important family of blue light-sensing proteins which control a wide variety of functions in cells. The primary light-activated step in the BLUF domain is not yet established. A number of experimental and theoretical studies points to a role for photoinduced electron transfer (PET) between a highly conserved tyrosine and the flavin chromophore to form a radical intermediate state. Here we investigate the role of PET in three different BLUF proteins, using ultrafast broadband transient infrared spectroscopy. We characterize and identify infrared active marker modes for excited and ground state species and use them to record photochemical dynamics in the proteins. We also generate mutants which unambiguously show PET and, through isotope labeling of the protein and the chromophore, are able to assign modes characteristic of both flavin and protein radical states. We find that these radical intermediates are not observed in two of the three BLUF domains studied, casting doubt on the importance of the formation of a population of radical intermediates in the BLUF photocycle. Further, unnatural amino acid mutagenesis is used to replace the conserved tyrosine with fluorotyrosines, thus modifying the driving force for the proposed electron transfer reaction; the rate changes observed are also not consistent with a PET mechanism. Thus, while intermediates of PET reactions can be observed in BLUF proteins they are not correlated with photoactivity, suggesting that radical intermediates are not central to their operation. Alternative nonradical pathways including a keto–enol tautomerization induced by electronic excitation of the flavin ring are considered

Ionization Probabilities through ultra-intense Fields in the extreme Limit

We continue our investigation concerning the question of whether atomic bound states begin to stabilize in the ultra-intense field limit. The pulses considered are essentially arbitrary, but we distinguish between three situations. First the total classical momentum transfer is non-vanishing, second not both the total classical momentum transfer and the total classical displacement are vanishing together with the requirement that the potential has a finite number of bound states and third both the total classical momentum transfer and the total classical displacement are vanishing. For the first two cases we rigorously prove, that the ionization probability tends to one when the amplitude of the pulse tends to infinity and the pulse shape remains fixed. In the third case the limit is strictly smaller than one. This case is also related to the high frequency limit considered by Gavrila et al.Comment: 16 pages LateX, 2 figure

Integrated random processes exhibiting long tails, finite moments and 1/f spectra

A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling assumption, takes on a form that is the basis of the results derived in the rest of the paper. One of these is an expansion for the cumulants, which are all finite, subject to mild conditions on the functions defining the process. This is in contrast with the Levy distribution -which can be obtained from our model in certain limits- which has no finite moments. The evaluation of the power spectrum and the form of the probability density function in the tails of the distribution shows that the model exhibits a 1/f spectrum and long tails in a natural way. A careful analysis of the characteristic function shows that it may be separated into a part representing a Levy processes together with another part representing the deviation of our model from the Levy process. This allows our process to be viewed as a generalization of the Levy process which has finite moments.Comment: Revtex (aps), 15 pages, no figures. Submitted to Phys. Rev.

A Grassmann integral equation

The present study introduces and investigates a new type of equation which is called Grassmann integral equation in analogy to integral equations studied in real analysis. A Grassmann integral equation is an equation which involves Grassmann integrations and which is to be obeyed by an unknown function over a (finite-dimensional) Grassmann algebra G_m. A particular type of Grassmann integral equations is explicitly studied for certain low-dimensional Grassmann algebras. The choice of the equation under investigation is motivated by the effective action formalism of (lattice) quantum field theory. In a very general setting, for the Grassmann algebras G_2n, n = 2,3,4, the finite-dimensional analogues of the generating functionals of the Green functions are worked out explicitly by solving a coupled system of nonlinear matrix equations. Finally, by imposing the condition G[{\bar\Psi},{\Psi}] = G_0[{\lambda\bar\Psi}, {\lambda\Psi}] + const., 0<\lambda\in R (\bar\Psi_k, \Psi_k, k=1,...,n, are the generators of the Grassmann algebra G_2n), between the finite-dimensional analogues G_0 and G of the (``classical'') action and effective action functionals, respectively, a special Grassmann integral equation is being established and solved which also is equivalent to a coupled system of nonlinear matrix equations. If \lambda \not= 1, solutions to this Grassmann integral equation exist for n=2 (and consequently, also for any even value of n, specifically, for n=4) but not for n=3. If \lambda=1, the considered Grassmann integral equation has always a solution which corresponds to a Gaussian integral, but remarkably in the case n=4 a further solution is found which corresponds to a non-Gaussian integral. The investigation sheds light on the structures to be met for Grassmann algebras G_2n with arbitrarily chosen n.Comment: 58 pages LaTeX (v2: mainly, minor updates and corrections to the reference section; v3: references [4], [17]-[21], [39], [46], [49]-[54], [61], [64], [139] added

Mechanically activated ion channel PIEZO1 is required for lymphatic valve formation

PIEZO1 is a cation channel that is activated by mechanical forces such as fluid shear stress or membrane stretch. PIEZO1 loss-of-function mutations in patients are associated with congenital lymphedema with pleural effusion. However, the mechanistic link between PIEZO1 function and the development or function of the lymphatic system is currently unknown. Here, we analyzed two mouse lines lacking PIEZO1 in endothelial cells (via Tie2Cre or Lyve1Cre) and found that they exhibited pleural effusion and died postnatally. Strikingly, the number of lymphatic valves was dramatically reduced in these mice. Lymphatic valves are essential for ensuring proper circulation of lymph. Mechanical forces have been implicated in the development of lymphatic vasculature and valve formation, but the identity of mechanosensors involved is unknown. Expression of FOXC2 and NFATc1, transcription factors known to be required for lymphatic valve development, appeared normal in Tie2Cre;Piezo1cKO mice. However, the process of protrusion in the valve leaflets, which is associated with collective cell migration, actin polymerization, and remodeling of cell–cell junctions, was impaired in Tie2Cre;Piezo1cKO mice. Consistent with these genetic findings, activation of PIEZO1 by Yoda1 in cultured lymphatic endothelial cells induced active remodeling of actomyosin and VE-cadherin+ cell–cell adhesion sites. Our analysis provides evidence that mechanically activated ion channel PIEZO1 is a key regulator of lymphatic valve formation

Femtosecond To Millisecond Dynamics Of Light Induced Allostery In The Avena Sativa LOV Domain

The rational engineering of photosensor proteins underpins the field of optogenetics, in which light is used for spatio-temporal control of cell signalling. Optogenetic elements function by converting electronic excitation of an embedded chromophore into structural changes on the microseconds to seconds timescale, which then modulate the activity of output domains responsible for biological signalling. Using time resolved vibrational spectroscopy coupled with isotope labelling we have mapped the structural evolution of the LOV2 domain of the flavin binding phototropin Avena sativa (AsLOV2) over 10 decades of time, reporting structural dynamics between 100 femtoseconds and one millisecond after optical excitation. The transient vibrational spectra contain contributions from both the flavin chromophore and the surrounding protein matrix. These contributions are resolved and assigned through the study of four different isotopically labelled samples. High signal-to-noise data permit the detailed analysis of kinetics associated with the light activated structural evolution. A pathway for the photocycle consistent with the data is proposed. The earliest events occur in the flavin binding pocket, where a sub-picosecond perturbation of the protein matrix occurs. In this perturbed environment the previously characterised reaction between triplet state isoalloxazine and an adjacent cysteine leads to formation of the adduct state; this step is shown to exhibit dispersive kinetics. This reaction promotes coupling of the optical excitation to successive time-dependent structural changes, initially in the -sheet then -helix regions of the AsLOV2 domain, which ultimately gives rise to J-helix unfolding, yielding the signalling state. This model is tested through point mutagenesis, elucidating in particular the key mediating role played by Q513

Reproducible isolation of lymph node stromal cells reveals site-dependent differences in fibroblastic reticular cells

Within lymph nodes, non-hematopoietic stromal cells organize and interact with leukocytes in an immunologically important manner. In addition to organizing T and B cell segregation and expressing lymphocyte survival factors, several recent studies have shown that lymph node stromal cells shape the naïve T cell repertoire, expressing self-antigens which delete self-reactive T cells in a unique and non-redundant fashion. A fundamental role in peripheral tolerance, in addition to an otherwise extensive functional portfolio, necessitates closer study of lymph node stromal cell subsets using modern immunological techniques; however this has not routinely been possible in the field, due to difficulties reproducibly isolating these rare subsets. Techniques were therefore developed for successful ex vivo and in vitro manipulation and characterization of lymph node stroma. Here we discuss and validate these techniques in mice and humans, and apply them to address several unanswered questions regarding lymph node composition. We explored the steady-state stromal composition of lymph nodes isolated from mice and humans, and found that marginal reticular cells and lymphatic endothelial cells required lymphocytes for their normal maturation in mice. We also report alterations in the proportion and number of fibroblastic reticular cells (FRCs) between skin-draining and mesenteric lymph nodes. Similarly, transcriptional profiling of FRCs revealed changes in cytokine production from these sites. Together, these methods permit highly reproducible stromal cell isolation, sorting, and culture

Photoactivation of the BLUF protein PixD Probed by the Site-Specific Incorporation of Fluorotyrosine Residues

The flavin chromophore in blue light using FAD (BLUF) photoreceptors is surrounded by a hydrogen bond network that senses and responds to changes in the electronic structure of the flavin on the ultrafast time scale. The hydrogen bond network includes a strictly conserved Tyr residue, and previously we explored the role of this residue, Y21, in the photoactivation mechanism of the BLUF protein AppA by the introduction of fluorotyrosine (F-Tyr) analogs that modulated the pKa and reduction potential of Y21 by 3.5 pH units and 200 mV, respectively. Although little impact on the forward (dark to light adapted form) photoreaction was observed, the change in Y21 pKa led to a 4,000-fold increase in the rate of dark state recovery. In the present work we have extended these studies to the BLUF protein PixD, where, in contrast to AppA, modulation in the Tyr (Y8) pKa has a profound impact on the forward photoreaction. In particular, a decrease in Y8 pKa by 2 or more pH units prevents formation of a stable light state, consistent with a photoactivation mechanism that involves proton transfer or proton coupled electron transfer from Y8 to the electronically excited FAD. Conversely, the effect of pKa on the rate of dark recovery is markedly reduced in PixD. These observations highlight very significant differences between the photocycles of PixD and AppA, despite their sharing highly conserved FAD binding architectures