48 research outputs found
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
Infrared problem for the Nelson model on static space-times
We consider the Nelson model with variable coefficients and investigate the
problem of existence of a ground state and the removal of the ultraviolet
cutoff. Nelson models with variable coefficients arise when one replaces in the
usual Nelson model the flat Minkowski metric by a static metric, allowing also
the boson mass to depend on position. A physical example is obtained by
quantizing the Klein-Gordon equation on a static space-time coupled with a
non-relativistic particle. We investigate the existence of a ground state of
the Hamiltonian in the presence of the infrared problem, i.e. assuming that the
boson mass tends to 0 at infinity
On the exit statistics theorem of many particle quantum scattering
We review the foundations of the scattering formalism for one particle
potential scattering and discuss the generalization to the simplest case of
many non interacting particles. We point out that the "straight path motion" of
the particles, which is achieved in the scattering regime, is at the heart of
the crossing statistics of surfaces, which should be thought of as detector
surfaces. We sketch a proof of the relevant version of the many particle flux
across surfaces theorem and discuss what needs to be proven for the foundations
of scattering theory in this context.Comment: 15 pages, 4 figures; to appear in the proceedings of the conference
"Multiscale methods in Quantum Mechanics", Accademia dei Lincei, Rome,
December 16-20, 200
Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential
Coupled-mode systems are used in physical literature to simplify the
nonlinear Maxwell and Gross-Pitaevskii equations with a small periodic
potential and to approximate localized solutions called gap solitons by
analytical expressions involving hyperbolic functions. We justify the use of
the one-dimensional stationary coupled-mode system for a relevant elliptic
problem by employing the method of Lyapunov--Schmidt reductions in Fourier
space. In particular, existence of periodic/anti-periodic and decaying
solutions is proved and the error terms are controlled in suitable norms. The
use of multi-dimensional stationary coupled-mode systems is justified for
analysis of bifurcations of periodic/anti-periodic solutions in a small
multi-dimensional periodic potential.Comment: 18 pages, no figure
Adiabatically coupled systems and fractional monodromy
We present a 1-parameter family of systems with fractional monodromy and
adiabatic separation of motion. We relate the presence of monodromy to a
redistribution of states both in the quantum and semi-quantum spectrum. We show
how the fractional monodromy arises from the non diagonal action of the
dynamical symmetry of the system and manifests itself as a generic property of
an important subclass of adiabatically coupled systems
Gauge-theoretic invariants for topological insulators: A bridge between Berry, Wess-Zumino, and Fu-Kane-Mele
We establish a connection between two recently-proposed approaches to the
understanding of the geometric origin of the Fu-Kane-Mele invariant
, arising in the context of 2-dimensional
time-reversal symmetric topological insulators. On the one hand, the
invariant can be formulated in terms of the Berry connection and
the Berry curvature of the Bloch bundle of occupied states over the Brillouin
torus. On the other, using techniques from the theory of bundle gerbes it is
possible to provide an expression for containing the square root
of the Wess-Zumino amplitude for a certain -valued field over the
Brillouin torus.
We link the two formulas by showing directly the equality between the above
mentioned Wess-Zumino amplitude and the Berry phase, as well as between their
square roots. An essential tool of independent interest is an equivariant
version of the adjoint Polyakov-Wiegmann formula for fields , of which we provide a proof employing only basic homotopy theory and
circumventing the language of bundle gerbes.Comment: 23 pages, 1 figure. To appear in Letters in Mathematical Physic
Quasiperiodic functions theory and the superlattice potentials for a two-dimensional electron gas
We consider Novikov problem of the classification of level curves of
quasiperiodic functions on the plane and its connection with the conductivity
of two-dimensional electron gas in the presence of both orthogonal magnetic
field and the superlattice potentials of special type. We show that the
modulation techniques used in the recent papers on the 2D heterostructures
permit to obtain the general quasiperiodic potentials for 2D electron gas and
consider the asymptotic limit of conductivity when . Using the
theory of quasiperiodic functions we introduce here the topological
characteristics of such potentials observable in the conductivity. The
corresponding characteristics are the direct analog of the "topological
numbers" introduced previously in the conductivity of normal metals.Comment: Revtex, 16 pages, 12 figure
Adiabatic approximation, Gell-Mann and Low theorem and degeneracies: A pedagogical example
We study a simple system described by a 2x2 Hamiltonian and the evolution of
the quantum states under the influence of a perturbation. More precisely, when
the initial Hamiltonian is not degenerate,we check analytically the validity of
the adiabatic approximation and verify that, even if the evolution operator has
no limit for adiabatic switchings, the Gell-Mann and Low formula allows to
follow the evolution of eigenstates. In the degenerate case, for generic
initial eigenstates, the adiabatic approximation (obtained by two different
limiting procedures) is either useless or wrong, and the Gell-Mann and Low
formula does not hold. We show how to select initial states in order to avoid
such failures.Comment: 6 pages, 2 figure
Z_2 Invariants of topological insulators as geometric obstructions
We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to â1. We investigate the existence of periodic and time-reversal invariant Bloch frames in dimensions 2 and 3. In 2d, the obstruction to the existence of such a frame is shown to be encoded in a Z2-valued topological invariant, which can be computed by a simple algorithm. We prove that the latter agrees with the Fu-Kane index. In 3d, instead, four Z2 invariants emerge from the construction, again related to the Fu-Kane-Mele indices. When no topological obstruction is present, we provide a constructive algorithm yielding explicitly a periodic and time-reversal invariant Bloch frame. The result is formulated in an abstract setting, so that it applies both to discrete models and to continuous ones
Plasma irisin is elevated in type 2 diabetes and is associated with increased E-selectin levels
BACKGROUND: Irisin is a hormone released mainly from skeletal muscle after exercise which increases adipose tissue energy expenditure. Adipocytes can also release irisin after exercise, acting as a local adipokine to induce white adipose tissue to take on a brown adipose tissue-like phenotype, suggesting that irisin and its receptor may represent a novel molecular target for the treatment of obesity and obesity-related diabetes. Previous reports provide conflicting evidence regarding circulating irisin levels in patients with type 2 diabetes (T2DM). METHODS: This study investigated plasma irisin concentrations in 79 T2DM individuals, assessing potential associations with measures of segmental body composition, markers of endothelial dysfunction and peripheral blood mononuclear cell telomere length (TL). RESULTS: Resting, overnight-fasted plasma irisin levels were significantly higher in this group of T2DM patients compared with levels we previously reported in healthy volunteers (p < 0.001). Moreover, plasma irisin displayed a positive correlation with body mass index (p = 0.04), body fat percentage (p = 0.03), HbA1c (p = 0.03) and soluble E-selectin (p < 0.001). A significant negative association was observed between plasma irisin and visceral adiposity (p = 0.006) in T2DM patients. Multiple regression analysis revealed that circulating soluble E-selectin levels could be predicted by plasma irisin (p = 0.004). Additionally, cultured human umbilical vein endothelial cells (HUVEC) exposed to 200 ng/ml irisin for 4 h showed a significant fourfold increase in E-selectin and 2.5-fold increase in ICAM-1 gene expression (p = 0.001 and p = 0.015 respectively), and there was a 1.8-fold increase in soluble E-selectin in conditioned media (p < 0.05). CONCLUSION: These data suggest that elevated plasma irisin in T2DM is associated with indices of adiposity, and that irisin may be involved in pro-atherogenic endothelial disturbances that accompany obesity and T2DM. Accordingly, irisin may constitute a potentially novel therapeutic opportunity in the field of obesity and cardiovascular diabetology