Quantum retrodiction in open systems

Quantum retrodiction involves finding the probabilities for various preparation events given a measurement event. This theory has been studied for some time but mainly as an interesting concept associated with time asymmetry in quantum mechanics. Recent interest in quantum communications and cryptography, however, has provided retrodiction with a potential practical application. For this purpose quantum retrodiction in open systems should be more relevant than in closed systems isolated from the environment. In this paper we study retrodiction in open systems and develop a general master equation for the backward time evolution of the measured state, which can be used for calculating preparation probabilities. We solve the master equation, by way of example, for the driven two-level atom coupled to the electromagnetic field.Comment: 12 pages, no figure

Measurement-driven dynamics for a coherently-excited atom

The phenomenon of telegraphing in a measurement-driven two-level atom was noted in Cresser et al. [Cresser, J.D.; Barnett, S.M.; Jeffers, J.; Pegg, D.T. Opt. Commun. 2006, 264, 352361]. Here we introduce two quantitative measures of telegraphing: one based on the accumulated measurement record and one on the evolution of the quantum state. We use these to analyse the dynamics of the atom over a wide range of parameters. We find, in particular, that the measures provide broadly similar statistics when the measurements are frequent, but differ widely when measurements are sparse. This is in line with intuition, and demonstrates the utility of both measures

Newtonian and Relativistic Cosmologies

Cosmological N-body simulations are now being performed using Newtonian gravity on scales larger than the Hubble radius. It is well known that a uniformly expanding, homogeneous ball of dust in Newtonian gravity satisfies the same equations as arise in relativistic FLRW cosmology, and it also is known that a correspondence between Newtonian and relativistic dust cosmologies continues to hold in linearized perturbation theory in the marginally bound/spatially flat case. Nevertheless, it is far from obvious that Newtonian gravity can provide a good global description of an inhomogeneous cosmology when there is significant nonlinear dynamical behavior at small scales. We investigate this issue in the light of a perturbative framework that we have recently developed, which allows for such nonlinearity at small scales. We propose a relatively straightforward "dictionary"---which is exact at the linearized level---that maps Newtonian dust cosmologies into general relativistic dust cosmologies, and we use our "ordering scheme" to determine the degree to which the resulting metric and matter distribution solve Einstein's equation. We find that Einstein's equation fails to hold at "order 1" at small scales and at "order $\epsilon$" at large scales. We then find the additional corrections to the metric and matter distribution needed to satisfy Einstein's equation to these orders. While these corrections are of some interest in their own right, our main purpose in calculating them is that their smallness should provide a criterion for the validity of the original dictionary (as well as simplified versions of this dictionary). We expect that, in realistic Newtonian cosmologies, these additional corrections will be very small; if so, this should provide strong justification for the use of Newtonian simulations to describe relativistic cosmologies, even on scales larger than the Hubble radius.Comment: 35 pages; minor change

Spatial opinion dynamics and the effects of two types of mixing

Spatially situated opinions that can be held with different degrees of conviction lead to spatiotemporal patterns such as clustering (homophily), polarization, and deadlock. Our goal is to understand how sensitive these patterns are to changes in the local nature of interactions. We introduce two different mixing mechanisms, spatial relocation and nonlocal interaction (“telephoning”), to an earlier fully spatial model (no mixing). Interestingly, the mechanisms that create deadlock in the fully spatial model have the opposite effect when there is a sufficient amount of mixing. With telephoning, not only is polarization and deadlock broken up, but consensus is hastened. The effects of mixing by relocation are even more pronounced. Further insight into these dynamics is obtained for selected parameter regimes via comparison to the mean-field differential equations

Retrodictive states and two-photon quantum imaging

We use retrodictive quantum theory to analyse two-photon quantum imaging systems. The formalism is particularly suitable for calculating conditional probability distributions.Comment: 5 pages, 3 figure

The Adiabatic Invariance of the Action Variable in Classical Dynamics

We consider one-dimensional classical time-dependent Hamiltonian systems with quasi-periodic orbits. It is well-known that such systems possess an adiabatic invariant which coincides with the action variable of the Hamiltonian formalism. We present a new proof of the adiabatic invariance of this quantity and illustrate our arguments by means of explicit calculations for the harmonic oscillator. The new proof makes essential use of the Hamiltonian formalism. The key step is the introduction of a slowly-varying quantity closely related to the action variable. This new quantity arises naturally within the Hamiltonian framework as follows: a canonical transformation is first performed to convert the system to action-angle coordinates; then the new quantity is constructed as an action integral (effectively a new action variable) using the new coordinates. The integration required for this construction provides, in a natural way, the averaging procedure introduced in other proofs, though here it is an average in phase space rather than over time.Comment: 8 page

Development of Analytical Models of T- and U-shaped Cantilever-based MEMS Devices for Sensing and Energy Harvesting Applications

Dynamic-mode cantilever-based structures supporting end masses are frequently used as MEMS/NEMS devices in application areas as diverse as chemical/biosensing, atomic force microscopy, and energy harvesting. This paper presents a new analytical solution for the free vibration of a cantilever with a rigid end mass of finite size. The effects of both translational and rotational inertia as well as horizontal eccentricity of the end mass are incorporated into the model. This model is general regarding the end-mass distribution/geometry and is validated here for the commonly encountered geometries of T- and U-shaped cantilevers. Comparisons with 3D FEA simulations and experiments on silicon and organic MEMS are quite encouraging. The new solution gives insight into device behavior, provides an efficient tool for preliminary design, and may be extended in a straightforward manner to account for inherent energy dissipation in the case of organic-based cantilevers

Portal vein thrombosis after laparoscopic splenectomy: an ongoing clinical challenge.

ObjectivesPortal vein thrombosis (PVT) following open splenectomy is a potentially lethal complication with an incidence of up to 6%. The objective of this report is to describe our management of a recent laparoscopic case, discuss current therapies, and consider antiplatelet therapy for prophylaxis.MethodsMedical records, laboratory studies, and imaging studies pertaining to a recent case of a laparoscopic splenectomy were examined. Current literature related to this topic was reviewed.ResultsA 16-year-old girl underwent laparoscopic splenectomy for idiopathic thrombocytopenic purpura. Her preoperative platelet count was 96K. She was discharged on postoperative day 1 after an uneventful operation including division of the splenic hilum with an endoscopic linear stapler. On postoperative day 20, she presented with a 5-day history of epigastric pain, nausea, and low-grade fevers without peritoneal signs. Her white blood cell count was 17.3; her platelets were 476K. Computed tomography demonstrated thrombosis of the splenic, superior mesenteric, and portal veins propagating into the liver. Heparinization was begun followed by an unsuccessful attempt at pharmacologic and mechanical thrombolysis by interventional radiology. Over the next 5 days, her pain resolved, she tolerated a full diet, was converted to oral anticoagulation and sent home. Follow-up radiographic studies demonstrated the development of venous collaterals and cavernous transformation of the portal vein.DiscussionNo standard therapy for PVT exists; several approaches have been described. These include systemic anticoagulation, systemic or regional medical thrombolysis, mechanical thrombolysis, and surgical thrombectomy. Unanswered questions exist about the most effective acute therapy, duration of anticoagulation, and the potential efficacy of routine prophylaxis with perioperative antiplatelet agents. PVT following splenectomy occurs with both the open and laparoscopic approach