Gutzwiller density functional theory for correlated electron systems

We develop a new density functional theory (DFT) and formalism for correlated electron systems by taking as reference an interacting electron system that has a ground state wavefunction which obeys exactly the Gutzwiller approximation for all one particle operators. The solution of the many electron problem is mapped onto the self-consistent solution of a set of single particle Schroedinger equations analogous to standard DFT-LDA calculations.Comment: 4 page

Entanglement, subsystem particle numbers and topology in free fermion systems

We study the relationship between bipartite entanglement, subsystem particle number and topology in a half-filled free fermion system. It is proposed that the spin-projected particle numbers can distinguish the quantum spin Hall state from other states, and can be used to establish a new topological index for the system. Furthermore, we apply the new topological invariant to a disordered system and show that a topological phase transition occurs when the disorder strength is increased beyond a critical value. It is also shown that the subsystem particle number fluctuation displays behavior very similar to that of the entanglement entropy. This provides a lower-bound estimation for the entanglement entropy, which can be utilized to obtain an estimate of the entanglement entropy experimentally.Comment: 14 pages, 6 figure

Concave Plasmonic Particles: Broad-Band Geometrical Tunability in the Near Infra-Red

Optical resonances spanning the Near and Short Infra-Red spectral regime were exhibited experimentally by arrays of plasmonic nano-particles with concave cross-section. The concavity of the particle was shown to be the key ingredient for enabling the broad band tunability of the resonance frequency, even for particles with dimensional aspect ratios of order unity. The atypical flexibility of setting the resonance wavelength is shown to stem from a unique interplay of local geometry with surface charge distributions

Norm estimates of complex symmetric operators applied to quantum systems

This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schr\"odinger operators. In particular, we propose a formula for computing the norm of a compact complex symmetric operator. This observation is applied to two concrete problems related to quantum mechanical systems. First, we give sharp estimates on the exponential decay of the resolvent and the single-particle density matrix for Schr\"odinger operators with spectral gaps. Second, we provide new ways of evaluating the resolvent norm for Schr\"odinger operators appearing in the complex scaling theory of resonances

Patterned Irradiation of YBa_2Cu_3O_(7-x) Thin Films

We present a new experiment on YBa_2Cu_3O_{7-x} (YBCO) thin films using spatially resolved heavy ion irradiation. Structures consisting of a periodic array of strong and weak pinning channels were created with the help of metal masks. The channels formed an angle of +/-45 Deg with respect to the symmetry axis of the photolithographically patterned structures. Investigations of the anisotropic transport properties of these structures were performed. We found striking resemblance to guided vortex motion as it was observed in YBCO single crystals containing an array of unidirected twin boundaries. The use of two additional test bridges allowed to determine in parallel the resistivities of the irradiated and unirradiated parts as well as the respective current-voltage characteristics. These measurements provided the input parameters for a numerical simulation of the potential distribution of the Hall patterning. In contrast to the unidirected twin boundaries in our experiment both strong and weak pinning regions are spatially extended. The interfaces between unirradiated and irradiated regions therefore form a Bose-glass contact. The experimentally observed magnetic field dependence of the transverse voltage vanishes faster than expected from the numerical simulation and we interpret this as a hydrodynamical interaction between a Bose-glass phase and a vortex liquid.Comment: 7 pages, 8 Eps figures included. Submitted to PR

Adiabatic Pair Creation

We give here the proof that pair creation in a time dependent potentials is possible. It happens with probability one if the potential changes adiabatically in time and becomes overcritical, that is when an eigenvalue enters the upper spectral continuum. The potential may be assumed to be zero at large negative and positive times. The rigorous treatment of this effect has been lacking since the pioneering work of Beck, Steinwedel and Suessmann in 1963 and Gershtein and Zeldovich in 1970.Comment: 53 pages, 1 figure. Editorial changes on page 22 f

Bloch bundles, Marzari-Vanderbilt functional and maximally localized Wannier functions

We consider a periodic Schroedinger operator and the composite Wannier functions corresponding to a relevant family of its Bloch bands, separated by a gap from the rest of the spectrum. We study the associated localization functional introduced by Marzari and Vanderbilt, and we prove some results about the existence and exponential localization of its minimizers, in dimension d < 4. The proof exploits ideas and methods from the theory of harmonic maps between Riemannian manifolds.Comment: 37 pages, no figures. V2: the appendix has been completely rewritten. V3: final version, to appear in Commun. Math. Physic

Abelian gauge potentials on cubic lattices

The study of the properties of quantum particles in a periodic potential subject to a magnetic field is an active area of research both in physics and mathematics; it has been and it is still deeply investigated. In this review we discuss how to implement and describe tunable Abelian magnetic fields in a system of ultracold atoms in optical lattices. After discussing two of the main experimental schemes for the physical realization of synthetic gauge potentials in ultracold set-ups, we study cubic lattice tight-binding models with commensurate flux. We finally examine applications of gauge potentials in one-dimensional rings.Comment: To appear on: "Advances in Quantum Mechanics: Contemporary Trends and Open Problems", G. Dell'Antonio and A. Michelangeli eds., Springer-INdAM series 201