Statistical mechanics of a Feshbach coupled Bose-Fermi gas in an optical lattice

We consider an atomic Fermi gas confined in a uniform optical lattice potential, where the atoms can pair into molecules via a magnetic field controlled narrow Feshbach resonance. The phase diagram of the resulting atom-molecule mixture in chemical and thermal equilibrium is determined numerically in the absence of interactions under the constraint of particle conservation. In the limiting cases of vanishing or large lattice depth we derive simple analytical results for important thermodynamic quantities. One such quantity is the dissociation energy, defined as the detuning of the molecular energy spectrum with respect to the atomic one for which half of the atoms have been converted into dimers. Importantly we find that the dissociation energy has a non-monotonic dependence on lattice depth.Comment: 9 pages, 5 figure

The Rescue of the US Auto Industry, Module B: Restructuring General Motors Through Bankruptcy

As the Global Financial Crisis worsened in 2008, credit markets tightened and a broader economic downturn developed, hitting the auto industry particularly hard. The crisis intensified a decade-long decline of the largest US auto manufacturers. Because of its size and importance to the economy, the US government decided to provide assistance to General Motors (GM) to sustain it while it developed plans for its long-term viability. Congress declined to authorize funding for the auto manufacturers, but in December 2008, Treasury provided a bridge loan to GM under the Troubled Assets Relief Program (TARP) to sustain the company until the Obama administration was in place in January 2009. Six months later, the administration provided debtor-in-possession (DIP) financing as GM went through an expedited bankruptcy process as the culminating event in GM’s restructuring. The government’s intervention in and $50 billion assistance to GM began in December 2008 and wasn’t completely wound down until December 2013, resulting in a$10.5 billion loss. This case discusses the bankruptcy, Treasury’s DIP financing, and Treasury’s unwinding of its equity stake in GM acquired as part of the restructuring

Portugal: Deposit Guarantee Fund

On November 3, 2008, the Portuguese government, through a formal legal decree, increased the country’s deposit insurance coverage from EUR 25,000 to EUR 100,000 (USD 31,750 to USD 127,000). The decree came in response to the Global Financial Crisis and a European Union recommendation that all member states increase their deposit coverage to at least EUR 50,000. Portugal’s deposit-guarantee fund, the Fundo de Garantia de Depósitos (or FGD in Portuguese), had existed since 1992. In 2010, the fund was called upon to cover approximately EUR 100 million in deposits of the failed commercial bank Banco Privado Português, S.A., which had EUR 2.9 billion in assets. In March 2009, EU officials increased the required limit for EU members to EUR 100,000. Portugal’s EUR 100,000 coverage was initially set to expire on December 31, 2011; however, the government made it permanent on December 26, 2011

The United Kingdom\u27s Special Liquidity Scheme (SLS) (U.K. GFC)

Following the collapse of Bear Stearns Companies in early 2008, it became clear that there was no immediate prospect that the asset-backed securities (ABS) markets would start to operate as they had previously. Financial institutions relied heavily on ABS as collateral in the interbank lending market for funding and liquidity. The Bank of England (BoE) introduced the Special Liquidity Scheme (SLS) in April 2008 as a temporary measure to address the immediate liquidity problems facing the UK banking system at the time. Under the SLS, banks could exchange high-quality assets that had temporarily become illiquid for liquid UK Treasury bills. In turn, banks could use these Treasury bills in private markets to obtain cash. During the nine months that the SLS was open, 32 banks and building societies, representing over 80% of the sterling balance sheets of eligible financial institutions, exchanged a total of £185 billion of eligible collateral for Treasury bills

Finland: Arsenal

Following a large-scale deregulation of the financial sector during the 1980s and the subsequent massive credit expansion, a banking crisis in Finland caused a sharp contraction in the economy in the early 1990s. One of the key policy responses to the crisis was the creation of an asset management company called Arsenal in 1992. The original purpose of Arsenal was to absorb, manage, and liquidate the bad assets of the Savings Bank of Finland (an entity created by the government-forced merger of 41 of the country’s 81 savings banks). During the following years, Arsenal expanded to become a group of multiple asset management companies dealing with the bad assets of other failed entities. The Arsenal Group, as the group later came to be known, was ultimately responsible for managing more than FIM 40 billion (approx. $8.1 billion) in assets. By 1999 more than 90% of the assets had been wound down. Arsenal was not placed in liquidation until 2003, at which time losses had reached nearly FIM 20 billion. In the most recent available financial statements, Arsenal reported that it was down to one employee with just a handful of assets outstanding in domestic and foreign bankruptcy court that were expected to be finalized within three years, at which point Arsenal would be dissolved

Finland’s 1992 Capital Injection

Following a large-scale deregulation of the financial sector during the 1980s and subsequent massive credit expansion, a banking crisis in Finland caused a sharp contraction in the economy in the early 1990s. To prevent the collapse of the banking system, the government offered FIM 8 billion in capital injections. Parliament appropriated the funds in the spring of 1992 and terms were defined in June 1992. The program was open to all banks, in proportion to their size, regardless of their solvency. In the fall of 1992, FIM 7.9 billion was deployed to 56 cooperative banks and 22 savings banks of which FIM 5.0 billion went to five banks. By January 1996 FIM 6.6 billion had been paid back and by November 1999 FIM 7.9 billion had been paid back with only one institution outstanding

1970 Commercial Paper Market Liquidity Crisis (U.S. Historical)

Penn Central Transportation Company (Penn Central), the resulting railroad company of the late 1960s merger of Pennsylvania Railroad and New York Central Railroad, filed for bankruptcy on June 21, 1970. The bankruptcy came in the middle of the 1969–70 recession and sparked a sharp downturn in the commercial paper market. The Federal Reserve did not intervene directly in the commercial paper market but rather increased funding options available to banks via the discount window and an amendment to Regulation Q. The banks then provided funds to corporations unable to acquire them from the commercial paper market. The liquidity crisis abated within a few weeks

The Federal Reserve’s Response to the 1987 Market Crash (U.S. Historical)

The S&P 500 lost 10% the week ending Friday, October 16, 1987, and lost an additional 20% the following Monday, October 19, 1987. The date would be remembered as Black Monday. The Federal Reserve (the Fed) responded to the crash in four distinct ways: (1) issuing a public statement promising to provide liquidity, as needed, “to support the economic and financial system”; (2) providing support to the Treasury securities market by injecting in-high-demand maturities into the market via reverse repurchase agreements; (3) allowing the federal funds rate to fall from 7.5% to 7.0% and below; and (4) intervening directly to allow the rescue of the largest options clearing firm in Chicago

The Rescue of the US Auto Industry, Module D: Emergency Assistance to Ally Financial (formerly GMAC)

In 2008, GMAC was a $200 billion company providing financing to General Motors customers. As the Global Financial Crisis entered a critical stage in early 2008, GMAC’s funding strategy and liquidity position were adversely affected by the significant disruption in credit markets and the broader economic downturn. This reduced access to financing, which impacted GMAC’s ability to provide automotive wholesale inventory and retail financing to General Motors and Chrysler. In late 2008 and early 2009 GM and Chrysler underwent a complex restructuring process. To restore liquidity to GMAC’s auto finance business, the Federal Reserve agreed to expedite GMAC’s conversion to a bank holding company and to provide access to several of its and the Federal Deposit Insurance Corporation’s emergency liquidity programs, which GMAC used heavily throughout 2009 and 2010. The FDIC also provided GMAC with access to its Temporary Liquidity Guarantee Program. The US Treasury agreed to provide capital under the Automotive Industry Financing Program authorized under the Emergency Economic Stabilization Act of 2008. From December 2008 to December 2009, the Treasury invested$17.2 billion into GMAC. When the last of the government-held shares were sold in December 2014, taxpayers had recouped $19.6 billion, for a net return of$2.4 billion

Angular momentum exchange between coherent light and matter fields

Full, three dimensional, time-dependent simulations are presented demonstrating the quantized transfer of angular momentum to a Bose-Einstein condensate from a laser carrying orbital angular momentum in a Laguerre-Gaussian mode. The process is described in terms of coherent Bragg scattering of atoms from a chiral optical lattice. The transfer efficiency and the angular momentum content of the output coupled vortex state are analyzed and compared with a recent experiment.Comment: 4 pages, 4 figure