Crash-Free Sequencing Strategies for Financial Development and Liberalization

This paper uses a stylized model of financial intermediation to characterize the exact circumstances along various paths of economic growth, financial development, and liberalization that can trigger a financial crisis. It shows how to avoid financial crises through proper sequencing of various financial development and liberalization measures. The results of the paper show that naive combinations of financial development and liberalization processes can give rise to financial crises. In some typical situations, in order to avoid a financial crisis, it is important that financial liberalization be accompanied by financial development, in the form of improvements in the financial sectorís efficiencies. In the case of fast growing economies, financial development becomes even more imperative. Copyright 2001, International Monetary Fund

Correlations in excited states of local Hamiltonians

Physical properties of the ground and excited states of a $k$-local Hamiltonian are largely determined by the $k$-particle reduced density matrices ($k$-RDMs), or simply the $k$-matrix for fermionic systems---they are at least enough for the calculation of the ground state and excited state energies. Moreover, for a non-degenerate ground state of a $k$-local Hamiltonian, even the state itself is completely determined by its $k$-RDMs, and therefore contains no genuine ${>}k$-particle correlations, as they can be inferred from $k$-particle correlation functions. It is natural to ask whether a similar result holds for non-degenerate excited states. In fact, for fermionic systems, it has been conjectured that any non-degenerate excited state of a 2-local Hamiltonian is simultaneously a unique ground state of another 2-local Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version of this conjecture states that any non-degenerate excited state of a 2-local Hamiltonian is uniquely determined by its 2-matrix among all the pure $n$-particle states. We construct explicit counterexamples to show that both conjectures are false. It means that correlations in excited states of local Hamiltonians could be dramatically different from those in ground states. We further show that any non-degenerate excited state of a $k$-local Hamiltonian is a unique ground state of another $2k$-local Hamiltonian, hence is uniquely determined by its $2k$-RDMs (or $2k$-matrix)

Complete Characterization of the Ground Space Structure of Two-Body Frustration-Free Hamiltonians for Qubits

The problem of finding the ground state of a frustration-free Hamiltonian carrying only two-body interactions between qubits is known to be solvable in polynomial time. It is also shown recently that, for any such Hamiltonian, there is always a ground state that is a product of single- or two-qubit states. However, it remains unclear whether the whole ground space is of any succinct structure. Here, we give a complete characterization of the ground space of any two-body frustration-free Hamiltonian of qubits. Namely, it is a span of tree tensor network states of the same tree structure. This characterization allows us to show that the problem of determining the ground state degeneracy is as hard as, but no harder than, its classical analog.Comment: 5pages, 3 figure

Power spectra of infragravity waves in a deep ocean

Author Posting. © American Geophysical Union, 2013. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geophysical Research Letters 40 (2013): 2159–2165, doi:10.1002/grl.50418.Infragravity waves (IGWs) play an important role in coupling wave processes in the ocean, ice shelves, atmosphere, and the solid Earth. Due to the paucity of experimental data, little quantitative information is available about power spectra of IGWs away from the shore. Here we use continuous, yearlong records of pressure at 28 locations on the seafloor off New Zealand's South Island to investigate spectral and spatial distribution of IGW energy. Dimensional analysis of diffuse IGW fields reveals universal properties of the power spectra observed at different water depths and leads to a simple, predictive model of the IGW spectra. While sources of IGWs off New Zealand are found to have a flat power spectrum, the IGW energy density has a pronounced dependence on frequency and local water depth as a result of the interaction of the waves with varying bathymetry.The collection of DPG data was supported by the National Science Foundation Continental Dynamics program under grants EAR-0409564, EAR-0409609, and EAR-0409835. This work is supported by the University of Colorado Innovative Seed Grant (IGP) “Study of Ocean Infragravity Waves with a Large Array of Seafloor Seismometers.

Ground-State Spaces of Frustration-Free Hamiltonians

We study the ground-state space properties for frustration-free Hamiltonians. We introduce a concept of `reduced spaces' to characterize local structures of ground-state spaces. For a many-body system, we characterize mathematical structures for the set $\Theta_k$ of all the $k$-particle reduced spaces, which with a binary operation called join forms a semilattice that can be interpreted as an abstract convex structure. The smallest nonzero elements in $\Theta_k$, called atoms, are analogs of extreme points. We study the properties of atoms in $\Theta_k$ and discuss its relationship with ground states of $k$-local frustration-free Hamiltonians. For spin-1/2 systems, we show that all the atoms in $\Theta_2$ are unique ground states of some 2-local frustration-free Hamiltonians. Moreover, we show that the elements in $\Theta_k$ may not be the join of atoms, indicating a richer structure for $\Theta_k$ beyond the convex structure. Our study of $\Theta_k$ deepens the understanding of ground-state space properties for frustration-free Hamiltonians, from a new angle of reduced spaces.Comment: 23 pages, no figur

Use of graphene as protection film in biological environments

Corrosion of metal in biomedical devices could cause serious health problems to patients. Currently ceramics coating materials used in metal implants can reduce corrosion to some extent with limitations. Here we proposed graphene as a biocompatible protective film for metal potentially for biomedical application. We confirmed graphene effectively inhibits Cu surface from corrosion in different biological aqueous environments. Results from cell viability tests suggested that graphene greatly eliminates the toxicity of Cu by inhibiting corrosion and reducing the concentration of Cu(2+) ions produced. We demonstrated that additional thiol derivatives assembled on graphene coated Cu surface can prominently enhance durability of sole graphene protection limited by the defects in graphene film. We also demonstrated that graphene coating reduced the immune response to metal in a clinical setting for the first time through the lymphocyte transformation test. Finally, an animal experiment showed the effective protection of graphene to Cu under in vivo condition. Our results open up the potential for using graphene coating to protect metal surface in biomedical application