Localized low-frequency Neumann modes in 2d-systems with rough boundaries

We compute the relative localization volumes of the vibrational eigenmodes in two-dimensional systems with a regular body but irregular boundaries under Dirichlet and under Neumann boundary conditions. We find that localized states are rare under Dirichlet boundary conditions but very common in the Neumann case. In order to explain this difference, we utilize the fact that under Neumann conditions the integral of the amplitudes, carried out over the whole system area is zero. We discuss, how this condition leads to many localized states in the low-frequency regime and show by numerical simulations, how the number of the localized states and their localization volumes vary with the boundary roughness.Comment: 7 pages, 4 figure

First Order Superfluid to Bose Metal Transition in Systems with Resonant Pairing

Systems showing resonant superfluidity, driven by an exchange coupling of strength $g$ between uncorrelated pairs of itinerant fermions and tightly bound ones, undergo a first order phase transition as $g$ increases beyond some critical value $g_c$. The superfluid phase for $g \leq g_c$ is characterized by a gap in the fermionic single particle spectrum and an acoustic sound-wave like collective mode of the bosonic resonating fermion pairs inside this gap. For $g>g_c$ this state gives way to a phase uncorrelated bosonic liquid with a $q^2$ spectrum.Comment: 5 pages, 3 figure

Educating Lawyers: Preparation for the Profession of Law

Examines the unique aspects and limitations of legal education, as part of a series of reports from the foundation's Preparation for the Professions Program

Valuing energy futures; a comparative analysis of value pools across UK energy system scenarios

Electricity markets in liberalised nations are composed primarily of private firms that make strategic decisions about how to secure competitive advantage. Energy transitions, driven by decarbonisation targets and technological innovation, will create new markets and destroy old ones in a re-configuration of the power sector. This research suggests that by 2050 up to 21bnGBP per year of new financial value is available in the UK electricity system, and that depending on scenario, these new values represent up to 31% of the entire electricity sector. To service these markets business model innovation and new firm strategies are needed in electric power provision. Energy scenarios can inform strategic decisions over business model adaptation, but to date scenario modelling has not directly addressed firm strategy and behaviour. This is due in part to neo-classical assumptions of firm rationality and perfect foresight. This research adopts a resource based view of the firm rooted in evolutionary economics to argue that quantifying the relative size of the markets created and destroyed by energy transitions can provide useful insight into firm behaviour and innovation policy

Exploiting environmental resonances to enhance qubit quality factors

We discuss dephasing times for a two-level system (including bias) coupled to a damped harmonic oscillator. This system is realized in measurements on solid-state Josephson qubits. It can be mapped to a spin-boson model with a spectral function with an approximately Lorentzian resonance. We diagonalize the model by means of infinitesimal unitary transformations (flow equations), and calculate correlation functions, dephasing rates, and qubit quality factors. We find that these depend strongly on the environmental resonance frequency $\Omega$; in particular, quality factors can be enhanced significantly by tuning $\Omega$ to lie below the qubit frequency $\Delta$.Comment: 5 psges, 5 figure

A metal-insulator transition as a quantum glass problem

We discuss a recent mapping of the Anderson-Mott metal-insulator transition onto a random field magnet problem. The most important new idea introduced is to describe the metal-insulator transition in terms of an order parameter expansion rather than in terms of soft modes via a nonlinear sigma model. For spatial dimensions d>6 a mean field theory gives the exact critical exponents. In an epsilon expansion about d=6 the critical exponents are identical to those for a random field Ising model. Dangerous irrelevant quantum fluctuations modify Wegner's scaling law relating the conductivity exponent to the correlation or localization length exponent. This invalidates the bound s>2/3 for the conductivity exponent s in d=3. We also argue that activated scaling might be relevant for describing the AMT in three-dimensional systems.Comment: 10 pp., REvTeX, 1 eps fig., Sitges Conference Proceedings, final version as publishe

Flow equations for QED in the light front dynamics

The method of flow equations is applied to QED on the light front. Requiring that the partical number conserving terms in the Hamiltonian are considered to be diagonal and the other terms off-diagonal an effective Hamiltonian is obtained which reduces the positronium problem to a two-particle problem, since the particle number violating contributions are eliminated. No infrared divergencies appear. The ultraviolet renormalization can be performed simultaneously.Comment: 15 pages, Latex, 3 pictures, Submitted to Phys.Rev.