Inequivalence of pure state ensembles for open quantum systems: the preferred ensembles are those that are physically realizable

An open quantum system in steady state $\hat\rho_{ss}$ can be represented by a weighted ensemble of pure states $\hat\rho_{ss}=\sum_{k}\wp_{k}\ket{\psi_k} \bra{\psi_k}$ in infinitely many ways. A physically realizable (PR) ensemble is one for which some continuous measurement of the environment will collapse the system into a pure state $\ket{\psi(t)}$, stochastically evolving such that the proportion of time for which $\ket{\psi(t)} = \ket{\psi_{k}}$ equals $\wp_{k}$. Some, but not all, ensembles are PR. This constitutes the preferred ensemble fact, with the PR ensembles being the preferred ensembles. We present the necessary and sufficient conditions for a given ensemble to be PR, and illustrate the method by showing that the coherent state ensemble is not PR for an atom laser.Comment: 5 pages, no figure

Non-Markovian stochastic Schr\"odinger equations: Generalization to real-valued noise using quantum measurement theory

Do stochastic Schr\"odinger equations, also known as unravelings, have a physical interpretation? In the Markovian limit, where the system {\em on average} obeys a master equation, the answer is yes. Markovian stochastic Schr\"odinger equations generate quantum trajectories for the system state conditioned on continuously monitoring the bath. For a given master equation, there are many different unravelings, corresponding to different sorts of measurement on the bath. In this paper we address the non-Markovian case, and in particular the sort of stochastic \sch equation introduced by Strunz, Di\' osi, and Gisin [Phys. Rev. Lett. 82, 1801 (1999)]. Using a quantum measurement theory approach, we rederive their unraveling which involves complex-valued Gaussian noise. We also derive an unraveling involving real-valued Gaussian noise. We show that in the Markovian limit, these two unravelings correspond to heterodyne and homodyne detection respectively. Although we use quantum measurement theory to define these unravelings, we conclude that the stochastic evolution of the system state is not a true quantum trajectory, as the identity of the state through time is a fiction.Comment: 17 pages, 3 figure

Removal of a single photon by adaptive absorption

We present a method to remove, using only linear optics, exactly one photon from a field-mode. This is achieved by putting the system in contact with an absorbing environment which is under continuous monitoring. A feedback mechanism then decouples the system from the environment as soon as the first photon is absorbed. We propose a possible scheme to implement this process and provide the theoretical tools to describe it

Symbiotic modeling: Linguistic Anthropology and the promise of chiasmus

Reflexive observations and observations of reflexivity: such agendas are by now standard practice in anthropology. Dynamic feedback loops between self and other, cause and effect, represented and representamen may no longer seem surprising; but, in spite of our enhanced awareness, little deliberate attention is devoted to modeling or grounding such phenomena. Attending to both linguistic and extra-linguistic modalities of chiasmus (the X figure), a group of anthropologists has recently embraced this challenge. Applied to contemporary problems in linguistic anthropology, chiasmus functions to highlight and enhance relationships of interdependence or symbiosis between contraries, including anthropology’s four fields, the nature of human being and facets of being human

The steady state quantum statistics of a non-Markovian atom laser

We present a fully quantum mechanical treatment of a single-mode atomic cavity with a pumping mechanism and an output coupling to a continuum of external modes. This system is a schematic description of an atom laser. In the dilute limit where atom-atom interactions are negligible, we have been able to solve this model without making the Born and Markov approximations. When coupling into free space, it is shown that for reasonable parameters there is a bound state which does not disperse, which means that there is no steady state. This bound state does not exist when gravity is included, and in that case the system reaches a steady state. We develop equations of motion for the two-time correlation in the presence of pumping and gravity in the output modes. We then calculate the steady-state output energy flux from the laser.Comment: 14 pages (twocloumn), 6 figure

The Gisin-Percival stochastic Schrödinger equation from standard quantum filtering theory

We show that the quantum state diffusion equation of Gisin and Percival, driven by complex Wiener noise, is equivalent up to a global stochastic phase to quantum trajectory models. With an appropriate feedback scheme, we set up an analogue continuous measurement model with exactly simulates the Gisin-Percival quantum state diffusion.Comment: Originally submitted to a Theoretical Physics journal but rejected with the re-submission instructions to drop my discussion and references to the papers of Gisin and Percival, which I consider unethical. To be now submitted to an appropriate Mathematical Physics journal instea

Binary-induced collapse of a compact, collisionless cluster

We improve and extend Shapiro's model of a relativistic, compact object which is stable in isolation but is driven dynamically unstable by the tidal field of a binary companion. Our compact object consists of a dense swarm of test particles moving in randomly-oriented, initially circular, relativistic orbits about a nonrotating black hole. The binary companion is a distant, slowly inspiraling point mass. The tidal field of the companion is treated as a small perturbation on the background Schwarzschild geometry near the hole; the resulting metric is determined by solving the perturbation equations of Regge and Wheeler and Zerilli in the quasi-static limit. The perturbed spacetime supports Bekenstein's conjecture that the horizon area of a near-equilibrium black hole is an adiabatic invariant. We follow the evolution of the system and confirm that gravitational collapse can be induced in a compact collisionless cluster by the tidal field of a binary companion.Comment: 9 Latex pages, 14 postscript figure

Functionality of aryl hydrocarbon receptors (AhR1 and AhR2) of white sturgeon (Acipenser transmontanus) and implications for the risk assessment of dioxin-like compounds

ABSTRACT: Worldwide, populations of sturgeons are endangered, and it is hypothesized that anthropogenic chemicals, including dioxin-like compounds (DLCs), might be contributing to the observed declines in populations. DLCs elicit their toxic action through activation of the aryl hydrocarbon receptor (AhR), which is believed to regulate most, if not all, adverse effects associated with exposure to these chemicals. Currently, risk assessment of DLCs in fishes uses toxic equivalency factors (TEFs) developed for the World Health Organization (WHO) that are based on studies of embryo-lethality with salmonids. However, there is a lack of knowledge of the sensitivity of sturgeons to DLCs, and it is uncertain whether TEFs developed by the WHO are protective of these fishes. Sturgeons are evolutionarily distinct from salmonids, and the AhRs of sturgeons differ from those of salmonids. Therefore, this study investigated the sensitivity of white sturgeon (Acipenser transmontanus) to DLCs in vitro via the use of luciferase reporter gene assays using COS-7 cells transfected with AhR1 or AhR2 of white sturgeon. Specifically, activation and relative potencies (RePs) of 2,3,7,8-tetrachloro-dibenzo-p-dioxin (TCDD), 2,3,4,7,8-pentachlorodibenzofuran, 2,3,7,8-tetrachloro-dibenzofuran, 3,3′,4,4′,5-pentachlorobiphenyl, 3,3′,4,4′-tetrachlorobiphenyl, and 2,3,3′,4,4′-pentachlorobiphenyl were determined for each AhR. It was demonstrated that white sturgeon expresses AhR1s and AhR2s that are both activated by DLCs with EC 50 values for 2,3,7,8-TCDD that are lower than those of any other AhR of vertebrates tested to date. Both AhRs of white sturgeon had RePs for polychlorinated dibenzofurans more similar to TEFs for birds, while RePs for polychlorinated biphenyls were most similar to TEFs for fishes. Measured concentrations of select DLCs in tissues of white sturgeon from British Columbia, Canada, were used to calculate toxic equivalents (TEQs) by use of TEFs for fishes used by the WHO and TCDD equivalents (TCDD-EQs) via the use of RePs for AhR2 of white sturgeon as determined by transfected COS-7 cells. TCDD-EQs calculated for endangered populations of white sturgeon were approximately 10-fold greater than TEQs and were within ranges known to cause adverse effects in other fishes, including other species of sturgeons. Therefore, TEFs used by the WHO might not adequately protect white sturgeon, illuminating the need for additional investigation into the sensitivity of these fish to DLCs