Deformed Fermi Surface Theory of Magneto-Acoustic Anomaly in Modulated Quantum Hall Systems Near /nu=1/2/nu=1/2

We introduce a new generic model of a deformed Composite Fermion-Fermi Surface (CF-FS) for the Fractional Quantum Hall Effect near $/nu=1/2$ in the presence of a periodic density modulation. Our model permits us to explain recent Surface Acoustic Wave observations of anisotropic anomalies [1,2] in sound velocity and attenuation- appearance of peaks and anisotropy - which originate from contributions to the conductivity tensor due to regions of the CF-FS which are flattened by the applied modulation. The calculated magnetic field and wave vector dependence of the CF conductivity,velocity shift and attenuation agree with experiments.Comment: Revised manuscript (cond-mat/9807044) 23 September 1998; 10 page

On the continuous spectral component of the Floquet operator for a periodically kicked quantum system

By a straightforward generalisation, we extend the work of Combescure from rank-1 to rank-N perturbations. The requirement for the Floquet operator to be pure point is established and compared to that in Combescure. The result matches that in McCaw. The method here is an alternative to that work. We show that if the condition for the Floquet operator to be pure point is relaxed, then in the case of the delta-kicked Harmonic oscillator, a singularly continuous component of the Floquet operator spectrum exists. We also provide an in depth discussion of the conjecture presented in Combescure of the case where the unperturbed Hamiltonian is more general. We link the physics conjecture directly to a number-theoretic conjecture of Vinogradov and show that a solution of Vinogradov's conjecture solves the physics conjecture. The result is extended to the rank-N case. The relationship between our work and the work of Bourget on the physics conjecture is discussed.Comment: 25 pages, published in Journal of Mathematical Physic

Green's Function and Unitary States in Many Fermion Systems

We discuss a class of mean field hamiltonians for interacting many-fermion systems characterized by their dynamical algebras. For such systems one can easily derive the finite temperature Green's function in an algebraically explicit way. This generalized Green's function G is well-known in the case of superconductivity, for example, where it possesses the pseudo-unitary property GG^+ = Ω^(-2)I (where Ω^(-2) is a scalar). In the case of Helium Three, however, this property of the Green's function is not automatic. By analogy with this latter case we define unitary systems (or the states of such systems) as those which satisfy this pdeudo-unitary constraint. Such constrained systems are particularly easy to treat both theoretically and experimentally; and we explore some of the consequences of unitarity in the cases of coexisting superconducting and density wave systems

On the spectrum of the periodic Dirac operator

The absolute continuity of the spectrum for the periodic Dirac operator $$\hat D=\sum_{j=1}^n(-i\frac {\partial}{\partial x_j}-A_j)\hat \alpha_j + \hat V^{(0)}+\hat V^{(1)}, x\in R^n, n\geq 3,$$ is proved given that either $A\in C(R^n;R^n)\cap H^q_{loc}(R^n;R^n)$, 2q > n-2, or the Fourier series of the vector potential $A:R^n\to R^n$ is absolutely convergent. Here, $\hat V^{(s)}=(\hat V^{(s)})^*$ are continuous matrix functions and \hat V^{(s)}\hat \alpha_j=(-1}^s\hat \alpha_j\hat V^{(s)} for all anticommuting Hermitian matrices $\hat \alpha_j$, $\hat \alpha_j^2=\hat I$, s=0,1.Comment: 17 page

An SU(8) Model for the Unification of Superconductivity, Charge and Spin Density Waves

We analyse a model Hamiltonian for a many-electron system which unifies superconductivity, charge density waves and spin density waves. We show that the spectrum generating algebra for this system is su(8), and identify all 63 generators of this Lie algebra as symmetry operators which are broken in transition to the condensed state, together with 56 order operators, whose expectations give the order parameters of the various phases present in the model. We tabulate the discrete symmetry properties of these operators. We construct a chain of subalgebras of sub-models with corresponding decoupled phases. We finally indicate how the finite temperature Green's Functions may be obtained and used to solve the problem of self-consistency of the order parameters in the model

Many Fermion Green Functions and Dynamical Algebra

The mean-field Hamiltonian for a many-fermion system is an element in a Dynamical Algebra - a classical Lie Algebra. The thermal Matsubara and T=0 Green Functions are sums of products of factors determined by certain structure constants of the algebra. These describe the automorphisms of the Algebra

Mechanism for Generation of Triplet Superconductivity

We show, using the relevant dynamical symmetry, that for a system in which singlet superconductivity and charge and spin density waves coexist, a triplet superconductivity operator is spontaneously generated, and has non-zero expectation value in the ground state

Dynamical SU(8) for phase-coexistence: Thermodynamics of the SO(4) x SO(4) submodel

We review a scheme for describing a multi-phase interacting system of electrons within the dynamical algebra su(8): we discuss the thermodynamics of a submodel which incorporates the relevant physics, and has so(4) ⊕ so(4) for its dynamical algebra. Talk delivered to the XVI International Colloquium on Group Theoretical Methods in Physics, Varna Bulgaria (June, 1987)