Arrival time is on Saturday, 29 July 2006, and you can check into your rooms after 4.00 pm. There are no special events planned for the evening of Saturday, but we presume that many people will meet at the first dinner at the Banff centre on Saturday evening
Abstracts appear below the schedule.
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## Alexander L. Burin: Many electron theory of 1/f-noise in hopping conductivityWe show that 1/f-noise in the variable range hopping regime is related to transitions of many-electrons clusters (fluctuators) between two almost degenerate states. Giant fluctuation times necessary for $1/f$-noise are provided by slow rate of simultaneous tunneling of many localized electrons and by large activation barriers for their consecutive rearrangements. The Hooge constant steeply grows with decreasing temperature because it is easier to find a slow fluctuator at lower temperatures. Our conclusions qualitatively agree with the low temperature observations of 1/f-noise in p-type silicon and GaAs.## Philip C E Stamp: Topological Coherence and DecoherenceTopological phase plays a central role in the dynamics of many quantum systems. Topological decoherence can thus play a dramatic role, which is studied in this talk for 2 systems: (i) A system of interacting qubits (and the related model of a quantum walk), with application to magnets and superconductors (ii) the dissipative Hofstadter model, and related models in condensed matter and string theory.## Mona Berciu: Green's function of a dressed particleWe present a new, highly efficient yet accurate approximation for the Green's functions of dressed particles, using the Holstein polaron as an example. Instead of summing a subclass of self-energy diagrams (e.g., the non-crossed ones, in the self-consistent Born approximation), we sum all the self-energy diagrams, but with each diagram averaged over its free propagators' momenta. The resulting Green's function satisfies exactly the first six spectral weight sum rules. All higher order sum rules are satisfied with great accuracy, becoming asymptotically exact for coupling both much larger and much smaller than the free particle bandwidth. Possible generalizations to other models will also be discussed.## Naoto Nagaosa: Theory of Spin Hall Effect - A New State of Matter?I will talk about theories of spin Hall effect with the focus on its quantum topological aspects. Especially, possible nontrivial topological number and its relevance to the localization problem/edge modes of the quantum spin Hall systems are discussed.## Shoucheng Zhang: The Persistent Spin HelixSpin-orbit coupled systems generally break the spin rotation symmetry. However, for a model with equal Rashba and Dresselhauss coupling constant (the ReD model), and for the [110] Dresselhauss model, a new type of SU(2) spin rotation symmetry is discovered. This symmetry is robust against spin-independent disorder and interactions, and is generated by operators whose wavevector depends on the coupling strength. It renders the spin lifetime infinite at this wavevector, giving rise to a Persistent Spin Helix (PSH). This remarakable prediction has recently been quantitatively confirmed in spin grating experiments.## Alexandre M. Zagoskin: Analog operation of an adiabatic quantum computer and approximate adiabatic algorithmsThere is a growing realization that standard approaches to quantum computing, too fragile to decoherence, are not realizable in the near future. The alternative paradigm of adiabatic quantum computing (AQC), where the solution is encoded in the ground state of the system evolving under an adiabatically slow change of a control parameter ?, seems more promising. Remaining in the ground state automatically protects the system against relaxation and dephasing. The main limitation imposed on AQC is the finite probability of excitation, via Landau-Zener tunneling, at any finite evolution speed (the adiabaticity parameter d?/dt). While the universality of quantum computation is a worthy goal, we can envision a more restricted class of problems, which can be solved by an approximate adiabatic approach (ìAA-problemsî), by operating the quantum computer as an analog, rather than digital, device. That is, their solutions can be mapped smoothly on the low-lying states of the system. By limiting ourselves to the AA-problems, we can demonstrate an exponential speed-up over classical computation. Examples include finding the ground state energy of a spin glass, and the travelling salesman problem. We show that the AA-algorithm for finding the ground state energy of a spin glass is exponentially faster than simulated annealing. Our results provide physical arguments in favour of Landau-Zener robustness and therefore polynomial efficiency of both exact and also approximate AQC.## Taejin Lee: The Exact Duality and the Magic Circles of the Dissipative Hofstadter ModelThe dissipative Hofstadter model describes quantum particles moving in two dimensions subject to a uniform magnetic field, a periodic potential and a dissipative force. We discuss the dissipative Hofstadter model in the framework of the boundary state formulation in string theory and construct exact boundary states for the model at the magic points using the fermion representation. The exact duality of the dissipative Hofstadter model is shown to be equivalent to the subgroup of T-duality symmetry group in string theory unbroken by the boundary periodic potential.## Jainendra K. Jain: Microscopic tests of abelian and non-abelian braiding statistics in the FQHEWhile abelian and non-abelian braiding statistics are widely thought to be realized in the FQHE, their microscopic tests have been few. A calculation by Kjonsberg and Myrheim in mid 1990s actually found that Laughlin's 1/3 quasiparticles do not possess a well defined braiding statistics. We (Gun Sang Jeon, Kenneth Graham, and JKJ) have shown that the composite fermion theory recovers meaningful braiding properties for the quasiparticles, at the same time bringing out many subtleties relevant to this issue. I will also report on our recent work (in collaboration with Nicolas Regnault and Csaba Toke) related to non-abelian braiding statistics for the quasiholes of the 5/2 state. We ask how closely the solutions of the short-range three-body interaction model represent the actual Coulomb solutions; the former forms the basis for non-abelian statistics. The issue of localization of quasiholes and quasiparticles of the 5/2 state in the presence of impurities willl also be discussed.## Ralf Schuetzhold: Adiabatic quantum algorithms and quantum phase transitionsIn the continuum limit (large number of qubits), adiabatic quantum algorithms display a remarkable similarity to sweeps through quantum phase transitions. With this insight, we propose a novel adiabatic quantum algorithm for the solution of 3-satisfiability (3-SAT) problems (exact cover), which is significantly faster than previous proposals according to numerical simulations. These findings suggest that adiabatic quantum algorithms can solve NP-complete problems such as 3-SAT much faster than the Grover search routine (quadratic enhancement), possibly even with an exponential speed-up.## Igor S. Tupitsyn: Decoherence in magnetic insulators: Magnon channelIn the last decade the quantum tunneling phenomenon in magnetic insulators has been attracting extensive interest. In particular, the crystals of magnetic molecules with large "central spin" S are under very active study. Molecules (central spins) in these crystals couple to each other via dipole-dipole and exchange interactions, couple to phonons and to nuclear spins. The early study of these systems in a low temperature regime has been concentrated mainly on the incoherent tunneling in low transverse (to the molecular anisotropy axis) magnetic fields. During the last several years more attention has been paid to the spin coherence phenomena. As it has been shown earlier, in magnetic insulators in large transverse fields there can be a field region in which the phonon and nuclear spin-mediated decoherence are drastically reduced. In my talk I am going to discuss the magnon decoherence channel arising from the dipole-dipole and exchange interactions between spins.## Jose Abel Hoyos Neto: Correlation function and entanglement entropy in random spin chainsUsing a simple renormalization group method, we relate and calculate the mean value of the spin-spin correlation function and the bipartite entanglement entropy in the random antiferromagnetic spin-1/2 chain. Implications of such relation are discussed as well as the localized nature of the ground state.## Valeri P. Frolov: A toy model for topology-change tansitionsWe discuss a toy model for topology-change transitions. This model includes a bulk 4-dimensional static spherically symmetric black hole and a test 3-dimensional brane interacting with the black hole. The brane is asymptotically flat and allows $O(2)$ group of symmetry. Such a brane--black-hole (BBH) system has two different phases. The first one is formed by solutions describing a brane crossing the horizon of the bulk black hole. In this case the internal induced geometry of the brane describes low (2+1) dimensional black hole. The other phase consists of solutions for branes which do not intersect the horizon and the induced geometry does not have a horizon. We study a critical solution at the threshold of the brane-black-hole formation, and the solutions which are close to it. In particular, we demonstrate, that there exists a striking similarity of the BBH system with the Choptuik critical collapse. We discuss how the effects of the finite thickness of the brane allows one to escape the infinite curvature problem in for the topology change transitions in the BBH system. We also briefly discuss the higher dimensional generalization of this problem.## Yoseph Imry: Quantum Noise and Quantum AmplificationBasic notions of quantum noise will be reviewed. It will be shown that a good way to measure noise is via the absorption/emission spectrum. The latter is often measured by amplifying the radiation emitted by the sample. This measurement motivates the study of fundamental uncertainty-type constraints on the amplification process. We shall review the generalization of the basic inequality on the noise produced by that process to the fermionic case. We shall then derive a new uncertainty relation on noise in transistor-type amplifiers. Some recent applications will be reviewed, if time permits.## Zelnikov Andrei: Scalar fields in 2D black holes: Exact solutions and quasi-normal modesWe study a nonminimal massive scalar field in a 2-dimensional black hole spacetime. We consider the black hole which is the solution of the 2d dilaton gravity derived from string-theoretical models. We found an explicit solution in a closed form for all modes and the Green function of the scalar field with an arbitrary mass and a nonminimal coupling to the curvature. Greybody factors, the Hawking radiation, and quasi-normal modes are calculated explicitly for this exactly solvable model.## Robert Raussendorf: A fault-tolerant one-way quantum computerWe describe a fault-tolerant one-way quantum computer on cluster states in three dimensions. The presented scheme uses methods of topological error correction resulting from a link between cluster states and Kitaev's surface codes. A quantum circuit is realized by choosing appropriate boundary conditions for the 3D cluster. The error threshold is 0.11 percent for each source in an error model with preparation-, gate-, storage- and measurement errors. Ref: quant-ph/0510135, joint work with J. Harrington and K. Goyal.## Di Xiao: Berry phase correction to electron density of states in solidsIt's been known that the Berry phase in semiclassical dynamics makes the equation of motion noncanonical. In the context of Bloch electron dynamics, we show that it leads to a modification of the phase-space density of states, whose significance is discussed in a number of examples. The effective quantum mechanics of Bloch electrons is also sketched, where the modified density of states plays an essential role.## Dmitri V. Fursaev: Quantum Entanglement in Critical Phenomena, Gravity, and HolographyA review of the properties of entanglement entropy which appears under spatial partition of a quantum system is given. A special attention is payed to critical phenomena in 2D condensed matter systems. It is conjectured that in a fundamental theory the ground state entanglement entropy per unit area equals $1/(4G_N)$, where $G_N$ is the Newton constant in the low-energy gravity sector of the theory. The ground state entanglement entropy in higher-dimensional condensed matter systems can be used to introduce an effective gravitational coupling and consider such systems as gravity analogs. We then discuss how the relation between the entropy and the gravity coupling can be justified in theories which admit a dual description in terms of the AdS gravity one dimension higher, and, in particular, in RS brane-world models. Finally, we present a proof of the holographic formula which relates the entanglement entropy in the theory on the brane to the area of a codimension 2 minimal hypersurface embedded in the bulk AdS space.## Mohammad Amin: Thermally Assisted Adiabatic Quantum ComputationUnderstanding how environment affects performance is central to designing practical quantum computer architectures. In certain models, such as the gate model of quantum computation, environment always degrades performance. In this presentation, I will introduce a new model of computation, thermally assisted adiabatic quantum computation (TAQC), where the presence of environment actually enhances the performance of the computational model. To demonstrate how this performance enhancement arises, I will describe the operation of both adiabatic quantum computation and TAQC models on the adiabatic Grover search algorithm.## Ali Rezakhani: Topological entanglement and quantum computationTopological quantum computation (TQC) has been proposed as a new paradigm for quantum computation. One of its appealing features, in addition to its rich mathematics, is its in-built tolerance against a wide class of local errors. Among the existing approaches to TQC, such as utilizing topological quantum field theory, using systems with topological degrees of freedom, and establishing a correspondence between knot theory and quantum entanglement, here I only concentrate on the last one. Following [1], I address the question of whether there exists any simple (yet fruitful) relation between topological and quantum mechanical entanglement, from two points of views. The first viewpoint is based on a proposed correspondence between knots and entangled states, which we refute by various physical arguments. The second viewpoint is a correspondence between braid operators and quantum entanglers, which is more promising. By using available classification of braid operators in two-dimensions, I show that among them there are quantum entanglers. This proves universality of braiding operators for QC. However, these quantum entanglers are insufficient to cover the whole special subclass of "maximally entangling entanglers" [2]. Overall, I argue that although braiding-entangling correspondence provides us with universality, it is not clear how it can show more promising features for TQC or new powerful quantum algorithms. [1] L. H. Kauffman and S. J. Lomonaco Jr., New J. Phys. 4, 73 (2002). [2] A. T. Rezakhani, Phys. Rev. A 70, 052313 (2004).## Andrew Hines: Quantum Walks, Quantum Gates, and Quantum ComputersQuantum walks refer to the dynamics of a particle on some arbitrary mathematical graph. The study of quantum walks was initially motivated by the potential to generate new kinds of quantum information processing algorithms. Interestingly quantum walks can also describe the time evolution of quantum algorithms, including Groverís search and Shor's algorithm. One can construct explicit mappings between the Hamiltonian of a multi-qubit quantum computer, gate sequences, and a quantum particle moving on some graph. Such new representations will provide the possibility for more easily studying decoherence in different quantum information processing systems. The mappings above allow us to easily move between the different representations, and to easily study the dynamics of quantum information processing. I will describe these mappings between quantum walks, quantum circuits, qubit-Hamiltonians and spin chains, giving simple examples using Groverís and Shorís algorithms and physical implementations. Using the hypercube, I will provide a simple illustration of how different implementations of the quantum walk imply different forms of decoherence.## Lara Thompson: Effective Magnus force on a magnetic vortexIn classical hydrodynamics, a Magnus force exists between a vortex and the hosting fluid acting transverse to their relative motion. There is a quantum Magnus force acting on vortices in superfluids and superconductors and an analogous force acting on magnetic vortices excited in spin systems. Couplings with the system quasiparticles can modify this to an effective Magnus force by introducting transverse damping forces. The existence and magnitude of such transverse damping are highly controversial and have not been settled by experiment. I derive the various damping forces on a vortex in a magnetic system, a system where we expect experiments can more accurately study vortex motion for comparison with theory. Despite the simplicity of the spin system, the results are general and should reveal quantitative behaviour for the superfluid/superconductor systems.## Boris Spivak: Is there a linewidth theory for semiconductor lasers?Semiconductor laser generation begins at a critical injection when the gain and loss spectra touch each other at a singular frequency. In the framework of the standard (Schawlow-Townes-Lax-Henry) theory, the finite linewidth results from the account of fluctuations associated with the random spontaneous emission processes. This approach is based on the assumption that in the mean-field approximation the singular frequency generation persists for injection levels higher than critical. We show that this assumption in the framework of the Boltzmann kinetic equation for electrons and photons is invalid and therefore the standard description of semiconductor laser linewidth lacks theoretical foundation. Experimenal support of the standard theory is also questionable.## Bill Unruh: Using Grover search to speed up a wide array of problems## Duncan Haldane: Generalizations of Fock space and the Pauli principle for Abelian and non-Abelian FQHE quasiparticlesAn underlying simplicity of the counting of many-particle states of systems of quasiholes of Laughlin, Moore-Read, and Read-Rezayi states makes possible explicit calculations of inhomogeneous systems of such quasi particles, based on projection into the common null space of extensive sets of k-particle annihilation operators, as a generalization of the k=1 case (projection into the lowest Landau level).## Gavin K Brennen: Building new states of matter with polar molecules: a route to topological orderIt has been shown that topological order can emerge in the ground states of spin models involving quasi-local interactions on a lattice. These states are good candidates for robust quantum memory storage and processing. However, such models usually involve interactions which are highly anisotropic in spatial and spin degrees of freedom and thus are non-trivial to design from fundamental interactions. I will describe a new toolbox for building lattice spin models using dipole-dipole coupled polar molecules trapped in an optical lattice. The interaction strengths are fast relative to decoherence times and tunable in range and spin character using several control fields. Well developed technologies for coherent control and measurement used in quantum optics may serve to verify properties of topologically ordered states such as measuring correlations functions, energy gaps, and quantum statistics of quasi-particle excitations. |