Coherent wave propagation in disordered media gives rise to many fascinating phenomena as diverse as universal conductance fluctuations in mesoscopic metals and speckle patterns in light scattering. Here, the theory of electromagnetic wave propagation in diffusive media is combined with information theory to show how interference affects the information transmission rate between antenna arrays. Nontrivial dependencies of the information capacity on the nature of the antenna arrays are found, such as the dimensionality of the arrays and their direction with respect to the local scattering medium. This approach provides a physical picture for understanding the importance of scattering in the transfer of information through wireless communications.The ongoing communications revolution has motivated researchers to look for novel ways to transmit information (1, 2). One recent development (3, 4) is the suggestion that, contrary to long-held beliefs, random scattering of microwave or radio signals may enhance the amount of information that can be transmitted on a particular channel. Prompted by this suggestion, we introduce a realistic physical model for a scattering environment and analytically evaluate the amount of information that can be transmitted between two antenna arrays for a number of example cases. On the one hand, this lays a new foundation for complex microwave signal modeling, an important task in a world with ever-increasing demand for wireless communication, and, on the other, introduces a new arena for physicists to test ideas concerning disordered media.From information theory (5), the capacity of a channel between a transmitter and a receiver, that is, the maximum rate of information transfer at a given frequency, can be described in terms of the average power of the signal S and the noise N at the receiver: C = log 2 (1+S/N ). More generally (2), the communication channel connecting several transmitters and receivers is described by a matrix G iα giving the amplitude of the received signal α due to transmitter i. The information carried by the channel can be characterized using several quantities, such as the capacity or mutual information, which are typically functionals of the matrix G, which must be known in order to predict these quantities. Often G cannot be predicted for actual systems, such as wireless communication networks or optical fibers, because of the complicated scattering and interference of waves that is involved. It is crucial, therefore, to develop physical models for the signal propagation, as it is only through such models that one can understand the real effects of scattering and interference on the amount of information that can be communicated.In many cases, only partial information is available for prediction; in these situations, one only has a statistical description of G. Instead of making assumptions about G directly, the usual procedure in information theory, we introduce statistical models for the physical environment from which we derive the properties of G. The adv...

In this paper, we study fractional quantum Hall composite fermion wavefunctions at filling fractions ν = 2/3, 3/5, and 4/7. At each of these filling fractions, there are several possible wavefunctions with different spin polarizations, depending on how many spin-up or spin-down composite fermion Landau levels are occupied. We calculate the energy of the possible composite fermion wavefunctions and we predict transitions between ground-states of different spin polarizations as the ratio of Zeeman energy to Coulomb energy is varied. Previously, several experiments have observed such transitions between states of differing spin polarization and we make direct comparison of our predictions to these experiments. For more detailed comparison between theory and experiment, we also include finite-thickness effects in our calculations. We find reasonable qualitative agreement between the experiments and composite fermion theory. Finally, we consider composite fermion states at filling factors ν = 2 + 2/3, 2 + 3/5, and 2 + 4/7. The latter two cases we predict to be spin polarized even at zero Zeeman energy.

We compute and compare even-and odd-parity superconducting order parameters of strontium ruthenate (Sr2RuO4) in the limit of weak interactions, resulting from a fully microscopic threedimensional model including spin-orbit coupling. We find that odd-parity helical and even-parity dwave order are favored for smaller and larger values of the Hund's coupling parameter J, respectively. Both orders are found compatible with specific heat data and the recently-reported nuclear magnetic resonance (NMR) Knight shift drop [A. Pustogow et al. arXiv:1904.00047 (2019]. The chiral p-wave order, numerically very competitive with helical order, sharply conflicts with the NMR experiment.

The composite fermion picture has had a remarkable number of recent successes both in the description of the fractional quantized Hall states and in the description of the even denominator Fermi-liquid like states. In this chapter, we give an introductory account of the Chern-Simons fermion theory, focusing on the description of the even denominator states as unusual Fermi liquids.

In this series of papers, we study a Hamiltonian model for 3+1d topological phases, based on a generalisation of lattice gauge theory known as "higher lattice gauge theory". Higher lattice gauge theory has so called "2-gauge fields" describing the parallel transport of lines, just as ordinary gauge fields describe the parallel transport of points. In the Hamiltonian model this is represented by having labels on the plaquettes of the lattice, as well as the edges. In this paper we summarize our findings in an accessible manner, with more detailed results and proofs to be presented in the other papers in the series. The Hamiltonian model supports both point-like and loop-like excitations, with non-trivial braiding between these excitations. We explicitly construct operators to produce and move these excitations, and use these to find the loop-loop and point-loop braiding relations. These creation operators also reveal that some of the excitations are confined, costing energy to separate. This is discussed in the context of condensation/confinement transitions between different cases of this model. We also discuss the topological charges of the model and use explicit measurement operators to re-derive a relationship between the number of charges measured by a 2-torus and the ground-state degeneracy of the model on the 3-torus. From these measurement operators, we can see that the ground state degeneracy on the 3-torus is related to the number of types of linked loop-like excitations.