Class of invariants for the 2D time-dependent Landau problem and harmonic oscillator in a magnetic field

We consider an isotropic two dimensional harmonic oscillator with arbitrarily time-dependent mass $M(t)$ and frequency $\Omega(t)$ in an arbitrarily time-dependent magnetic field $B(t)$. We determine two commuting invariant observables (in the sense of Lewis and Riesenfeld) $L,I$ in terms of some solution of an auxiliary ordinary differential equation and an orthonormal basis of the Hilbert space consisting of joint eigenvectors $\phi_\lambda$ of $L,I$. We then determine time-dependent phases $\alpha_\lambda(t)$ such that the $\psi_\lambda(t)=e^{i\alpha_\lambda}\phi_\lambda$ are solutions of the time-dependent Schr\"odinger equation and make up an orthonormal basis of the Hilbert space. These results apply, in particular to a two dimensional Landau problem with time-dependent $M,B$, which is obtained from the above just by setting $\Omega(t) \equiv 0$. By a mere redefinition of the parameters, these results can be applied also to the analogous models on the canonical non-commutative plane.Comment: 13 pages, 3 references adde

Sparse polynomial space approach to dissipative quantum systems: Application to the sub-ohmic spin-boson model

We propose a general numerical approach to open quantum systems with a coupling to bath degrees of freedom. The technique combines the methodology of polynomial expansions of spectral functions with the sparse grid concept from interpolation theory. Thereby we construct a Hilbert space of moderate dimension to represent the bath degrees of freedom, which allows us to perform highly accurate and efficient calculations of static, spectral and dynamic quantities using standard exact diagonalization algorithms. The strength of the approach is demonstrated for the phase transition, critical behaviour, and dissipative spin dynamics in the spin boson modelComment: 4 pages, 4 figures, revised version accepted for publication in PR

Stability of Impurities with Coulomb Potential in Graphene with Homogeneous Magnetic Field

Given a 2-dimensional no-pair Weyl operator with a point nucleus of charge Z, we show that a homogeneous magnetic field does not lower the critical charge beyond which it collapses.Comment: J. Math. Phys. (in press

Asymptotic and exact series representations for the incomplete Gamma function

Using a variational approach, two new series representations for the incomplete Gamma function are derived: the first is an asymptotic series, which contains and improves over the standard asymptotic expansion; the second is a uniformly convergent series, completely analytical, which can be used to obtain arbitrarily accurate estimates of $\Gamma(a,x)$ for any value of $a$ or $x$. Applications of these formulas are discussed.Comment: 8 pages, 4 figure

Quasinormal modes and stability of the rotating acoustic black hole: numerical analysis

The study of the quasinormal modes (QNMs) of the 2+1 dimensional rotating draining bathtub acoustic black hole, the closest analogue found so far to the Kerr black hole, is performed. Both the real and imaginary parts of the quasinormal (QN) frequencies as a function of the rotation parameter B are found through a full non-linear numerical analysis. Since there is no change in sign in the imaginary part of the frequency as B is increased we conclude that the 2+1 dimensional rotating draining bathtub acoustic black hole is stable against small perturbations.Comment: 6 pages, ReVTeX4. v2. References adde

Expansions of the exponential integral in incomplete gamma functions

AbstractAn apparently new expansion of the exponential integral E1 in incomplete gamma functions is presented and shown to be a limiting case of a more general expansion given by Tricomi in 1950 without proof. This latter expansion is proved here by interpreting it as a “multiplication theorem”. A companion result, not mentioned by THcomi, holds for the complementary incomplete gamma function and can be applied to yield an expansion connecting E1 of different arguments. A general method is described for converting a power series into an expansion in incomplete gamma functions. In a special case, this provides an alternative derivation of Tricomi's expansion. Numerical properties of the new expansion for E1 are discussed

Thyroid hormones, blood plasma metabolites and haematological parameters in relationship to milk yield in dairy cows

To study their relationship to milk yield, the concentrations, in jugular venous blood, of thyroxine iodine (T4I), thyroxine (T4), 3,5,3'-tri-iodothyronine (T3), glucose, non-esterified fatty acids (NEFA), triglycerides, phospholipids, cholesterol, total protein, albumin, urea, haemoglobin and packed cell volume (PCV) have been measured in 36 cows (Simmental, Swiss Brown, Holstein and Simmental × Holstein) of different ages during a full lactation, pregnancy, dry period, parturition and 150 days of the ensuing lactation. Thyroid hormones and triglycerides were negatively, and total protein, globulin, cholesterol and phospholipids were positively, correlated with uncorrected or corrected milk yield during several periods of lactation, whereas glucose, NEFA, albumin, urea, haemoglobin and packed cell volume were not correlated with milk yield. The 10 animals with the highest milk yield (18·9 to 23·5 kg/day) exhibited significantly lower values of T4I, T4, T3 and glucose, significantly higher levels of total protein and globulin and tended to have higher levels of NEFA than the 10 cows with the lowest milk yield (10·9 to 14·3 kg/day) throughout or during certain periods of lactation, whereas concentrations of triglycerides, phospholipids, cholesterol, albumin, haemoglobin and PCV did not differ. Changes in T4I, T4, T3, glucose and total protein during lactation were also influenced by age, presumably associated with an increase in milk production with age. T3 was consistently lowest and cholesterol and phospholipids, during later stages of lactation, were highest in Holsteins, which had the highest milk yields of all breeds. Changes of blood parameters were mainly caused by shifts in energy and protein metabolism in association with level of milk productio

Eigenvalue distributions from a star product approach

We use the well-known isomorphism between operator algebras and function spaces equipped with a star product to study the asymptotic properties of certain matrix sequences in which the matrix dimension $D$ tends to infinity. Our approach is based on the $su(2)$ coherent states which allow for a systematic 1/D expansion of the star product. This produces a trace formula for functions of the matrix sequence elements in the large-$D$ limit which includes higher order (finite-$D$) corrections. From this a variety of analytic results pertaining to the asymptotic properties of the density of states, eigenstates and expectation values associated with the matrix sequence follows. It is shown how new and existing results in the settings of collective spin systems and orthogonal polynomial sequences can be readily obtained as special cases. In particular, this approach allows for the calculation of higher order corrections to the zero distributions of a large class of orthogonal polynomials.Comment: 25 pages, 8 figure