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Jill Disis, email@example.com 3:16 p.m. EST November 24, 2015
Marion County Prosecutor Denise Robinson discusses details about the Amanda Blackburn case. Two suspects appeared in court Tuesday. (Jill Disis / The Star)
1:07 p.m. update: The Marion County Prosecutor’s Office has requested an enhancement on the murder charge filed against a suspect in the Amanda Blackburn killing because Blackburn was pregnant.
If Larry Taylor is convicted of Blackburn’s murder, the enhancement could add an additional six to 20 years behind bars. Blackburn was 12 weeks pregnant when she died.
The enhancement would come into play should Taylor be convicted of or plead guilty to murder, according to prosecutor’s office spokeswoman Peg McLeish. At that point, she said, the state would have to make its case that the killing caused the termination of Blackburn’s pregnancy.
10:34 a.m. update: The two men facing murder charges in Amanda Blackburn’s slaying appeared at a court hearing Tuesday, where a judge entered not guilty pleas for them.
During the 20-minute hearing, public defenders were assigned to Taylor and Watson, who gave “yes” and “no” answers to the judge’s perfunctory questions.
Tuesday’s court appearance will also likely be the last until Jan. 8, when the two are scheduled for a pre-trial conference hearing. In the meantime, local authorities will be tasked with processing additional evidence taken from the crime scenes — something officials expect will take time to resolve.
“It doesn’t quite work like on television,” said Marion County Deputy Prosecutor Denise Robinson. “It’s a process that can take weeks and into months in this case. So the crime lab has quite a bit of work to do on the case.”
Robinson said Taylor’s case could be under consideration for the death penalty, though she added that process has yet to be started.
Uncertainty also swirls around the fate of Diano Gordon, a third man police have accused of being involved in the string of burglaries that led to Blackburn’s death. Gordon, who is named in a probable cause affidavit, has not been charged. Robinson said prosecutors are waiting for test results and other information before determining what charges may be filed against him.
Gordon is currently being held at the Marion County Jail on an unrelated parole violation.
Earlier: The crime spree that ended Amanda Blackburn’s life began with a series of burglaries carried out across the Northside of Indianapolis.
The Blackburn home was the third burglary in the early-morning hours of Nov. 10. The perpetrators, police said, were after money. But the chaos ended around 7 a.m., police said, when one of the suspects — a teenager — leaned over Blackburn’s body and shot her in the back of the head.
Then he leaned further, police said. He looked at her face. And he watched her bleed.
That harrowing account of events was made public Monday as the city’s top law enforcers announced a slew of charges against two suspects, accused triggerman Larry Taylor, 18, and suspected accomplice Jalen Watson, 21.
“We promised you … that we would go after those violent individuals in our community,” Indianapolis Metropolitan Police Chief Rick Hite said. “(Police) put in a lot of time to bring justice.”
Taylor was charged with 13 counts, including murder, burglary, theft, robbery, criminal confinement, auto theft and a misdemeanor count of carrying a handgun without a license. Watson is facing 10 counts, including murder, burglary, theft, robbery and auto theft.
A third person suspected of involvement, 24-year-old Diano Gordon, is mentioned in court documents and was named at a news conference Monday, but he has not been charged. Officials say Gordon is being held in the Marion County Jail on an unrelated parole violation. It’s unclear what type of charges, if any, might be filed against him.
The arrests came nearly two weeks after Blackburn’s husband, Davey Blackburn, found his wife in critical condition in their shared home on Sunnyfield Court. Amanda Blackburn, 28, was 12 weeks pregnant when she was shot multiple times. She died two days later.
The Blackburns, who moved to Indianapolis from South Carolina two years ago and founded Resonate Church, drew significant interest across the country as Davey Blackburn began speaking out on national media about his wife’s death.
He released a statement Monday after receiving news of the arrests.
“Though everything inside of me wants to hate, be angry and slip into despair, I choose the route of forgiveness, grace and hope,” a portion of the statement read. “Today I am deciding to love, not hate. Today I am deciding to extend forgiveness, not bitterness. Today I am deciding to hope, not despair. By Jesus’ power at work within us, the best is still yet to come.”
Newly released court documents reveal the most complete account yet of how investigators think the crime happened — along with how, through a combination of DNA testing, cellphone records, surveillance footage and cooperating individuals, investigators ultimately pinned their suspects.
The timeline detailed in charging documents began around 4:30 a.m. the day Blackburn was shot, when a woman living about 10 miles from the Blackburn home awoke to find her apartment burglarized. She told police that burglars stole her cellphone, laptop, purse, keys and 2007 Chrysler Sebring. The woman’s security system, court documents say, took pictures of three people.
Police claim the Sebring became a getaway vehicle as the suspects drove across town to burglarize more homes in the 2800 block of Sunnyfield Court. One home on that block was burglarized around 5:30 a.m. Court documents say the men ripped a window screen and unlocked a patio door before stealing a laptop, Tiffany pearl necklace, pink sweater, bag of oranges, four televisions and other items.
The Blackburn home, two doors down on Sunnyfield, was targeted next. Police said the suspects entered the unlocked door after Davey Blackburn left to go to a gym at 6:11 a.m.
According to court documents, the men did not immediately decide to kill Amanda Blackburn. Instead, documents allege Taylor hit her with his gun, stole her bank cards and threw them in the getaway car with Watson and Gordon. Those two then drove to two ATMs, attempting to withdraw money. They communicated several times via phone with Taylor, who remained in the Blackburn house.
A cooperating individual who is unidentified in court records provided a narrative of that morning to police. That person told investigators that the two men in the car planned to leave Taylor behind after successfully withdrawing money from an ATM on 86th Street. But Taylor, court documents say, “threatened to kill the woman if they left him.”
Ultimately, the two decided to return for Taylor. Court documents attribute that decision to another person who called them and said Taylor was “family” and could not be left behind.
It’s not clear when Blackburn was shot. A neighbor later told police she heard two gunshots and what sounded like a woman’s scream about 6:45 a.m. According to the unidentified cooperating individual, Taylor later told several people that he shot Blackburn in the back of the head.
After picking up Taylor, court documents say, the two men dropped him off in a different neighborhood with a bag of stolen property and stashed the Sebring elsewhere.
That Sebring, which was recovered late Nov. 11 about 3 miles east of the Blackburn home, would later become the first piece of evidence that helped investigators track down their suspects. Inside the stolen vehicle, police found a denied ATM transaction notice for Blackburn’s missing debit card.
More critically, detectives also found a pink sweater stolen from the other home on Sunnyfield Court. That evidence, Marion County Prosecutor Terry Curry said, gave officials a “significant break” in the case via a DNA swab.
DNA found on the sweater was run through the FBI’s DNA index system. It returned a match for Watson, who has a prior felony conviction for burglary. Court documents claim Watson used the sweater to conceal his face as he attempted to use Blackburn’s stolen debit card at area ATMs.
Pieces began falling into place with that match. Investigators pulled phone numbers they say belonged to Watson and Gordon, whom they identified as close associates. According to phone records, their numbers pinged cell towers in areas where the Nov. 10 burglaries occurred.
Phone records also placed Taylor’s phone at the scene of the crime. Additional research led investigators to Taylor, who was interviewed Thursday.
During that interview, Taylor would tell police only that he “possibly” rode in the Sebring and stopped on Sunnyfield Court, claiming he “was so messed up he could not remember.” Watson and Gordon also were taken into custody that day on unrelated parole violations after questioning about the killing.
Taylor, meanwhile, would not elude arrest for long. Saturday, court documents say, police interviewed the unnamed “cooperating individual” who gave them the sequence of events leading to Blackburn’s death — including a confession to the killing from Taylor himself. Taylor was arrested late Sunday.
That person characterized the crimes as motivated by greed, telling investigators the group “wanted more money” as they drove to their targets.
Ultimately, the unnamed individual told police, Taylor confessed to the crime at a later rendezvous point, where he told several people “he killed the woman.”
“Taylor stated that she charged at him and he shot her somewhere in the upper body so he would not be scratched,” the person told police.
Then Taylor shot her in the back of the head.
IndyStar reporter Justin Mack on Monday’s developments in the Amanda Blackburn homicide case.
Star reporters Madeline Buckley and Vic Ryckaert contributed to this story. Call Star reporter Jill Disis at (317) 444-6137. Follow her on Twitter: @jdisis.
One of the main ways US policy encourages the uptake of new clean energy and energy efficiency technologies is through the use of tax credits. There are tax credits for qualified windows, boilers, air conditioners, insulation, and more.
The US is something of an outlier in this. In the KPMG Green Tax Index — a ranking of countries according how much they use tax penalties and incentives to achieve sustainability goals — the US ranks number one. Notably, the US is 14th in the use of tax penalties. It is America’s profligate use of tax incentives, mainly tax credits, that vaults it to number one overall.
Some new research brings troubling news about those tax credits. To put it bluntly: They are highly inequitable. Most of the money goes to relatively affluent consumers.
Let’s look quickly at the research, touch on how the credits might be improved, and then discuss the political implications.
Clean energy tax credits mostly accrue to the affluent
The research was done by Severin Borenstein and Lucas Davis at the Energy Institute at HAAS, in UC Berkeley. (An early blog post on the conclusions is here. A slideshow summary is here. The full paper is here.) Borenstein and Davis use IRS tax return data to profile the recipients of federal clean energy tax credits. They focused on the five biggest:
Between 2006 and 2012 the largest categories of investments were energy-efficient windows ($4.0 billion), qualified furnaces ($2.4 billion), qualified air conditioners and water heaters ($2.4 billion), ceiling and wall insulation ($2.0 billion), and solar photovoltaic systems ($1.8 billion).
Here’s what the spread looks like for residential energy credits:
I will spare you the graphs for the other credits, because they look more or less the same, with higher income filers claimed larger credits and a larger overall portion of the credit money.
Bottom line, of the $18 billion spent on federal energy tax credits since 2006:
The bottom three income quintiles have received about 10% of all credits, while the top quintile has received about 60%. The most extreme is the program aimed at electric vehicles, where we find that the top income quintile has received about 90% of all credits.
This is regressive. Is it more regressive than alternatives? Yes.
Other “tax expenditures” in general, and most other tax credits in particular, are also regressive. (The main exception is the earned income tax credit.) But they are not as regressive as these energy credits. A carbon tax that returns the revenue through tax or lump sum rebates is also less regressive.
Energy tax credits are also “horizontally inequitable,” in that they exclude large number of people who might otherwise be eligible.
For one thing, they are “nonrefundable,” which means they only pay out insofar as you have tax liability. They can’t push your tax liability below zero. And if your federal income tax liability is already zero — like 40 percent of Americans — you’re not eligible at all.
Also, energy tax credits exclude the entire rental market. Renters can’t make capital investments in their homes, and landlords often face split incentives.
Both these features exacerbate the inequity of the credits, as they disproportionately exclude those with lower income.
This suggests a couple of obvious, immediate ways to improve energy tax credits. First, they should be made refundable. It’s absurd that they aren’t — there’s no policy rationale for it. And second, there should be more attention to how to create incentives for landlords. (That’s a complicated subject best saved for another post.)
What about broader implications? I would offer a few considerations in (somewhat unenthusiastic) defense of energy tax credits.
Not everything is a climate policy
The main point of the research, indeed something of an obsession among economists generally and EI @ HAAS economists specifically, is that energy tax credits are less effective than price-based instruments like a carbon tax. To most economists, climate policies are either a carbon price or “second best.” We needn’t rehearse all that again.
I’ll just say that not everything is a climate policy, i.e., not everything should be judged on how cost-effectively it reduces net carbon emissions. A carbon tax targets that metric directly and is most likely to optimize for it. But in this fallen world of ours, so full of sin and temptation, policymakers sometimes target things other than economy-wide, technology-neutral, economically optimal means to social ends. Sometimes they want particular domestic industries or markets to grow, and carbon taxes are a roundabout means to that end. Instead, we get industrial policy, which is as old as industry itself.
(Is it helping those industries? The paper also compares sales of energy technologies before and after the credits are implemented and concludes they had little impact, but that conclusion seems more tentative to me.)
Not everything is redistributive
Borenstein and Davis conclude that “it would seem to be difficult to argue for these policies on distributional grounds.” And that’s true. But maybe they don’t need to be justified on those grounds. Progressivity is a valuable overall goal for policy, but not every individual policy has to have progressive impacts. Certainly it’s easy to imagine any number of policies (including, for example, a boost in the EITC) that could easily offset the regressivity of energy tax credits.
Beyond that, if the US had guaranteed health care, housing, and basic income, like the Scandinavian countries beloved by Bernie Sanders, the particular distributional effects of small-bore clean energy policies would probably be of much less concern. Sigh.
New markets tend to skew toward the wealthy
Almost any policy meant to stimulate fledgling markets is going to benefit better-off customers, because new technologies tend to be expensive, and better-off customers are the ones with money. Cellphones started out as a tool of the idle rich; now they are key to the economic well-being of hundreds of millions in the developing world. Solar panels, electric cars, and hyperefficient boilers are following the same path. But in the beginning, it’s inevitably going to be wealthier people driving demand.
What is the political alternative to tax credits?
Yes, tax credits kind of suck as policy, but … compared to what?
The reason the US tops the world in tax incentives is that they are a perfect hack of our dysfunctional political economy. For decades, conservatives have demonized taxes and put in place balanced budget and paygo laws. Consequently, politicians aren’t allowed to talk about raising taxes, except on the very rich.
However, if you give a favored company or industry a tax break, you’re not raising taxes at all. You’re lowering them! Now you can indulge in industrial policy and maintain your small-government bona fides at the same time. Sweet deal.
Of course, the impact on the federal budget is exactly the same. Whether it’s a tax break or a direct subsidy, it’s a federal expenditure; it leaves the feds with less revenue. But the semantics makes all the difference in a context where taxes are demonized.
Thus, more and more policy is channeled through tax expenditures. They are tucked away in the tax code; for the most part, only the industry that benefits from them even knows they exist (and works to maintain them). Because they’re hidden, and because they are skewed to those with federal tax liability, they tend to be strongly regressive.
What’s worse, many of the consumers who benefit from them don’t even know it. The submerged state tends to act through private business, via taxes, and thus manifests to the consumer as the private sector. So people have no idea what government is doing for them (or to them).
It’s a bad scene, pretty much designed for rent seeking. But what are clean energy interests supposed to do, unilaterally disarm? US politics is more dysfunctional than ever. There’s no carbon tax on the horizon. And even if there were, there would still be social and economic reasons to support growth in particular domestic markets.
Tax expenditures aren’t even a “second best” policy. They’re much farther down the list than that. But in the current political economy, they may be an “only possible” policy, in which case the relevant comparison is not a carbon tax, but nothing at all.
Interpretive dance. Is there anything it can’t do?
Sure, most people use it to express the subtleties of the human experience and the innermost fluctuations of the soul, but if you’re Florence Metz, you use it for a wholly different purpose: to explain your doctoral thesis on water protection policy.
Metz, a graduate student at Switzerland’s University of Bern, is the winner of this year’s “Dance Your Ph.D.” contest, beating out 31 other doctoral theses for the annual competition’s top honor. Metz’s routine, based on her work studying the policies around water protection and conservation, tops off at just under 10 minutes, in which “several dancing styles (hip-hop, house, salsa, acrobatics) stand for diverse political groups, which fight over the use and the protection of water resources.”
Now in its eighth year, the Dance Your Ph.D. contest is split into four categories: Social Sciences, Chemistry, Physics, and Biology. Winners in each category take home $500, with Metz’s grand-prize-winning routine earning her an additional $500, as well as a trip to Stanford University for a special screening of her dance video.
The winners in the contest’s other categories:
Biology: Pearl Lee, a Ph.D. student at Australia’s University of Sydney, for “Cellular interactions with tropoelastin.”
Physics: Merritt Moore, a Ph.D. student at the University of Oxford, for “Exploring multi-photon states for quantum information applications.”
And Jyaysi Desai, a Ph.D. student at the Ludwig Maximilian University of Munich, for “Molecular mechanisms involved in neutrophil extracellular trap (NET) formation,” which won both the Chemistry and Audience Favorite awards.
While silly and fun, the contest is also a fairly serious attempt to bridge the gap between high-level scientific study and broader appreciation outside what might otherwise be a siloed field. The contest explains on its website:
A panel of judges will score each Ph.D. dance with 3 parameters: scientific merit, artistic merit, and creative combination of the science and art. Basically, to win this contest, you have to impress the judges. Some of them are scientists, some of them are artists. Your dance has to convey something essential about your Ph.D. research. Whatever that is, the judges need to “get it”. But you also have to make something that is fun to watch. Sure, it can be funny. But if so, it should also be impressively creative. And put some effort into the “Description” text for your video. This is really important. Steer clear of jargon.
Metz’s prize marks the first time in the contest’s eight years that a social scientist has won top honors. As she told the publication Science, which sponsors the dance-off: “My main aim with this video was to make people laugh. This bridge between academia and the nonacademic world is crucial.”
The complete list of entry videos can be found here.
The United States’ senior population is growing quickly, and so is the need to manage their care. Most seniors want to remain at home rather than spend their final days in a nursing home, which presents the seniors and those who care for them a thorny problem.
Software developer People Power thinks it has a solution based on its DIY home-security system. The company thinks that with some minor modifications, its Presence app—which supports a variety of sensors and can convert any Android or iOS device with a camera into a home security camera—can be put to use for in-home elder care.
People Power is calling the service Presence Pro Care, and has launched an Indiegogo campaign to support its efforts. In addition to the preexisting features ported from its security service, Presence Pro Care will track medications and monitor a person’s daily activities. The data is then analyzed, and caregivers are notified if the service notices any aberrations in the person’s daily routine.
Currently the service is expected to retail for anywhere from $149 to $699, depending on the features purchased, when it starts shipping in mid-2016. A $15-per-month service charge will also apply.
Why this matters: If you’ve ever been a part of elder care and the decision-making process that comes with it, you know why People Power’s planned service makes sense. Often the biggest disputes between family, caregivers, and those being cared for is the ability to stay at home and live independently. There is data that suggests those who stay out of nursing homes live longer, so something like Presence Pro Care would be an option.
Help, I’ve fallen and I can’t get up!
Presence Pro Care still offers the same functionality that services like Life Alert do, including the alert button pendant that most people are already familiar with. From there the service is significantly different, as it not only calls emergency responders, but also alerts a predetermined group of caregivers to incidents as well.
The monitoring services are also much better. To date, most services have focused on the reactive—i.e., the pendant button—and not the proactive, where monitoring plays a large part in the service offering. Here problems are acted upon without the need for the person to initiate them.
This is the reason why many of us—including myself—have had to go against the interests of those being cared for safety’s sake. Visiting nurses and in-home caregivers are prohibitively expensive, and often not an option.
That said, something like People Power’s planned service could be welcome news for those who would rather not have to make that difficult decision.
On Monday, Shares of Energy Transfer Equity LP (NYSE:ETE), lost -0.23% to $19.01.
Energy Transfer Partners, and Sunoco, declared the dropdown to SUN of the remaining 68.42% interest in Sunoco, LLC and 100% interest in the legacy Sunoco retail business for about $2.226 billion. The transaction will be effective as of January 1, 2016 and is predictable to close in February 2016.
SUN will pay to ETP about $2.2 billion in cash (counting the predictable value of working capital) and will issue to ETP about 5.7 million SUN common units valued at about $194 million based on the five-day volume-weighted average price of SUN’s common units as of November 13, 2015. Pro forma for the dropdown transaction and related equity private placement, ETP will remain the largest unit holder of SUN with an approximate 46% LP interest , reflecting ETP’s continued confidence in SUN’s business and future growth prospects.
The timing of this dropdown transaction is driven by the view that accelerating the dropdown of the remaining retail marketing and wholesale fuel assets to SUN was in the best interest of all parties. SUN anticipates that, following the completion of this transaction, it will not need to raise any additional equity financing in 2016. The transaction is also predictable to be credit neutral to SUN and to be accretive to distributable cash flow and predictable distributions per unit for SUN in 2016 and thereafter.
Energy Transfer Equity, L.P., through its auxiliaries, provides diversified energy-related services in the Unites States. It owns and operates about 7,700 miles of natural gas transportation pipelines and 3 natural gas storage facilities located in the state of Texas; and about 12,800 miles of interstate natural gas pipeline.
Shares of CTI Bio Pharma Corp (NASDAQ:CTIC), inclined 9.09% to $1.20, during its last trading session.
CTI Bio Pharma Corp. (CTI Bio Pharma or the Company) (NASDAQ and MTA: CTIC), declared that the United Kingdom’s National Cancer Research Institute (NCRI) Haematological Oncology Clinical Studies Group has chosen to advance tosedostat, the Company’s investigative oral aminopeptidase inhibitor, to the second stage of a randomized clinical trial of low-dose cytarabine plus or minus tosedostat in older patients with Acute Myeloid Leukemia (AML) or high risk Myelodysplastic Syndrome (MDS). The AML Less Intensive (LI-1) trial is designed as a “Pick-a-Winner” trial to be able to simultaneously test a number of promising agents added to standard therapy with low-dose cytarabine in older patients with AML or MDS who are unfit for standard aggressive induction therapy. Nine regimens have been tested in the Pick-a-Winner program, of which only 4, counting tosedostat, have passed the initial hurdle for progression (which requires evidence of an improvement in remission rate with acceptable safety). The ultimate aim of the trial is to identify treatments that can double the 2-year survival of patients in this group. Based on the randomized Phase 2 interim analysis, the trial administration group determined that tosedostat should proceed to the next stage of the study. It is anticipated that an additional 110 patients will be required in such phase. A further evaluation will take place before the intended expansion to a 400 patient Phase 3 trial.
Tosedostat is a potential first-in-class selective inhibitor of aminopeptidases, which are enzymes required by some tumor cells, but not normal cells, to provide a source of amino acids necessary for growth and tumor cell survival.
“A large portion of older patients and patients with comorbid conditions are poorly suited for conventional intensive chemotherapy due to a high rate of treatment-related mortality. For these patients, there is a noteworthy un met need for effective and well tolerated alternative therapies,” said Jack Singer, M.D., Chief Scientific Officer of CTI Bio Pharma. “We are happy that tosedostat has been selected to continue in this trial and is moving forward to the next stage. Tosedostat has demonstrated encouraging clinical activity in three preceding Phase 2 studies in both first-line AML in older patients and in patients who relapsed following standard therapies. Tosedostat is an oral agent given once daily on an outpatient basis that has not been associated with drug-related blood count suppression.”
CTI Bio Pharma Corp., a biopharmaceutical company, engages in the acquisition, development, and commercialization of novel targeted therapies for blood-related cancers in the United States and internationally. It primarily focuses on the commercialization of PIXUVRI, an aza-anthracenedione derivative for the treatment of adult patients with multiply relapsed or refractory aggressive B-cell non-Hodgkin lymphoma in the European Union.
Finally, Shares of Master card Inc (NYSE:MA), ended its last trade with -0.12% loss, and closed at $99.38.
Business Wire declares the newest episode of Biz Wire TV Accelerator Report, part of their Biz Wire TV news-show series. Now available on www.BusinessWire.com, the show serves as a preview of forthcoming IPOs, planned earnings declarations, recent funding declarations and trends to watch in the forthcoming week.
This week’s episode features:
Sprint (NYSE:S) introduces biggest wireless offer in U.S. history. Tweet this!
MasterCard (MA) is giving support to nearly 40 early-stage companies in its first global Start Path class. Tweet this!
ElMindA raises $28 million in series C financing. Tweet this!
Liquid Asset Brands LLC and Spirits Investment Partners LLC make $14 million investment in Stolen Spirits. Tweet this!
AirGrub declares $1.5 million in funding. Tweet this!
Plus, a preview of some forthcoming market moving events such as Existing Home Sales, GDP, Consumer Confidence, Durable Goods Orders, Jobless Claims and New Home Sales.
BizWireTV and BizWireTV Accelerator Report are hosted by Erin Ade. Tune in to watch Erin’s reports for BizWireTV each Sunday and Friday
MasterCard Incorporated, a technology company, provides transaction processing and other payment-related products and services in the United States and internationally. The company facilitates the processing of payment transactions, counting authorization, clearing, and settlement, in addition to delivers related products and services.
In preceeding work it has been shown that diagrammatic transport13,14 gives precise results for diffusive and localizing photons in complex random media. We constitute a diagrammatic field theory ansatz for light in a diffusive system including interferences15,16 that incorporates non-linear effects and gain. All types of light-matter interactions depend not only on the material and the passive refractive index as well as the mobility of electrons, but further on the locally impinging light intensity, the photon number. It has to be pointed out, that the refractive index of the scatterers has to be renormalized selfconsistently due to intense pumping. This is equivalent to a shift of the gain spectrum with respect to impinging intensity taking into account in this case that the threshold of a random laser is defined as the stationary state. Consequentially we treat second order non-linear response of the bulk material when the order is defined in the electromagnetic field E. It has been seen in the previous section, that gain processes –Imϵs lead to a retardation of coherent intensity due to a finite life-time of the electronic excitation. ϵs is the permittivity of the scatterer. Frequency conversion, in other words spectral loss or gain, leads to a change of the photon statistics respectively. The refractive index of the material is responding to these processes and especially it is responding due to spatially non-uniform or non-homogeneous procedures. These procedures are present in every system containing any boundary, meaning in any realistic setup.
Theoretically the non-linearity is established by a doubly nested self-consistency: In the following we line out the description for correlation and coherence of light in terms of the electromagnetic wave and the photon as particle.
The photon density response, the four-point correlator is derived from the Bethe-Salpeter equation of photons,
that is in the most essential form written including six independent position coordinates
The indices mark independent positions within space. Primes denote the selfconsistency procedure of the diagram. The irreducible vertex γ in Eq. (2) is the heart of the formalism. It contains all possible interference effects enhanced by maximally crossed diagrams (Cooperons) which lead to a sophisticated current relaxation kernel, the memory term that renormalizes the diffusion constant D. We emphasize here that we assume independent monodisperse scatterers here and the Cooperon diagram is the leading order diagram under ensemble average where physically relevant system size is larger than the wavelength of light. The importance of the Cooperon has been clearly proven from our considerations of Anderson localizing systems in transmission with qualitative as well as quantitative validity13. The memory kernel is crucial for the random laser mode. It establishes spatial correlation and coherence whereas the temporal coherence of lasing emission is driven by the interplay between these transport processes and the non-linear response of the material. The Ward identity as such is the vital feature in photonic transport and in diagrammatic theory of two-particle propagators in general. It connects the single-particle Feynman-graph with the two-particle quantity17,18 in conserving media (Imϵs = Imϵb = 0), and in recent work15 it is generalized to guarantee local energy conservation, or specifically energy non-conservation for complex matter.
We write the Bethe-Salpeter equation as Boltzmann- or kinetic equation Eq. (4). The Fourier transformation and the expansion into momenta yields the exact continuity equation for the correlator Φ with spatial dependencies due to the loss channels at the boundaries of the finite system and additionally the current density relation.
ΔG = GR − GA. p, p′ and p″ are momenta. The scatterer’s geometric properties are represented within the self-consistent complex valued scattering matrices T of the Schwinger-Dyson equation G = G0 + G0TG which leads to the solution for the Green’s function GR and GA of the electromagnetic field, the light wave. The ZnO scatterer’s initial permittivity is given by Reϵs = 4.0164, the imaginary part Imϵs, the microscopic gain, is computed self-consistently yielding gain saturation. The photon density emitted from the amplifying Mie particles is derived by means of coupling to the rate equation system (see previous section). It is self-consistently connected the dielectric function ϵ = ϵL + ϵNL. Finally we arrive at nonlinear feedback in both, electromagnetic wave transport and photon intensity transport for scalar waves. The scalar approach is especially suitable to model absolutely randomized particle systems. Further the Mie character develops with reducing particle size into a Rayleigh scatterer and strong non-isotropies which might influence the vector-character are consequentially not given. Only in setups of pronounced Mie type scatterers as well as order or quasi-order we expect the vector-character of light to become important. Random lasing in such setups has not been investigated theoretically as well as experimentally so far.
Within grand canonical (open) ensembles of random lasers the entropy is increased by photonic intensity transport processes. Nevertheless transport in the meaning at hand is based on the time reversal symmetry of the single particle Green’s function describing the propagation of the electromagnetic wave. This time reversal symmetry is diagrammatically not broken. We describe the laser dynamics within a laser rate equation system that is suitable for non-linear processes or quantum cascades12. The advantage is obvious since nonradiative decay processes within that system act directly on the electronic subsystem, the particle, and so enter directly the non-linear complex refractive index and the self-energy Σ of the single independent Mie scatterer, modelled as the complex scattering or T matrix. For clarity it shall be pointed out that the complex refractive index acts equally absorbing or emitting under time reversibility. Microcanonically the time evolution is flipped, however the system evolves grand-canonically open14.
The described procedure of modeling disorder and dissipation guarantees the completeness of the ‘ab initio’ description of the propagating light intensity by the four-point correlator Φ = AΦϵϵ + BΦJϵ here given in terms of the momenta. Φϵϵ equals the energy density and ΦJϵ equals the energy current, A and B are pre-factor terms derived in16. The framework yields all specific transport characteristics, e.g. the scattering mean free path ls and includes all interference effects. The mode is described efficiently by the determination of the correlation length ξ with respect to various loss channels. This length ξ in non-linear systems marks a decay of the intensity to 1/e. It is of a qualitative different importance than the localization length in the Anderson sense14, because the diffusion constant is D≠0 in complex media. In other words, the state in this case has a finite lifetime compared to the immanent infinite lifetime of an Anderson localized state in a passive system. The Bethe-Salpeter equation is solved in a sophisticated regime of real space and momentum and the description for the energy density Φϵϵ(Q, Ω) is derived which is computed regarding energy conservation
The numerator Nω is the local density of photonic modes LDOS renormalized due to amplification and absorption of the electromagnetic wave. Q equals the center of mass momentum of the propagator denoted in Wigner coordinates, Ω is the center of mass frequency and D is the self-consistently derived diffusion constant. c1, c2 are coefficients having a non-trivial form of only numerical relevance. Following the formal analytical structure of ref. 16 up to the result of Eq. (28) under the additional assumption of boundaries as well as the coupling to laser rate equations (Eq. (1)) leads actually to some more sophisticated term. This result has to be reformed algebraically until it fits in it’s structure a formal diffusion pole again. The above mentioned form of the energy density Φϵϵ (Eq. (5)) emerges. A divergence, that is marked by critical scales in the unlimited system of16, is here instead replaced by the phase transition towards lasing. Consequentially modes derived as the characterising result here equal not only coherent transport of photons but they rather equal lasing modes caused by the inverted electronic sub-system in quasi-equilibrium, the stationary state.
The structure of the Bethe-Salpeter equation and the diffusion pole will be discussed in the following. The excitation process is uniform in space. Interferences gain weight on long paths in-plane of the large scaled random laser sample. The physics of maximally crossed diagrams therefore significantly dominates the coherence properties: Dissipation and losses due to spontaneous emission and non-radiative decay are in principle homogeneous, however they depend of course very well on the impinging energy density and the resulting non-linear response. As consequence these properties change with the position relative to the samples boundaries if the latter are lossy. All channels are represented within the pole of Eq. (5) resulting in separate dissipative length scales ζ due to homogeneous losses, and χd due to gain and absorption that go along with photonic transport and the open or strongly absorbing boundaries. All dissipation processes enter the mass term of the diffusion equation:
By solving of the non-classical diffusion equation Eq. (6) the coefficients c1 and c2 are selfconsistently derived. Non-classical is defined as to consider light, as explained above, diagrammatically not just as a wave but in addition as particle (photon) current. Finally, we derive the spatial distribution of energy density:
The nonlinear self-consistent microscopic random laser gain γ21n2 incorporates the influences of both length scales χd and ζ,
and therefore represents the physical properties of the random laser samples within the absorptive boundaries. γ21 is the transition rate of stimulated emission and n2 equals the selfconsistent occupation of the upper laser level. The abbreviation ASE on the right of Eq. (7) represents all transport terms yielding amplified spontaneous emission.
The holidays are extra hard for one Osceola County family who lost their loved one to what they said was a senseless crime.
Around this time nine years ago, Carmen Molina said she was preparing for a burial instead of making Thanksgiving plans.
Her son-in-law, Alejandro Rivera, was shot and killed around 4:45 a.m. on Nov. 20, 2006 at the Willows Village apartments in Kissimmee.
Investigators said Rivera and Hector Santiago were apartment-sitting for a friend, when three or four Hispanic men robbed and shot them. Both Rivera and Santiago died from their injuries.
“We are asking — no matter how long it has been — we are seeking justice,” Molina said. “We want nobody to forget our case.”
Molina said the young men spent their day at a downtown Orlando club promoting Rivera’s new CD. She wondered if they were followed home.
One thing Molina said she does know is the robbers took Santiago’s jewelry, including a Jesus pendant — evidence which Kissimmee police said they hope could lead to a killer.
“It could be the smallest little bit of information that you, as the caller, may think is nothing, but it’s that one piece we may need that could bust this case wide open and solve it for us,” said Kissimmee police spokeswoman Stacie Miller.
Rivera left behind a 2-year-old son, now 11. Molina said it’s been hard watching her grandson grow up without a father.
(Courtesy Carmen Molina)
“We know that someone out there knows something, and I think it’s about time you come forward,” Molina added.
Rivera’s mother died several years ago, never getting closure in her son’s case.
Crime Stoppers are offering a $5,000 reward for any information in the shooting deaths of Alejandro Rivera and Hector Santiago in 2006. If you can help investigators solve this case, call (800) 226-TIPS (8477).