Bosonic behavior of entangled fermions

Two bound, entangled fermions form a composite boson, which can be treated as an elementary boson as long as the Pauli principle does not affect the behavior of many such composite bosons. The departure of ideal bosonic behavior is quantified by the normalization ratio of multi-composite-boson states. We derive the two-fermion-states that extremize the normalization ratio for a fixed single-fermion purity P, and establish general tight bounds for this indicator. For very small purities, P<1/N^2, the upper and lower bounds converge, which allows to quantify accurately the departure from perfectly bosonic behavior, for any state of many composite bosons.Comment: 9 pages, 5 figures, accepted by PR

Integrative therapists’ clinical experiences of personal blind spots: an interpretative phenomenological analysis

This study uses Interpretative Phenomenological Analysis to explore integrative psychotherapists’ lived experience of recognising a personal blind spot in their therapeutic work. The five female participants aged between 42-60 years have between two and twenty years clinical experience. Each participant was interviewed on two separate occasions, with a period of one month between interviews. The inductive approach of IPA sought to capture the richness and complexity of participants’ lived emotional experiences. Given the methodological challenges uncovering the implicit domain of participants’ blind spots, researcher reflexivity served as a secondary but integral data source and provided the experiential context from which meaningful findings emerged. Three superordinate themes and seven subthemes emerged from the interviews: Feeling under pressure, Facing a Blind Spot and finding the missing piece, and Holding my own. Theme one explores participants’ loss of self-awareness when personal vulnerabilities are triggered by client work. It also describes maladaptive coping skills such as avoidance, employed to cope with feelings of vulnerability and shame. Theme two describes the process of facing a personal blind spot where participants recognise the impact of their personal needs and history on their therapeutic work. Theme three describes how self-compassion helps participants develop an expanded sense of self-awareness and capacity to be emotionally responsive to their clients despite their personal difficulties. The findings suggest that when shame is hidden and unacknowledged, it impacts on therapists’ ability to be emotionally responsive to their clients’ concerns. Furthermore, unacknowledged shame is a primary cause of therapeutic ruptures in their clinical work. The study recommends that continued research be undertaken into resilience towards shame in order to prepare and protect therapists against the normative force of subjective negative self-appraisal when they experience feelings of incompetence in their therapeutic work. Some aspects of these findings can be found in previous research on countertransference with participants of varying experience and varying therapeutic modalities. Given the centrality of the therapeutic relationship as a vehicle for successful therapeutic outcome, research that furthers our understanding of therapist emotional resilience and personal efficacy can help guide training and supervision

A Scalable Correlator Architecture Based on Modular FPGA Hardware, Reuseable Gateware, and Data Packetization

A new generation of radio telescopes is achieving unprecedented levels of sensitivity and resolution, as well as increased agility and field-of-view, by employing high-performance digital signal processing hardware to phase and correlate large numbers of antennas. The computational demands of these imaging systems scale in proportion to BMN^2, where B is the signal bandwidth, M is the number of independent beams, and N is the number of antennas. The specifications of many new arrays lead to demands in excess of tens of PetaOps per second. To meet this challenge, we have developed a general purpose correlator architecture using standard 10-Gbit Ethernet switches to pass data between flexible hardware modules containing Field Programmable Gate Array (FPGA) chips. These chips are programmed using open-source signal processing libraries we have developed to be flexible, scalable, and chip-independent. This work reduces the time and cost of implementing a wide range of signal processing systems, with correlators foremost among them,and facilitates upgrading to new generations of processing technology. We present several correlator deployments, including a 16-antenna, 200-MHz bandwidth, 4-bit, full Stokes parameter application deployed on the Precision Array for Probing the Epoch of Reionization.Comment: Accepted to Publications of the Astronomy Society of the Pacific. 31 pages. v2: corrected typo, v3: corrected Fig. 1

Random walk generated by random permutations of {1,2,3, ..., n+1}

We study properties of a non-Markovian random walk $X^{(n)}_l$, $l =0,1,2, >...,n$, evolving in discrete time $l$ on a one-dimensional lattice of integers, whose moves to the right or to the left are prescribed by the \text{rise-and-descent} sequences characterizing random permutations $\pi$ of $[n+1] = \{1,2,3, ...,n+1\}$. We determine exactly the probability of finding the end-point $X_n = X^{(n)}_n$ of the trajectory of such a permutation-generated random walk (PGRW) at site $X$, and show that in the limit $n \to \infty$ it converges to a normal distribution with a smaller, compared to the conventional P\'olya random walk, diffusion coefficient. We formulate, as well, an auxiliary stochastic process whose distribution is identic to the distribution of the intermediate points $X^{(n)}_l$, $l < n$, which enables us to obtain the probability measure of different excursions and to define the asymptotic distribution of the number of "turns" of the PGRW trajectories.Comment: text shortened, new results added, appearing in J. Phys.

A Physicist's Proof of the Lagrange-Good Multivariable Inversion Formula

We provide yet another proof of the classical Lagrange-Good multivariable inversion formula using techniques of quantum field theory.Comment: 9 pages, 3 diagram

Exact expressions for correlations in the ground state of the dense O(1) loop model

Conjectures for analytical expressions for correlations in the dense O$(1)$ loop model on semi infinite square lattices are given. We have obtained these results for four types of boundary conditions. Periodic and reflecting boundary conditions have been considered before. We give many new conjectures for these two cases and review some of the existing results. We also consider boundaries on which loops can end. We call such boundaries ''open''. We have obtained expressions for correlations when both boundaries are open, and one is open and the other one is reflecting. Also, we formulate a conjecture relating the ground state of the model with open boundaries to Fully Packed Loop models on a finite square grid. We also review earlier obtained results about this relation for the three other types of boundary conditions. Finally, we construct a mapping between the ground state of the dense O$(1)$ loop model and the XXZ spin chain for the different types of boundary conditions.Comment: 25 pages, version accepted by JSTA

Numerical Estimation of the Asymptotic Behaviour of Solid Partitions of an Integer

The number of solid partitions of a positive integer is an unsolved problem in combinatorial number theory. In this paper, solid partitions are studied numerically by the method of exact enumeration for integers up to 50 and by Monte Carlo simulations using Wang-Landau sampling method for integers up to 8000. It is shown that, for large n, ln[p(n)]/n^(3/4) = 1.79 \pm 0.01, where p(n) is the number of solid partitions of the integer n. This result strongly suggests that the MacMahon conjecture for solid partitions, though not exact, could still give the correct leading asymptotic behaviour.Comment: 6 pages, 4 figures, revtex