Hamiltonian and Linear-Space Structure for Damped Oscillators: I. General Theory

The phase space of $N$ damped linear oscillators is endowed with a bilinear map under which the evolution operator is symmetric. This analog of self-adjointness allows properties familiar from conservative systems to be recovered, e.g., eigenvectors are "orthogonal" under the bilinear map and obey sum rules, initial-value problems are readily solved and perturbation theory applies to the_complex_ eigenvalues. These concepts are conveniently represented in a biorthogonal basis.Comment: REVTeX4, 10pp., 1 PS figure. N.B.: `Alec' is my first name, `Maassen van den Brink' my family name. v2: extensive streamlinin

Quantizing the damped harmonic oscillator

We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that unitary dilation of the contraction semigroup governing the dynamics of the system is a logical extension of the doubling procedure, and it allows one to avoid the mathematical difficulties encountered with the previous method.Comment: 4 pages, no figure

Low-frequency characterization of quantum tunneling in flux qubits

We propose to investigate flux qubits by the impedance measurement technique (IMT), currently used to determine the current--phase relation in Josephson junctions. We analyze in detail the case of a high-quality tank circuit coupled to a persistent-current qubit, to which IMT was successfully applied in the classical regime. It is shown that low-frequency IMT can give considerable information about the level anticrossing, in particular the value of the tunneling amplitude. An interesting difference exists between applying the ac bias directly to the tank and indirectly via the qubit. In the latter case, a convenient way to find the degeneracy point in situ is described. Our design only involves existing technology, and its noise tolerance is quantitatively estimated to be realistic.Comment: 6 pages, 11 figures, to appear in Phys.Rev.

Sign- and magnitude-tunable coupler for superconducting flux qubits

We experimentally confirm the functionality of a coupling element for flux-based superconducting qubits, with a coupling strength $J$ whose sign and magnitude can be tuned {\it in situ}. To measure the effective $J$, the groundstate of a coupled two-qubit system has been mapped as a function of the local magnetic fields applied to each qubit. The state of the system is determined by directly reading out the individual qubits while tunneling is suppressed. These measurements demonstrate that $J$ can be tuned from antiferromagnetic through zero to ferromagnetic.Comment: Updated text and figure

The Free Quon Gas Suffers Gibbs' Paradox

We consider the Statistical Mechanics of systems of particles satisfying the $q$-commutation relations recently proposed by Greenberg and others. We show that although the commutation relations approach Bose (resp.\ Fermi) relations for $q\to1$ (resp.\ $q\to-1$), the partition functions of free gases are independent of $q$ in the range $-1<q<1$. The partition functions exhibit Gibbs' Paradox in the same way as a classical gas without a correction factor $1/N!$ for the statistical weight of the $N$-particle phase space, i.e.\ the Statistical Mechanics does not describe a material for which entropy, free energy, and particle number are extensive thermodynamical quantities.Comment: number-of-pages, LaTeX with REVTE

Flory-Huggins theory for athermal mixtures of hard spheres and larger flexible polymers

A simple analytic theory for mixtures of hard spheres and larger polymers with excluded volume interactions is developed. The mixture is shown to exhibit extensive immiscibility. For large polymers with strong excluded volume interactions, the density of monomers at the critical point for demixing decreases as one over the square root of the length of the polymer, while the density of spheres tends to a constant. This is very different to the behaviour of mixtures of hard spheres and ideal polymers, these mixtures although even less miscible than those with polymers with excluded volume interactions, have a much higher polymer density at the critical point of demixing. The theory applies to the complete range of mixtures of spheres with flexible polymers, from those with strong excluded volume interactions to ideal polymers.Comment: 9 pages, 4 figure

Stability and quasi-normal modes of charged black holes in Born-Infeld gravity

In this paper we study the stability and quasi-normal modes of scalar perturbations of black holes. The static charged black hole considered here is a solution to Born-Infeld electrodynamics coupled to gravity. We conclude that the black hole is stable. We also compare the stability of it with its linear counter-part Reissner-Nordstrom black hole. The quasi-normal modes are computed using the WKB method. The behavior of these modes with the non-linear parameter, temperature, mass of the scalar field and the spherical index are analyzed in detail.Comment: Latex, 17 pages, 13 figures, some sections edited, references adde