Representation Theory of Lattice Current Algebras

Lattice current algebras were introduced as a regularization of the left- and right moving degrees of freedom in the WZNW model. They provide examples of lattice theories with a local quantum symmetry U_q(\sg). Their representation theory is studied in detail. In particular, we construct all irreducible representations along with a lattice analogue of the fusion product for representations of the lattice current algebra. It is shown that for an arbitrary number of lattice sites, the representation categories of the lattice current algebras agree with their continuum counterparts.Comment: 35 pages, LaTeX file, the revised version of the paper, to be published in Commun. Math. Phys. , the definition of the fusion product for lattice current algebras is correcte

Causality and quantum interference in time-delayed laser-induced nonsequential double ionization

We perform a detailed analysis of the importance of causality within the strong-field approximation and the steepest-descent framework for the recollision-excitation with subsequent tunneling ionization (RESI) pathway in laser-induced nonsequential double ionization (NSDI). In this time-delayed pathway, an electron returns to its parent ion and, by recolliding with the core, gives part of its kinetic energy to excite a second electron at a time t′. The second electron then reaches the continuum at a later time t by tunneling ionization. We show that, if t′ and t are complex, the condition that recollision of the first electron occurs before tunnel ionization of the second electron translates into boundary conditions for the steepest-descent contours and thus puts constraints on the saddles to be taken when computing the RESI transition amplitudes. We also show that this generalized causality condition has a dramatic effect on the shapes of the RESI electron momentum distributions for few-cycle laser pulses. Physically, causality determines how the dominant sets of orbits of an electron returning to its parent ion can be combined with the dominant orbits of a second electron tunneling from an excited state. All features encountered are analyzed in terms of such orbits and their quantum interference

The path-coalescence transition and its applications

We analyse the motion of a system of particles subjected a random force fluctuating in both space and time, and experiencing viscous damping. When the damping exceeds a certain threshold, the system undergoes a phase transition: the particle trajectories coalesce. We analyse this transition by mapping it to a Kramers problem which we solve exactly. In the limit of weak random force we characterise the dynamics by computing the rate at which caustics are crossed, and the statistics of the particle density in the coalescing phase. Last but not least we describe possible realisations of the effect, ranging from trajectories of raindrops on glass surfaces to animal migration patterns.Comment: 4 pages, 3 figures; revised version, as publishe

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

On demand entanglement in double quantum dots via coherent carrier scattering

We show how two qubits encoded in the orbital states of two quantum dots can be entangled or disentangled in a controlled way through their interaction with a weak electron current. The transmission/reflection spectrum of each scattered electron, acting as an entanglement mediator between the dots, shows a signature of the dot-dot entangled state. Strikingly, while few scattered carriers produce decoherence of the whole two-dots system, a larger number of electrons injected from one lead with proper energy is able to recover its quantum coherence. Our numerical simulations are based on a real-space solution of the three-particle Schroedinger equation with open boundaries. The computed transmission amplitudes are inserted in the analytical expression of the system density matrix in order to evaluate the entanglement.Comment: 20 pages, 5 figure

Calogero-Sutherland Approach to Defect Blocks

Extended objects such as line or surface operators, interfaces or boundaries play an important role in conformal field theory. Here we propose a systematic approach to the relevant conformal blocks which are argued to coincide with the wave functions of an integrable multi-particle Calogero-Sutherland problem. This generalizes a recent observation in 1602.01858 and makes extensive mathematical results from the modern theory of multi-variable hypergeometric functions available for studies of conformal defects. Applications range from several new relations with scalar four-point blocks to a Euclidean inversion formula for defect correlators.Comment: v2: changes for clarit

D-branes in the WZW model

It is stated in the literature that D-branes in the WZW-model associated with the gluing condition J = - \bar{J} along the boundary correspond to branes filling out the whole group volume. We show instead that the end-points of open strings are rather bound to stay on `integer' conjugacy classes. In the case of SU(2) level k WZW model we obtain k-1 two dimensional Euclidean D-branes and two D particles sitting at the points e and -e.Comment: 2 pages, LaTe

Random-matrix theory of amplifying and absorbing resonators with PT or PTT' symmetry

We formulate gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical realizations of such systems we consider a PT or a PTT' time-reversal symmetry, which impose different constraints on magneto-optical effects, and then focus on five common settings. For each of these, we determine the eigenvalue distribution in the complex plane in the short-wavelength limit, which reveals that the fraction of real eigenvalues among all eigenvalues in the spectrum vanishes if all classical scales are kept fixed. Numerically, we find that the transition from real to complex eigenvalues in the various ensembles display a different dependence on the coupling strength between the two resonators. These differences can be linked to the level spacing statistics in the hermitian limit of the considered models.Comment: 19 pages, 9 figure

Topological tight-binding models from nontrivial square roots

We describe a versatile mechanism that provides tight-binding models with an enriched, topologically nontrivial band structure. The mechanism is algebraic in nature, and leads to tight-binding models that can be interpreted as a nontrivial square root of a parent lattice Hamiltonian—in analogy to the passage from a Klein-Gordon equation to a Dirac equation. In the tight-binding setting, the square-root operation admits to induce spectral symmetries at the expense of broken crystal symmetries. As we illustrate in detail for a simple one-dimensional example, the emergent and inherited spectral symmetries equip the energy gaps with independent topological quantum numbers that control the formation of topologically protected states. We also describe an implementation of this system in silicon photonic structures, outline applications in higher dimensions, and provide a general argument for the origin and nature of the emergent symmetries, which are typically nonsymmorphic

Crossover of conductance and local density of states in a single-channel disordered quantum wire

The probability distribution of the mesoscopic local density of states (LDOS) for a single-channel disordered quantum wire with chiral symmetry is computed in two different geometries. An approximate ansatz is proposed to describe the crossover of the probability distributions for the conductance and LDOS between the chiral and standard symmetry classes of a single-channel disordered quantum wire. The accuracy of this ansatz is discussed by comparison with a large-deviation ansatz introduced by Schomerus and Titov in Phys. Rev. B \textbf{67}, 100201(R) (2003).Comment: 19 pages, 5 eps figure