Nonperturbative results for the mass dependence of the QED fermion determinant

The fermion determinant in four-dimensional quantum electrodynamics in the presence of O(2)XO(3) symmetric background gauge fields with a nonvanishing global chiral anomaly is considered. It is shown that the leading mass singularity of the determinant's nonperturbative part is fixed by the anomaly. It is also shown that for a large class of such fields there is at least one value of the fermion mass at which the determinant's nonperturbative part reduces to its noninteracting value.Comment: This is an extended version of the author's paper in Phys.Rev.D81(2010)10770

Generalized Wannier Functions

We consider single particle Schrodinger operators with a gap in the en ergy spectrum. We construct a complete, orthonormal basis function set for the inv ariant space corresponding to the spectrum below the spectral gap, which are exponentially localized a round a set of closed surfaces of monotonically increasing sizes. Estimates on the exponential dec ay rate and a discussion of the geometry of these surfaces is included

Designing colloidal ground state patterns using short-range isotropic interactions

DNA-coated colloids are a popular model system for self-assembly through tunable interactions. The DNA-encoded linkages between particles theoretically allow for very high specificity, but generally no directionality or long-range interactions. We introduce a two-dimensional lattice model for particles of many different types with short-range isotropic interactions that are pairwise specific. For this class of models, we address the fundamental question whether it is possible to reliably design the interactions so that the ground state is unique and corresponds to a given crystal structure. First, we determine lower limits for the interaction range between particles, depending on the complexity of the desired pattern and the underlying lattice. Then, we introduce a `recipe' for determining the pairwise interactions that exactly satisfies this minimum criterion, and we show that it is sufficient to uniquely determine the ground state for a large class of crystal structures. Finally, we verify these results using Monte Carlo simulations.Comment: 19 pages, 7 figure

Pauli-Fierz model with Kato-class potentials and exponential decays

Generalized Pauli-Fierz Hamiltonian with Kato-class potential \KPF in nonrelativistic quantum electrodynamics is defined and studied by a path measure. \KPF is defined as the self-adjoint generator of a strongly continuous one-parameter symmetric semigroup and it is shown that its bound states spatially exponentially decay pointwise and the ground state is unique.Comment: We deleted Lemma 3.1 in vol.

On the existence of impurity bound excitons in one-dimensional systems with zero range interactions

We consider a three-body one-dimensional Schr\"odinger operator with zero range potentials, which models a positive impurity with charge $\kappa > 0$ interacting with an exciton. We study the existence of discrete eigenvalues as $\kappa$ is varied. On one hand, we show that for sufficiently small $\kappa$ there exists a unique bound state whose binding energy behaves like $\kappa^4$, and we explicitly compute its leading coefficient. On the other hand, if $\kappa$ is larger than some critical value then the system has no bound states

Monte Carlo Renormalization of 2d Simplicial Quantum Gravity Coupled to Gaussian Matter

We extend a recently proposed real-space renormalization group scheme for dynamical triangulations to situations where the lattice is coupled to continuous scalar fields. Using Monte Carlo simulations in combination with a linear, stochastic blocking scheme for the scalar fields we are able to determine the leading eigenvalues of the stability matrix with good accuracy both for c = 1 and c = 10 theories.Comment: 17 pages, 7 figure

Detection and Implications of a Time-reversal breaking state in underdoped Cuprates

We present general symmetry considerations on how a Time-reversal breaking state may be detected by angle-resolved photoemission using circularly polarized photons as has been proposed earlier. Results of recent experiments utilizing the proposal in underdoped cuprates are analysed and found to be consistent in their symmetry and magnitude with a theory of the Copper-Oxides. These togather with evidence for a quantum critical point and marginal Fermi-liquid properties near optimum doping suggest that a valid microscopic theory of the phenomena in the cuprates has been found.Comment: A statement on detecting the Anyon state is added and some typos are subtracte

Magnetocapacitance effect in perovskite-superlattice based multiferroics

We report the structural and magnetoelectrical properties of La$_{0.7}$Ca$_{0.3}$MnO$_3$/BaTiO$_3$ perovskite superlattices grown on (001)-oriented SrTiO$_3$ by the pulsed laser deposition technique. Magnetic hysteresis loops together with temperature dependent magnetic properties exhibit well-defined coercivity and magnetic transition temperature (T$_C$) \symbol{126}140 K. $DC$ electrical studies of films show that the magnetoresistance (MR) is dependent on the BaTiO$_3$ thickness and negative $MR$ as high as 30% at 100K are observed. The $AC$ electrical studies reveal that the impedance and capacitance in these films vary with the applied magnetic field due to the magnetoelectrical coupling in these structures - a key feature of multiferroics. A negative magnetocapacitance value in the film as high as 3% per tesla at 1kHz and 100K is demonstrated, opening the route for designing novel functional materials.Comment: To be published in Applied Physics Letter

Hamilton's turns as visual tool-kit for designing of single-qubit unitary gates

Unitary evolutions of a qubit are traditionally represented geometrically as rotations of the Bloch sphere, but the composition of such evolutions is handled algebraically through matrix multiplication [of SU(2) or SO(3) matrices]. Hamilton's construct, called turns, provides for handling the latter pictorially through the as addition of directed great circle arcs on the unit sphere S$^2 \subset \mathbb{R}^3$, resulting in a non-Abelian version of the parallelogram law of vector addition of the Euclidean translation group. This construct is developed into a visual tool-kit for handling the design of single-qubit unitary gates. As an application, it is shown, in the concrete case wherein the qubit is realized as polarization states of light, that all unitary gates can be realized conveniently through a universal gadget consisting of just two quarter-wave plates (QWP) and one half-wave plate (HWP). The analysis and results easily transcribe to other realizations of the qubit: The case of NMR is obtained by simply substituting $\pi/2$ and $\pi$ pulses respectively for QWPs and HWPs, the phases of the pulses playing the role of the orientation of fast axes of these plates.Comment: 16 Pages, 14 Figures, Published versio

Singular Continuous Spectrum for the Laplacian on Certain Sparse Trees

We present examples of rooted tree graphs for which the Laplacian has singular continuous spectral measures. For some of these examples we further establish fractional Hausdorff dimensions. The singular continuous components, in these models, have an interesting multiplicity structure. The results are obtained via a decomposition of the Laplacian into a direct sum of Jacobi matrices