We derive the filtering equation for Markovian systems undergoing homodyne measurement in the situation where the output processes being monitored are squeezed. The filtering theory applies to case where the system is driven by Fock noise (that, quan
tum input processes in a coherent state) and where the output is mixed with a squeezed signal. It also applies to the case of a system driven by squeezed noise, but here there is a physical restriction to emission/absorption coupling only. For the special case of a cavity mode where the dynamics is linear, we are able to derive explicitly the filtered estimate $pi_t (a)$ for the mode annihilator $a$ based on the homodyne quadrature observations up to time $t$.
The strong interaction between Rydberg atoms can be used to control the strength and character of the interatomic interaction in ultracold gases by weakly dressing the atoms with a Rydberg state. Elaborate theoretical proposals for the realization of
various complex phases and applications in quantum simulation exist. Also a simple model has been already developed that describes the basic idea of Rydberg dressing in a two-atom basis. However, an experimental realization has been elusive so far. We present a model describing the ground state of a Bose-Einstein condensate dressed with a Rydberg level based on the Rydberg blockade. This approach provides an intuitive understanding of the transition from pure twobody interaction to a regime of collective interactions. Furthermore it enables us to calculate the deformation of a three-dimensional sample under realistic experimental conditions in mean-field approximation. We compare full three-dimensional numerical calculations of the ground state to an analytic expression obtained within Thomas-Fermi approximation. Finally we discuss limitations and problems arising in an experimental realization of Rydberg dressing based on our experimental results. Our work enables the reader to straight forwardly estimate the experimental feasibility of Rydberg dressing in realistic three-dimensional atomic samples.
We present a mathematical model which explains and interprets a novel form of short-term potentiation, which was found to be use-, but not time-dependent, in experiments done on Lymnaea neurons. The high degree of potentiation is explained using a mo
del of synaptic metaplasticity, while the use-dependence (which is critically reliant on the presence of kinase in the experiment) is explained using a model of a stochastic and bistable biological switch.
Cells of almost all solid tissues are connected with gap junctions which permit the direct transfer of ions and small molecules, integral to regulating coordinated function in the tissue. The pancreatic islets of Langerhans are responsible for secret
ing the hormone insulin in response to glucose stimulation. Gap junctions are the only electrical contacts between the beta-cells in the tissue of these excitable islets. It is generally believed that they are responsible for synchrony of the membrane voltage oscillations among beta-cells, and thereby pulsatility of insulin secretion. Most attempts to understand connectivity in islets are often interpreted, bottom-up, in terms of measurements of gap junctional conductance. This does not, however explain systematic changes, such as a diminished junctional conductance in type 2 diabetes. We attempt to address this deficit via the model presented here, which is a learning theory of gap junctional adaptation derived with analogy to neural systems. Here, gap junctions are modelled as bonds in a beta-cell network, that are altered according to homeostatic rules of plasticity. Our analysis reveals that it is nearly impossible to view gap junctions as homogeneous across a tissue. A modified view that accommodates heterogeneity of junction strengths in the islet can explain why, for example, a loss of gap junction conductance in diabetes is necessary for an increase in plasma insulin levels following hyperglycemia.
The coupling of electrons to matter is at the heart of our understanding of material properties such as electrical conductivity. One of the most intriguing effects is that electron-phonon coupling can lead to the formation of a Cooper pair out of two
repelling electrons, the basis for BCS superconductivity. Here we study the interaction of a single localized electron with a Bose-Einstein condensate (BEC) and show that it can excite phonons and eventually set the whole condensate into a collective oscillation. We find that the coupling is surprisingly strong as compared to ionic impurities due to the more favorable mass ratio. The electron is held in place by a single charged ionic core forming a Rydberg bound state. This Rydberg electron is described by a wavefunction extending to a size comparable to the dimensions of the BEC, namely up to 8 micrometers. In such a state, corresponding to a principal quantum number of n=202, the Rydberg electron is interacting with several tens of thousands of condensed atoms contained within its orbit. We observe surprisingly long lifetimes and finite size effects due to the electron exploring the wings of the BEC. Based on our results we anticipate future experiments on electron wavefunction imaging, investigation of phonon mediated coupling of single electrons, and applications in quantum optics.
In this paper we demonstrate connections between three seemingly unrelated concepts. (1) The discrete isoperimetric problem in the infinite binary tree with all the leaves at the same level, $ {mathcal T}_{infty}$: The $n$-th edge isoperimetric n
umber $delta(n)$ is defined to be $min_{|S|=n, S subset V({mathcal T}_{infty})} |(S,bar{S})|$, where $(S,bar{S})$ is the set of edges in the cut defined by $S$. (2) Signed almost binary partitions: This is the special case of the coin-changing problem where the coins are drawn from the set ${pm (2^d - 1): $d$ is a positive integer}$. The quantity of interest is $tau(n)$, the minimum number of coins necessary to make change for $n$ cents. (3) Certain Meta-Fibonacci sequences: The Tanny sequence is defined by $T(n)=T(n{-}1{-}T(n{-}1))+T(n{-}2{-}T(n{-}2))$ and the Conolly sequence is defined by $C(n)=C(n{-}C(n{-}1))+C(n{-}1{-}C(n{-}2))$, where the initial conditions are $T(1) = C(1) = T(2) = C(2) = 1$. These are well-known meta-Fibonacci sequences. The main result that ties these three together is the following: $$ delta(n) = tau(n) = n+ 2 + 2 min_{1 le k le n} (C(k) - T(n-k) - k).$$ Apart from this, we prove several other results which bring out the interconnections between the above three concepts.
We obtain an exact finite-size expression for the probability that a percolation hull will touch the boundary, on a strip of finite width. Our calculation is based on the q-deformed Knizhnik--Zamolodchikov approach, and the results are expressed in t
erms of symplectic characters. In the large size limit, we recover the scaling behaviour predicted by Schramms left-passage formula. We also derive a general relation between the left-passage probability in the Fortuin--Kasteleyn cluster model and the magnetisation profile in the open XXZ chain with diagonal, complex boundary terms.
We present a model of predatory traders interacting with each other in the presence of a central reserve (which dissipates their wealth through say, taxation), as well as inflation. This model is examined on a network for the purposes of correlating
complexity of interactions with systemic risk. We suggest the use of selective networking to enhance the survival rates of arbitrarily chosen traders. Our conclusions show that networking with doomed traders is the most risk-free scenario, and that if a trader is to network with peers, it is far better to do so with those who have less intrinsic wealth than himself to ensure individual, and perhaps systemic stability.
The Antarctic Impulsive Transient Antenna (ANITA) completed its second long-duration balloon flight in January 2009, with 31 days aloft (28.5 live days) over Antarctica. ANITA searches for impulsive coherent radio Cherenkov emission from 200 to 1200
MHz, arising from the Askaryan charge excess in ultra-high energy neutrino-induced cascades within Antarctic ice. This flight included significant improvements over the first flight in the payload sensitivity, efficiency, and a flight trajectory over deeper ice. Analysis of in-flight calibration pulses from surface and sub-surface locations verifies the expected sensitivity. In a blind analysis, we find 2 surviving events on a background, mostly anthropogenic, of 0.97+-0.42 events. We set the strongest limit to date for 1-1000 EeV cosmic neutrinos, excluding several current cosmogenic neutrino models.
The MAGIC collaboration recently reported the detection of the quasar 3C279 at > 100 GeV gamma-ray energies. Here we present simultaneous optical (BVRI) and X-ray (RXTE PCA) data from the day of the VHE detection and discuss the implications of the s
nap-shot spectral energy distribution for jet models of blazars. A one-zone synchrotron-self-Compton origin of the entire SED, including the VHE gamma-ray emission can be ruled out. The VHE emission could, in principle, be interpreted as Compton upscattering of external radiation (e.g., from the broad-line regions). However, such an interpretation would require either an unusually low magnetic field of B ~ 0.03 G or an unrealistically high Doppler factor of Gamma ~ 140. In addition, such a model fails to reproduce the observed X-ray flux. This as well as the lack of correlated variability in the optical with the VHE gamma-ray emission and the substantial gamma-gamma opacity of the BLR radiation field to VHE gamma-rays suggests a multi-zone model. In particular, an SSC model with an emission region far outside the BLR reproduces the simultaneous X-ray -- VHE gamma-ray spectrum of 3C279. Alternatively, a hadronic model is capable of reproducing the observed SED of 3C279 reasonably well. However, the hadronic model requires a rather extreme jet power of L_j ~ 10^{49} erg s^{-1}, compared to a requirement of L_j ~ 2 X 10^{47} erg s^{-1} for a multi-zone leptonic model.
