We determine analytically the phase diagram of the toric code model in a parallel magnetic field which displays three distinct regions. Our study relies on two high-order perturbative expansions in the strong- and weak-field limit, as well as a large
-spin analysis. Calculations in the topological phase establish a quasiparticle picture for the anyonic excitations. We obtain two second-order transition lines that merge with a first-order line giving rise to a multicritical point as recently suggested by numerical simulations. We compute the values of the corresponding critical fields and exponents that drive the closure of the gap. We also give the one-particle dispersions of the anyonic quasiparticles inside the topological phase.
Semiclassical methods can now explain many mesoscopic effects (shot-noise, conductance fluctuations, etc) in clean chaotic systems, such as chaotic quantum dots. In the deep classical limit (wavelength much less than system size) the Ehrenfest time (
the time for a wavepacket to spread to a classical size) plays a crucial role, and random matrix theory (RMT) ceases to apply to the transport properties of open chaotic systems. Here we summarize some of our recent results for shot-noise (intrinsically quantum noise in the current through the system) in this deep classical limit. For systems with perfect coupling to the leads, we use a phase-space basis on the leads to show that the transmission eigenvalues are all 0 or 1 -- so transmission is noiseless [Whitney-Jacquod, Phys. Rev. Lett. 94, 116801 (2005), Jacquod-Whitney, Phys. Rev. B 73, 195115 (2006)]. For systems with tunnel-barriers on the leads we use trajectory-based semiclassics to extract universal (but non-RMT) shot-noise results for the classical regime [Whitney, Phys. Rev. B 75, 235404 (2007)].
Consider any representation $phi$ of a finite-dimensional Lie algebra $g$ by derivations of the completed symmetric algebra $hat{S}(g^*)$ of its dual. Consider the tensor product of $hat{S}(g^*)$ and the exterior algebra $Lambda(g)$. We show that the
representation $phi$ extends canonically to the representation $tildephi$ of that tensor product algebra. We construct an exterior derivative on that algebra, giving rise to a twisted version of the exterior differential calculus with the enveloping algebra in the role of the coordinate algebra. In this twisted version, the commutators between the noncommutative differentials and coordinates are formal power series in partial derivatives. The square of the corresponding exterior derivative is zero like in the classical case, but the Leibniz rule is deformed.
Let X be an n-dimensional Calabi-Yau with ordinary double points, where n is odd. Friedman showed that for n=3 the existence of a smoothing of X implies a specific type of relation between homology classes on a resolution of X. (The converse is also
true, due to work of Friedman, Kawamata and Tian.) We sketch a more topological proof of this result, and then extend it to higher dimensions. For n>3 the Yukawa product on the middle dimensional (co)homology plays an unexpected role. We also discuss a converse, proving it for nodal Calabi-Yau hypersurfaces in projective space.
We provide a full characterization of the oblique projector $U(VU)^+V$ in the general case where the range of $U$ and the null space of $V$ are not complementary subspaces. We discuss the new result in the context of constrained least squares minimization.
We provide a new characterization of mean-variance hedging strategies in a general semimartingale market. The key point is the introduction of a new probability measure $P^{star}$ which turns the dynamic asset allocation problem into a myopic one. Th
e minimal martingale measure relative to $P^{star}$ coincides with the variance-optimal martingale measure relative to the original probability measure $P$.
(Original) Recent high-resolution spectra of the Type Ia SN 2006X have revealed the presence of time-variable and blueshifted Na I D features, interpreted by Patat et al. as originating in circumstellar material within the progenitor system. The vari
ation seen in SN 2006X induces relatively large changes in the total Na I D equivalent width ($Deltarm{EW}approx 0.5 unicode{x212B}$ in just over two weeks), that would be detectable at lower resolutions. We have used a large data set comprising 2400 low-resolution spectra of 450 Type Ia supernovae (SNe Ia) obtained by the CfA Supernova Program to search for variable Na I D features. Out of the 31 SNe Ia (including SN 2006X) in which we could have detected similar EW variations, only one other (SN 1999cl) shows variable Na I D features, with an even larger change over a similar ~10-day timescale ($Deltarm{EW} = 1.66 pm 0.21 unicode{x212B}$). Interestingly, both SN 1999cl and SN 2006X are the two most highly-reddened objects in our sample, raising the possibility that the variability is connected to dusty environments. (Erratum) The large variation in the Na I D equivalent width observed in SN 1999cl results in fact from a measurement error. Our new measurements show that the EW variation is significantly lower, at $0.43 pm 0.14 unicode{x212B}$. While the EW variation remains statistically significant (3.1$sigma$ different from zero), it is now below the detection threshold of 0.5 $unicode{x212B}$ derived from the Monte Carlo simulations published in the original paper. As a result, SN 1999cl should no longer be considered as an object displaying variable Na I D lines in our study. The fraction of SNe Ia in our sample displaying Na I D lines thus goes from $sim$6% (2/31) in the original study to $sim$3% (1/31) in the revised analysis, SN 2006X being the only SN Ia in our sample with variable Na I D lines.
Lattice contribution to the electronic self-energy in complex correlated oxides is a fascinating subject that has lately stimulated lively discussions. Expectations of electron-phonon self-energy effects for simpler materials, such as Pd and Al, have
resulted in several misconceptions in strongly correlated oxides. Here we analyze a number of arguments claiming that phonons cannot be the origin of certain self-energy effects seen in high-$T_c$ cuprate superconductors via angle resolved photoemission experiments (ARPES), including the temperature dependence, doping dependence of the renormalization effects, the inter-band scattering in the bilayer systems, and impurity substitution. We show that in light of experimental evidences and detailed simulations, these arguments are not well founded.
The configuration interaction (CI) method for calculating the exact eigenstates of a quantum-mechanical few-body system is problematic when applied to particles interacting through contact forces. In dimensions higher than one the approach fails due
to the pathology of the Dirac delta-potential, making it impossible to reach convergence by gradually increasing the size of the Hilbert space. However, this problem may be cured in a rather simple manner by renormalizing the strength of the contact potential when diagonalizing in a truncated Hilbert space. One hereby relies on the comparison of the CI results to the two-body ground-state energy obtained by the exact solution of the Schroedinger equation for a regularized contact interaction. We here discuss a scheme that provides cutoff-independent few-body physical observables. The method is applied to a few-body system of ultracold atoms confined by a two-dimensional harmonic oscillator.
Aims:We aim to significantly increase the number of detected extra-solar planets in a magnitude-limited sample to improve our knowledge of their orbital element distributions and thus obtain better constraints for planet-formation models. Methods:
Radial-velocity data were taken at Haute-Provence Observatory (OHP, France) with the ELODIE echelle spectrograph. Results: We report the presence of a planet orbiting HD 196885 A, with an orbital period of 1349 days. This star was previously suggested to host a 386 -day planet, but we cannot confirm its existence. We also detect the presence of a stellar companion, HD 196885 B, and give some constraints on its orbit.
