The presence of noise is normally associated with a decrease in the optimal performance of any detection or information processing scheme. However, this is not always the case, as illustrated by the phenomenon of stochastic resonance where the response of a non-linear system displays a resonant-like dependence on the noise strength. I will discuss stochastic resonance (SR) effects in weakly driven coupled quantum systems. I will show that both dynamical and information theoretic measures of the system's response can be introduced that exhibit a non-monotonic behaviour as a function of the noise strength. The relation between lack of monotonicity in the response and the presence of quantum correlations will be analyzed, showing that there are parameter regimes where the breakdown of a linear response can be associated to the presence of entanglement. I will also argue that a chain of coupled spin systems can exhibit a form of array-enhanced response, where the sensitivity of a single resonator to a weak driving signal is enhanced as a result of the nearest-neighbour coupling. These results enlarge the domain where SR effects exist and should be observable in state-of-the-art arrays of superconducting qubits.

This is joint work with J.A. Green and M. Schocker. We study the Littelmann path model for the case gln. In this case, Littelmann's paths become words, and we work with the combinatorics of words. This leads to the representation theory of the Littelmann algebra which is a close analogue of the Schur algebra.

We discuss two integrable Hamiltonians describing the physics of interconversion of bosonic atoms and di-atomic molecules. By mapping the energy spectrums of these models onto a pair of Schrodinger equations we are able to establish a spectral equivalence between a Hermitian Schrodinger problem and a PT-symmetric Schrodinger equation.

TBA

The Hamiltonian of an open quantum system is non-Hermitian. Its eigenvalues and eigenfunctions are complex and energy dependent. They determine the spectroscopic properties of the system. The eigenvalues may cross in the complex energy plane. The crossing points are branch points that separate the scenario with avoided level crossings from that without any crossing in the complex energy plane. Mathematically, the first case is characterized by level repulsion, the second one by widths bifurcation. The topology of the branch points is different from that of diabolic points: the geometric phase is twice the Berry phase. Physically, the branch points in the complex energy plane cause some stabilization of the system and reduce the phase rigidity of the scattering wave function.

Please follow this link for details: http://www.city.ac.uk/sems/mathematics/speciallectures.html

Please follow this link for details: http://www.city.ac.uk/sems/mathematics/speciallectures.html

Please follow this link for details: http://www.city.ac.uk/sems/mathematics/speciallectures.html

In the first part of the talk, I will briefly review two complementary methods for the analytical study of two-dimensional critical phenomena: Conformal Field Theory (CFT) and Stochastic Loewner Evolution (SLE). I will then discuss some recent progress in understanding their connection, via the identification of some probabilities of SLE with correlation functions involving the bulk stress-energy tensor in CFT.

Due to the short notice of change of seminar there is currently not an abstract available. Note: Peter West's seminar previously announced for this day has been postponed to next term.

The abstract can be found at http://www.city.ac.uk/sems/mathematics/seminars.html

tba

I will present an overview over work on the construction of Baxter's Q-operator. The latter is a an auxiliary tool in diagonalizing the Hamiltonian of integrable spin-chains. This is an alternative approach to the Bethe ansatz and has several advantages over the latter. I will highlight the representation theoretic construction of the Q-operator and discuss how this approach leads to a difference equation (called the quantum Wronskian) which is sufficient to determine the spectrum of the spin-chain Hamiltonian. In contrast to the Bethe ansatz equations which are of polynomial order (= number of sites of the chain) the quantum Wronskian leads to a system of quadratic equations. I will also briefly discuss how the Q-operator allows for an alternative description of the trace functional used in the recent discussion of correlation functions by Boos, Jimbo, Miwa, Smirnov and Takeyama.

The abstract can be found at http://www.city.ac.uk/sems/mathematics/seminars.html

For the abstract follow this link: http://www.staff.city.ac.uk/c.korff/citysem.html

The escape out of open quantum systems can be characterised by quasibound states, which are solutions of the wave equation subject to outgoing boundary conditions. The energy eigenvalue of a quasibound state is complex, and the imaginary part is associated to the decay rate of the state. Quasibound states can be observed, e.g., as the lasing modes of optical microresonators. Random-matrix theory gives a wealth of information on quasibound states in disordered media, such as random dielectrics. Interesting systems are, however, ballistic (clean), and scattering only takes place at the (often complicated) confinements. I discuss the similarities and differences between quasibound states in disordered and ballistic systems. A semiclassical analysis reveals that ballistic systems feature a set of quasibound states which decay very quickly (faster even than the classical time of flight). The remaining long-lived quasibound states obey random-matrix statistics, just as in disordered systems, but renormalized in compliance with a recently proposed fractal Weyl law. I illustrate these results numerically for a model system, the open kicked rotator.

The propagation of particles in random backgrounds is of interest from several points of view. Disordered media is one but my own originates in discretized quantum gravity. I will discuss some of the background and the motivation for this. Recently there has been considerable progress in obtaining essentially exact results for some problems of this type. The methods are actually very simple and intuitive and I'll explain how they work. Finally there are of course many open problems still and I'll close with them.

In my talk, I shall present results that have been obtained in collaboration with Tini Garske, on mutation-selection models which describe the evolution of two- or four-letter sequences. Mutation is modelled as a Markov process, and selection is introduced via a fitness function, which assigns a reproductive fitness to each sequence. We consider permutation-invariand fitness functions, or, more generally, Hopfield-type fitness functions, where the fitness is determined by the overlap with a number of given reference sequences. For infinite sequence length, the equilibrium properties of the sequence space models can be determined from a simple maximum principle, which also proves to be a good approximation for the case of finite sequence length.

Baxter's Q-operator is the quantum counterpart of the Baecklund transformation from the theory of classical Hamiltonian integrable systems. The Q-operator, which depends on a complex parameter called spectral, shares common eigenfunctions with the Hamiltonians of a quantum integrable system and satisfies a differential or difference equation in the spectral parameter. Using the Calogero-Sutherland model as an example we shall discuss the construction of the Q-operator and comment on its application for the separation of variables.

The abstract is available at http://www.staff.city.ac.uk/c.korff/citysem.html