Semiclassical transport in nearly symmetric quantum dots II: symmetry-breaking due to asymmetric leads

In this work - the second of a pair of articles - we consider transport through spatially symmetric quantum dots with leads whose widths or positions do not obey the spatial symmetry. We use the semiclassical theory of transport to find the symmetry-induced contributions to weak localization corrections and universal conductance fluctuations for dots with left-right, up-down, inversion and four-fold symmetries. We show that all these contributions are suppressed by asymmetric leads, however they remain finite whenever leads intersect with their images under the symmetry operation. For an up-down symmetric dot, this means that the contributions can be finite even if one of the leads is completely asymmetric. We find that the suppression of the contributions to universal conductance fluctuations is the square of the suppression of contributions to weak localization. Finally, we develop a random-matrix theory model which enables us to numerically confirm these results.Comment: (18pages - 9figures) This is the second of a pair of articles (v3 typos corrected - including in equations

Significance of Ghost Orbit Bifurcations in Semiclassical Spectra

Gutzwiller's trace formula for the semiclassical density of states in a chaotic system diverges near bifurcations of periodic orbits, where it must be replaced with uniform approximations. It is well known that, when applying these approximations, complex predecessors of orbits created in the bifurcation ("ghost orbits") can produce pronounced signatures in the semiclassical spectra in the vicinity of the bifurcation. It is the purpose of this paper to demonstrate that these ghost orbits themselves can undergo bifurcations, resulting in complex, nongeneric bifurcation scenarios. We do so by studying an example taken from the Diamagnetic Kepler Problem, viz. the period quadrupling of the balloon orbit. By application of normal form theory we construct an analytic description of the complete bifurcation scenario, which is then used to calculate the pertinent uniform approximation. The ghost orbit bifurcation turns out to produce signatures in the semiclassical spectrum in much the same way as a bifurcation of real orbits would.Comment: 20 pages, 6 figures, LATEX (IOP style), submitted to J. Phys.

Testing Spatial Noncommutativity via Rydberg Atoms

The possibility of testing spatial noncommutativity via Rydberg atoms is explored. An atomic dipole of a cold Rydberg atom is arranged in appropriate electric and magnetic field, so that the motion of the dipole is constrained to be planar and rotationally symmetric. Spatial noncommutativity leads to that the canonical angular momentum possesses fractional values. In the limit of vanishing kinetic energy, the dominate value of the lowest canonical angular momentum takes $\hbar/2$. Furthermore, in the limit of eliminating magnetic field, the dominate value of the lowest canonical angular momentum changes from $\hbar/2$ to $\hbar/4$. This result is a clear signal of spatial noncommutativity. An experimental verification of this prediction is suggested.Comment: 10 pages. Physical Review Letters (in press

Quark-Gluon Plasma/Black Hole duality from Gauge/Gravity Correspondence

The Quark-Gluon Plasma (QGP) is the QCD phase of matter expected to be formed at small proper-times in the collision of heavy-ions at high energy. Experimental observations seem to favor a strongly coupled QCD plasma with the hydrodynamic properties of a quasi-perfect fluid, i.e. rapid thermalization (or isotropization) and small viscosity. The theoretical investigation of such properties is not obvious, due to the the strong coupling. The Gauge/Gravity correspondence provides a stimulating framework to explore the strong coupling regime of gauge theories using the dual string description. After a brief introduction to Gauge/Gravity duality, and among various existing studies, we focus on challenging problems of QGP hydrodynamics, such as viscosity and thermalization, in terms of gravitational duals of both the static and relativistically evolving plasma. We show how a Black Hole geometry arises naturally from the dual properties of a nearly perfect fluid and explore the lessons and prospects one may draw for actual heavy ion collisions from the Gauge/Gravity duality approach.Comment: 6 pages, 4 figures, invited talk at the EPS HEP 2007 Conference, Manchester (UK), and at the ``Deuxiemes rencontres PQG-France'', Etretat (2007); reference adde

Commutator Anomaly in Noncommutative Quantum Mechanics

In this letter, firstly, the Schr$\ddot{o}$dinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space-space and space-momentum as well as momentum-momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical observable operators in NCQM are discussed.Comment: 7 page

A Scaling Limit With Many Noncommutativity Parameters

We derive the worldsheet propagator for an open string with different magnetic fields at the two ends, and use it to compute two distinct noncommutativity parameters, one at each end of the string. The usual scaling limit that leads to noncommutative Yang-Mills can be generalized to a scaling limit in which both noncommutativity parameters enter. This corresponds to expanding a theory with U(N) Chan-Paton factors around a background U(1)^N gauge field with different magnetic fields in each U(1).Comment: 14 pages, harvma

D-branes with Lorentzian signature in the Nappi-Witten model

Lorentzian signature D-branes of all dimensions for the Nappi-Witten string are constructed. This is done by rewriting the gluing condition $J_+=FJ_-$ for the model chiral currents on the brane as a well posed first order differential problem and by solving it for Lie algebra isometries $F$ other than Lie algebra automorphisms. By construction, these D-branes are not twined conjugacy classes. Metrically degenerate D-branes are also obtained.Comment: 22 page

The flux of noncommutative U(1) instanton through the fuzzy spheres

From the ADHM construction on noncommutative $R_{\theta}^4$ we investigate different U(1) instanton solutions tied by isometry trasformations. These solutions present a form of vector fields in noncommutative $R_{\theta}^3$ vector space which makes possible the calculus of their fluxes through fuzzy spheres. We establish the noncommutative analog of Gauss theorem from which we show that the flux of the U(1) instantons through fuzzy spheres does not depend on the radius of these spheres and it is invariant under isometry transformations.Comment: 18 pages, new version to appear in Int. Jour. of Mod. Phys.

Poisson Geometry in Constrained Systems

Constrained Hamiltonian systems fall into the realm of presymplectic geometry. We show, however, that also Poisson geometry is of use in this context. For the case that the constraints form a closed algebra, there are two natural Poisson manifolds associated to the system, forming a symplectic dual pair with respect to the original, unconstrained phase space. We provide sufficient conditions so that the reduced phase space of the constrained system may be identified with a symplectic leaf in one of those. In the second class case the original constrained system may be reformulated equivalently as an abelian first class system in an extended phase space by these methods. Inspired by the relation of the Dirac bracket of a general second class constrained system to the original unconstrained phase space, we address the question of whether a regular Poisson manifold permits a leafwise symplectic embedding into a symplectic manifold. Necessary and sufficient for this is the vanishing of the characteristic form-class of the Poisson tensor, a certain element of the third relative cohomology.Comment: 41 pages, more detailed abstract in paper; v2: minor corrections and an additional referenc