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

The mechanism of non-blocking inhibition of sodium channels revealed by conformation-selective photolabeling

Sodium channel inhibitors can be used to treat hyperexcitability-related diseases, including epilepsies, pain syndromes, neuromuscular disorders, and cardiac arrhythmias. The applicability of these drugs is limited by their nonspecific effect on physiological function. They act mainly by sodium channel block and in addition by modulation of channel kinetics. While channel block inhibits healthy and pathological tissue equally, modulation can preferentially inhibit pathological activity. An ideal drug designed to target the sodium channels of pathological tissue would act predominantly by modulation. Thus far, no such drug has been described.Patch-clamp experiments with ultra-fast solution exchange and photolabeling-coupled electrophysiology were applied to describe the unique mechanism of riluzole on Nav1.4 sodium channels. In silico docking experiments were used to study the molecular details of binding.We present evidence that riluzole acts predominantly by non-blocking modulation. We propose that, being a relatively small molecule, riluzole is able to stay bound to the binding site, but nonetheless stay off the conduction pathway, by residing in one of the fenestrations. We demonstrate how this mechanism can be recognized.Our results identify riluzole as the prototype of this new class of sodium channel inhibitors. Drugs of this class are expected to selectively prevent hyperexcitability, while having minimal effect on cells firing at a normal rate from a normal resting potential

The integrity of the HMR complex is necessary for centromeric binding and reproductive isolation in Drosophila

Postzygotic isolation by genomic conflict is a major cause for the formation of species. Despite its importance, the molecular mechanisms that result in the lethality of interspecies hybrids are still largely unclear. The genus Drosophila, which contains over 1600 different species, is one of the best characterized model systems to study these questions. We showed in the past that the expression levels of the two hybrid incompatibility factors Hmr and Lhr diverged in the two closely related Drosophila species, D. melanogaster and D. simulans, resulting in an increased level of both proteins in interspecies hybrids. The overexpression of the two proteins also leads to mitotic defects, a misregulation in the expression of transposable elements and decreased fertility in pure species. In this work, we describe a distinct six subunit protein complex containing HMR and LHR and analyse the effect of Hmr mutations on complex integrity and function. Our experiments suggest that HMR needs to bring together components of centromeric and pericentromeric chromatin to fulfil its physiological function and to cause hybrid male lethality

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

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.

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

Local Ca2+ signals couple activation of TRPV1 and ANO1 sensory ion channels

ANO1 (TMEM16A) is a Ca2+-activated Cl− channel (CaCC) expressed in peripheral somatosensory neurons that are activated by painful (noxious) stimuli. These neurons also express the Ca2+-permeable channel and noxious heat sensor TRPV1, which can activate ANO1. Here, we revealed an intricate mechanism of TRPV1-ANO1 channel coupling in rat dorsal root ganglion (DRG) neurons. Simultaneous optical monitoring of CaCC activity and Ca2+ dynamics revealed that the TRPV1 ligand capsaicin activated CaCCs. However, depletion of endoplasmic reticulum (ER) Ca2+ stores reduced capsaicin-induced Ca2+ increases and CaCC activation, suggesting that ER Ca2+ release contributed to TRPV1-induced CaCC activation. ER store depletion by plasma membrane–localized TRPV1 channels was demonstrated with an ER-localized Ca2+ sensor in neurons exposed to a cell-impermeable TRPV1 ligand. Proximity ligation assays established that ANO1, TRPV1, and the IP3 receptor IP3R1 were often found in close proximity to each other. Stochastic optical reconstruction microscopy (STORM) confirmed the close association between all three channels in DRG neurons. Together, our data reveal the existence of ANO1-containing multichannel nanodomains in DRG neurons and suggest that coupling between TRPV1 and ANO1 requires ER Ca2+ release, which may be necessary to enhance ANO1 activation

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