Fractal energy carpets in non-Hermitian Hofstadter quantum mechanics

We study the non-Hermitian Hofstadter dynamics of a quantum particle with biased motion on a square lattice in the background of a magnetic field. We show that in quasi-momentum space the energy spectrum is an overlap of infinitely many inequivalent fractals. The energy levels in each fractal are space-filling curves with Hausdorff dimension 2. The band structure of the spectrum is similar to a fractal spider net in contrast to the Hofstadter butterfly for unbiased motion.Comment: 12 pages, 18 figures. Fractal properties of the energy levels are visualised in the supplementary video material https://www.youtube.com/watch?v=ODS3QVkPTP

On the Lieb-Liniger model in the infinite coupling constant limit

We consider the one-dimensional Lieb-Liniger model (bosons interacting via 2-body delta potentials) in the infinite coupling constant limit (the so-called Tonks-Girardeau model). This model might be relevant as a description of atomic Bose gases confined in a one-dimensional geometry. It is known to have a fermionic spectrum since the N-body wavefunctions have to vanish at coinciding points, and therefore be symmetrizations of fermionic Slater wavefunctions. We argue that in the infinite coupling constant limit the model is indistinguishable from free fermions, i.e., all physically accessible observables are the same as those of free fermions. Therefore, Bose-Einstein condensate experiments at finite energy that preserve the one-dimensional geometry cannot test any bosonic characteristic of such a model

Arithmetic area for m planar Brownian paths

We pursue the analysis made in [1] on the arithmetic area enclosed by m closed Brownian paths. We pay a particular attention to the random variable S{n1,n2, ...,n} (m) which is the arithmetic area of the set of points, also called winding sectors, enclosed n1 times by path 1, n2 times by path 2, ...,nm times by path m. Various results are obtained in the asymptotic limit m->infinity. A key observation is that, since the paths are independent, one can use in the m paths case the SLE information, valid in the 1-path case, on the 0-winding sectors arithmetic area.Comment: 12 pages, 2 figure

Vortex structures in rotating Bose-Einstein condensates

We present an analytical solution for the vortex lattice in a rapidly rotating trapped Bose-Einstein condensate (BEC) in the lowest Landau level and discuss deviations from the Thomas-Fermi density profile. This solution is exact in the limit of a large number of vortices and is obtained for the cases of circularly symmetric and narrow channel geometries. The latter is realized when the trapping frequencies in the plane perpendicular to the rotation axis are different from each other and the rotation frequency is equal to the smallest of them. This leads to the cancelation of the trapping potential in the direction of the weaker confinement and makes the system infinitely elongated in this direction. For this case we calculate the phase diagram as a function of the interaction strength and rotation frequency and identify the order of quantum phase transitions between the states with a different number of vortex rows.Comment: 17 pages, 12 figures, with addition

Two-dimensional NMR lineshape analysis of single, multiple, zero and double quantum correlation experiments

NMR spectroscopy provides a powerful approach for the characterisation of chemical exchange and molecular interactions by analysis of series of experiments acquired over the course of a titration measurement. The appearance of NMR resonances undergoing chemical exchange depends on the frequency difference relative to the rate of exchange, and in the case of one-dimensional experiments chemical exchange regimes are well established and well known. However, two-dimensional experiments present additional complexity, as at least one additional frequency difference must be considered. Here we provide a systematic classification of chemical exchange regimes in two-dimensional NMR spectra. We highlight important differences between exchange in HSQC and HMQC experiments, that on a practical level result in more severe exchange broadening in HMQC spectra, but show that complementary alternatives to the HMQC are available in the form of HZQC and HDQC experiments. We present the longitudinal relaxation optimised SOFAST-H(Z/D)QC experiment for the simultaneous acquisition of sensitivity-enhanced HZQC and HDQC spectra, and the longitudinal and transverse relaxation optimised BEST-ZQ-TROSY for analysis of large molecular weight systems. We describe the application of these experiments to the characterisation of the interaction between the Hsp90 N-terminal domain and a small molecule ligand, and show that the independent analysis of HSQC, HMQC, HZQC and HDQC experiments provides improved confidence in the fitted dissociation constant and dissociation rate. Joint analysis of such data may provide improved sensitivity to detect and analyse more complex multi-state interaction mechanisms such as induced fit or conformational selection

Integer Partitions and Exclusion Statistics

We provide a combinatorial description of exclusion statistics in terms of minimal difference $p$ partitions. We compute the probability distribution of the number of parts in a random minimal $p$ partition. It is shown that the bosonic point $p=0$ is a repulsive fixed point for which the limiting distribution has a Gumbel form. For all positive $p$ the distribution is shown to be Gaussian.Comment: 16 pages, 4 .eps figures include

Projection on higher Landau levels and non-commutative geometry

The projection of a two dimensional planar system on the higher Landau levels of an external magnetic field is formulated in the language of the non commutative plane and leads to a new class of star products.Comment: 12 pages, latex, corrected versio

The lagrangian description of representations of the Poincare group

The construction of lagrangians describing the various representations of the Poincare group is given in terms of the BRST approach.Comment: 8 pages, Latex, style file espcrc2.sty. Talk given at the D.V. Volkov Memorial Conference ``Supersymmetry and Quantum Field Theory'', July 25-30, 2000, Kharkov, to be published in the Nuclear Physics B Conference Supplement

Observations on the Topological Structure in 2d Gravity Coupled to Minimal Matter

By using a bosonization we uncover the topological gravity structure of Labastida, Pernici and Witten in ordinary $2d$ gravity coupled to $(p,q)$ minimal models. We study the cohomology class associated with the fermionic charge of the topological gravity which is shown to be isomorphic to that of the total $BRST$ charge. One of the ground ring generators of $c_M <1$ string theory is found to be in the equivariant cohomology of this fermionic charge.Comment: 13 pages, plain tex, UG-5/94 Some clarifying statements and two new references adde

K-matrices for non-abelian quantum Hall states

Two fundamental aspects of so-called non-abelian quantum Hall states (the q-pfaffian states and more general) are a (generalized) pairing of the participating electrons and the non-abelian statistics of the quasi-hole excitations. In this paper, we show that these two aspects are linked by a duality relation, which can be made manifest by considering the K-matrices that describe the exclusion statistics of the fundamental excitations in these systems.Comment: LaTeX, 12 page