Discrete Nonlinear Schr{\"o}dinger Breathers in a Phonon Bath

We study the dynamics of the discrete nonlinear Schr{\"o}dinger lattice initialized such that a very long transitory period of time in which standard Boltzmann statistics is insufficient is reached. Our study of the nonlinear system locked in this {\em non-Gibbsian} state focuses on the dynamics of discrete breathers (also called intrinsic localized modes). It is found that part of the energy spontaneously condenses into several discrete breathers. Although these discrete breathers are extremely long lived, their total number is found to decrease as the evolution progresses. Even though the total number of discrete breathers decreases we report the surprising observation that the energy content in the discrete breather population increases. We interpret these observations in the perspective of discrete breather creation and annihilation and find that the death of a discrete breather cause effective energy transfer to a spatially nearby discrete breather. It is found that the concepts of a multi-frequency discrete breather and of internal modes is crucial for this process. Finally, we find that the existence of a discrete breather tends to soften the lattice in its immediate neighborhood, resulting in high amplitude thermal fluctuation close to an existing discrete breather. This in turn nucleates discrete breather creation close to a already existing discrete breather

Comment on "Can one predict DNA Transcription Start Sites by Studying Bubbles?"

Comment on T.S. van Erp, S. Cuesta-Lopez, J.-G. Hagmann, and M. Peyrard, Phys. Rev. Lett. 95, 218104 (2005) [arXiv: physics/0508094]

Absence of Wavepacket Diffusion in Disordered Nonlinear Systems

We study the spreading of an initially localized wavepacket in two nonlinear chains (discrete nonlinear Schroedinger and quartic Klein-Gordon) with disorder. Previous studies suggest that there are many initial conditions such that the second moment of the norm and energy density distributions diverge as a function of time. We find that the participation number of a wavepacket does not diverge simultaneously. We prove this result analytically for norm-conserving models and strong enough nonlinearity. After long times the dynamical state consists of a distribution of nondecaying yet interacting normal modes. The Fourier spectrum shows quasiperiodic dynamics. Assuming this result holds for any initially localized wavepacket, a limit profile for the norm/energy distribution with infinite second moment should exist in all cases which rules out the possibility of slow energy diffusion (subdiffusion). This limit profile could be a quasiperiodic solution (KAM torus)

Quantum transport in carbon nanotubes

Carbon nanotubes are a versatile material in which many aspects of condensed matter physics come together. Recent discoveries, enabled by sophisticated fabrication, have uncovered new phenomena that completely change our understanding of transport in these devices, especially the role of the spin and valley degrees of freedom. This review describes the modern understanding of transport through nanotube devices. Unlike conventional semiconductors, electrons in nanotubes have two angular momentum quantum numbers, arising from spin and from valley freedom. We focus on the interplay between the two. In single quantum dots defined in short lengths of nanotube, the energy levels associated with each degree of freedom, and the spin-orbit coupling between them, are revealed by Coulomb blockade spectroscopy. In double quantum dots, the combination of quantum numbers modifies the selection rules of Pauli blockade. This can be exploited to read out spin and valley qubits, and to measure the decay of these states through coupling to nuclear spins and phonons. A second unique property of carbon nanotubes is that the combination of valley freedom and electron-electron interactions in one dimension strongly modifies their transport behaviour. Interaction between electrons inside and outside a quantum dot is manifested in SU(4) Kondo behavior and level renormalization. Interaction within a dot leads to Wigner molecules and more complex correlated states. This review takes an experimental perspective informed by recent advances in theory. As well as the well-understood overall picture, we also state clearly open questions for the field. These advances position nanotubes as a leading system for the study of spin and valley physics in one dimension where electronic disorder and hyperfine interaction can both be reduced to a very low level.Comment: In press at Reviews of Modern Physics. 68 pages, 55 figure

Bulk and surface magnetoinductive breathers in binary metamaterials

We study theoretically the existence of bulk and surface discrete breathers in a one-dimensional magnetic metamaterial comprised of a periodic binary array of split-ring resonators. The two types of resonators differ in the size of their slits and this leads to different resonant frequencies. In the framework of the rotating-wave approximation (RWA) we construct several types of breather excitations for both the energy-conserved and the dissipative-driven systems by continuation of trivial breather solutions from the anticontinuous limit to finite couplings. Numerically-exact computations that integrate the full model equations confirm the quality of the RWA results. Moreover, it is demonstrated that discrete breathers can spontaneously appear in the dissipative-driven system as a results of a fundamental instability.Comment: 10 pages, 16 figure

The Prime Directive

Agency costs dominate academic thinking about corporate governance. The central challenge is to devise legal rules to align the interests of the managers (the agents) with those of the shareholders (the principals). This preoccupation is misplaced. Whether it is finding a baby-sitter or a dean, the challenge of hiring the right person dwarfs the challenge of aligning that person’s incentives. The central task for corporate governance—its Prime Directive—.0is to ensure that the right person is running the business. In this essay, we suggest that the challenge of aligning the managers\u27 incentives has been drastically overstated and the way in which legal rules affect hiring (and firing) decisions has been too often ignored. The current preoccupation with executive compensation runs the risk of inducing the board to worry more about the details of the employment contract rather than selecting the best person in the first instance. More important, the law can play an important role ensuring bad managers are fired. The market for corporate control does this, but debt contracts also play a crucial role, one that has been largely neglected. Covenants in debt contracts can insure that underperforming managers are called to task. Indeed, they may be as important as the market for corporate control

Fourt (or Five) Easy Lessons from Enron

Temptation. It lies at the heart of financial swindles. The promise of 50% returns in three months can lure thousands of investors-so too can a stock that soars 500% in three years. But those who are tempted are often skeptical. Before they invest, they want to know how one can enjoy such supracompetitive returns. The answer usually is a facially plausible story, though with a bit of mystery attached. The mystery is often touted as the reason that the investment opportunity is exclusive to the entrepreneur who discovered it. It is what ensures that the gains are not competed away. The classic case remains that of Charles Ponzi. While not a very adept con artist-he was caught several times-in a six-month period in 1920, Ponzi convinced ten thousand investors to part with an aggregate of $9.5 million. He promised amazing returns-50% in ninety days. As a testament to his financial wizardry, Ponzi often paid off his investors in half the time he had initially promised. How could he work such financial magic? Allegedly, Ponzi had discovered a lucrative arbitrage opportunity in postal reply coupons. Postal reply coupons allowed the sender of a letter to ensure that the recipient in another country would be able to obtain sufficient postage to respond. For example, a letter writer in America would purchase a reply coupon here and send it along with a letter to a relative in another country, say, Spain. The Spanish relative could then redeem the coupon for Spanish stamps sufficient to send a reply. Ponzi noticed a pricing discrepancy in the postal reply coupons. One could buy a coupon in one country for, say, one penny, and redeem it in another for six cents worth of stamps. This opportunity existed because exchange rates had been set in a postal convention in 1906, well before the outbreak of the Great War. The Great War changed the relative value of many currencies, but the rates for postal exchange coupons remained fixed. The failure to adjust the exchange rates on postal reply coupons meant that a trader could buy a postal reply coupon in a country where the relative value of the currency had declined, redeem it in a country where the relative value of the currency had increased, and turn a profit. There were, in theory, gains to be had by exploiting government inertia. But transaction costs limit any opportunity to profit from arbitrage. Consider the steps necessary to exploit this state of affairs. Money would be gathered in the United States. This money then had to be converted into a foreign currency and put in the hands of an agent in the appropriate foreign country. The agent would have to buy the postal reply coupons in large quantity, although there were limits on the number of coupons that could be bought at one time. The agent then had to send the coupons back to the United States. Another agent would have to redeem them. Given these elaborate requirements, it is hard to imagine how anyone could purchase a sufficient number of reply coupons to support the millions of dollars that Ponzi collected

Private Debt and the Missing Lever of Corporate Governance

Traditional approaches to corporate governance focus exclusively on shareholders and neglect the large and growing role of creditors. Today’s creditors craft elaborate covenants that give them a large role in the affairs of the corporation. While they do not exercise their rights in sunny times when things are going well, these are not the times that matter most. When a business stumbles, creditors typically enjoy powers that public shareholders never have, such as the ability to replace the managers and install those more to their liking. Creditors exercise these powers even when the business is far from being insolvent and continues to pay its debts. Bankruptcy provides no sanctuary as senior lenders ensure that their powers either go unchecked or are enhanced. The powers that modern lenders wield rival in importance the hostile takeover in disciplining poor or underperforming managers. This essay explores these powers and begins the task of integrating this lever of corporate governance into the modern account of corporate law