We show that a central 1/r n singular potential (with n ≥ 2) is renormalized by a one-parameter square-well counterterm; low-energy observables are made independent of the square-well width by adjusting the square-well strength. We find a closed form expression for the renormalization-group evolution of the square-well counterterm.

We consider O(αs) corrections to the squared masses of the pseudo-Goldstone excitations about the ground state of dense quark matter. We show that these contributions tend to destabilize the vacuum, leading to a surprisingly complex phase structure for quark matter as a function of quark mass, even for small αs. In particular we find two new phases of CFL quark matter possibly relevant for the real world, for whichθQCD = π/2. 03.75.Fi,26.60.+c, The dependence of the QCD vacuum on the masses of the light quarks is most efficiently analyzed by means of a chiral Lagrangian, which allows one to systematically compute corrections to the chirally symmetric vacuum in a power expansion in the quark masses. The utility of the chiral Lagrangian approach is that it properly accounts for the lightest QCD excitations, the pseudo Goldstone bosons (PGBs), whose masses vanish in the chiral limit and which therefore have the most important role in determining the vacuum structure for small quark mass. In addition to allowing one to compute perturbative corrections to the vacuum structure, the chiral Lagrangian also allows one to investigate phase transitions at critical values of the quark masses. An example of such a phase transition was first discovered by Dashen In hadronic matter at nonzero baryon density, more complicated phase transitions have been investigated using chiral Lagrangians, including both pion [2] and kaon condensation [3,4]. More recently, chiral Lagrangians have been used to analyze the vacuum structure of dense quark matter near the chiral limit. It has been convincingly argued that for degenerate quarks such a system should be color superconducting [5], and that for three massless flavors the color-flavor-locked (CFL) ground state is preferred [6,7,8]. Chiral perturbation theory can be used to describe the ground state and excitations of CFL matter away from the chiral limit [9,10,11]. It is already known that the phase structure is much more complicated than in the vacuum case. In particular, an analysis to leading order in both quark masses * abk4@phys.washington.edu † dbkaplan@phys.washington.edu ‡ thomas schaefer@ncsu.edu and the QCD coupling constant α s reveals a phase transition to a kaon condensed phase along a line in the m s -m plane [12,13,14], where m s is the strange quark mass, and for simplicity we are considering the isospin limit, m u = m d = m. In this Letter we show that the leading order calculation does not capture the full complexity of the quark matter ground state, and that there exist new phases revealed at sub-leading order in α s at small quark mass in the m s -m plane which could be relevant for the real world.The reason that O(α s ) effects are important is that the leading order result exhibits an accidental degeneracy which is only lifted at next-to-leading order. Once O(α s ) effects are included the meson masses receive negative corrections to their squared masses which can be larger than the leading order contributions, even for small α s . In particular, a meson of mass M...

Methylammonium lead iodide perovskite (MAPbI) is a promising material for photovoltaic devices. A modification of MAPbI into confined nanostructures is expected to further increase efficiency of solar energy conversion. Photoexcited dynamic processes in a MAPbI quantum dot (QD) have been modeled by many-body perturbation theory and nonadiabatic dynamics. A photoexcitation is followed by either exciton cooling (EC), its radiative (RR) or nonradiative recombination (NRR), or multiexciton generation (MEG) processes. Computed times of these processes fall in the order of MEG < EC < RR < NRR, where MEG is on the order of a few femtoseconds, EC is in the picosecond range, while RR and NRR are on the order of nanoseconds. Computed time scales indicate which electronic transition pathways can contribute to increase in charge collection efficiency. Simulated mechanisms of relaxation and their rates show that quantum confinement promotes MEG in MAPbI QDs.

We study the effective field theory for fermions in the color-flavor locked (CFL) phase of high density QCD. The effective theory contains a flavor nonet of baryons interacting with a nonet of pseudoscalar Goldstone bosons as well as a singlet scalar Goldstone boson. The theory is similar to chiral perturbation theory in the one-baryon sector. We explain how to incorporate quark mass terms and study the spectrum as a function of the strange quark mass. Without meson condensation gapless baryon modes appears if the strange quark mass exceeds a critical value m 2 s /(2p F ) = ∆, where p F is the Fermi momentum and ∆ is the gap in the chiral limit. We show that kaon condensation leads to a rearrangement of the baryon spectrum and shifts the critical strange quark mass for the appearance of a gapless mode to higher values.

Using expansion technique proposed by Nishida and Son ͓Phys. Rev. Lett. 97, 050403 ͑2006͔͒ we derive an effective Lagrangian ͑Ginzburg-Landau-type functional͒ of the degenerate unitary Fermi gas to the nextto-leading order in . It is demonstrated that for many realistic situations it is sufficient to retain leading order terms in the derivative expansion. The functional is used to study vortex structure in the symmetric gas, and interface between normal and superfluid phases in the polarized gas. Typical vortex size, r 0 k F = 0.92, where k F is Fermi momentum, agrees well with results of previous work ͓A. Bulgac and Y. Yu, Phys. Rev. Lett. 91, 190404 ͑2003͔͒. Surface free energy is about 3 times larger than the value previously quoted in the literature.