Topological structures of adiabatic phase for multi-level quantum systems

The topological properties of adiabatic gauge fields for multi-level (three-level in particular) quantum systems are studied in detail. Similar to the result that the adiabatic gauge field for SU(2) systems (e.g. two-level quantum system or angular momentum systems, etc) have a monopole structure, the curvature two-forms of the adiabatic holonomies for SU(3) three-level and SU(3) eight-level quantum systems are shown to have monopole-like (for all levels) or instanton-like (for the degenerate levels) structures.Comment: 15 pages, no figures. Accepted by J.Phys.

Gapped optical excitations from gapless phases: imperfect nesting in unconventional density waves

We consider the effect of imperfect nesting in quasi-one-dimensional unconventional density waves in the case, when the imperfect nesting and the gap depends on the same wavevector component. The phase diagram is very similar to that in a conventional density wave. The density of states is highly asymmetric with respect to the Fermi energy. The optical conductivity at T=0 remains unchanged for small deviations from perfect nesting. For higher imperfect nesting parameter, an optical gap opens, and considerable amount of spectral weight is transferred to higher frequencies. This makes the optical response of our system very similar to that of a conventional density wave. Qualitatively similar results are expected in d-density waves.Comment: 8 pages, 7 figure

The Probability of an Eigenvalue Number Fluctuation in an Interval of a Random Matrix Spectrum

We calculate the probability to find exactly $n$ eigenvalues in a spectral interval of a large random $N \times N$ matrix when this interval contains $s \ll N$ eigenvalues on average. The calculations exploit an analogy to the problem of finding a two-dimensional charge distribution on the interface of a semiconductor heterostructure under the influence of a split gate.Comment: 4 pages, postscrip

A Parametrization of Bipartite Systems Based on SU(4) Euler Angles

In this paper we give an explicit parametrization for all two qubit density matrices. This is important for calculations involving entanglement and many other types of quantum information processing. To accomplish this we present a generalized Euler angle parametrization for SU(4) and all possible two qubit density matrices. The important group-theoretical properties of such a description are then manifest. We thus obtain the correct Haar (Hurwitz) measure and volume element for SU(4) which follows from this parametrization. In addition, we study the role of this parametrization in the Peres-Horodecki criteria for separability and its corresponding usefulness in calculating entangled two qubit states as represented through the parametrization.Comment: 23 pages, no figures; changed title and abstract and rewrote certain areas in line with referee comments. To be published in J. Phys. A: Math. and Ge

Casimir force in the rotor model with twisted boundary conditions

We investigate the three dimensional lattice XY model with nearest neighbor interaction. The vector order parameter of this system lies on the vertices of a cubic lattice, which is embedded in a system with a film geometry. The orientations of the vectors are fixed at the two opposite sides of the film. The angle between the vectors at the two boundaries is $\alpha$ where $0 \le \alpha \le \pi$. We make use of the mean field approximation to study the mean length and orientation of the vector order parameter throughout the film---and the Casimir force it generates---as a function of the temperature $T$, the angle $\alpha$, and the thickness $L$ of the system. Among the results of that calculation are a Casimir force that depends in a continuous way on both the parameter $\alpha$ and the temperature and that can be attractive or repulsive. In particular, by varying $\alpha$ and/or $T$ one controls \underline{both} the sign \underline{and} the magnitude of the Casimir force in a reversible way. Furthermore, for the case $\alpha=\pi$, we discover an additional phase transition occurring only in the finite system associated with the variation of the orientations of the vectors.Comment: 14 pages, 9 figure

Calculation of the Coherent Synchrotron Radiation Impedance from a Wiggler

Most studies of Coherent Synchrotron Radiation (CSR) have only considered the radiation from independent dipole magnets. However, in the damping rings of future linear colliders, a large fraction of the radiation power will be emitted in damping wigglers. In this paper, the longitudinal wakefield and impedance due to CSR in a wiggler are derived in the limit of a large wiggler parameter $K$. After an appropriate scaling, the results can be expressed in terms of universal functions, which are independent of $K$. Analytical asymptotic results are obtained for the wakefield in the limit of large and small distances, and for the impedance in the limit of small and high frequencies.Comment: 10 pages, 8 figure

Calculation of the unitary part of the Bures measure for N-level quantum systems

We use the canonical coset parameterization and provide a formula with the unitary part of the Bures measure for non-degenerate systems in terms of the product of even Euclidean balls. This formula is shown to be consistent with the sampling of random states through the generation of random unitary matrices

Semi-classical buckling of stiff polymers

A quantitative theory of the buckling of a worm like chain based on a semi-classical approximation of the partition function is presented. The contribution of thermal fluctuations to the force-extension relation that allows to go beyond the classical Euler buckling is derived in the linear and non-linear regime as well. It is shown that the thermal fluctuations in the nonlinear buckling regime increase the end-to-end distance of the semiflexible rod if it is confined to 2 dimensions as opposed to the 3 dimensional case. Our approach allows a complete physical understanding of buckling in D=2 and in D=3 below and above the Euler transition.Comment: Revtex, 17 pages, 4 figure

Electrostatics of Edge States of Quantum Hall Systems with Constrictions: Metal--Insulator Transition Tuned by External Gates

The nature of a metal--insulator transition tuned by external gates in quantum Hall (QH) systems with point constrictions at integer bulk filling, as reported in recent experiments of Roddaro et al. [1], is addressed. We are particularly concerned here with the insulating behavior--the phenomena of backscattering enhancement induced at high gate voltages. Electrostatics calculations for QH systems with split gates performed here show that observations are not a consequence of interedge interactions near the point contact. We attribute the phenomena of backscattering enhancement to a splitting of the integer edge into conducting and insulating stripes, which enable the occurrence of the more relevant backscattering processes of fractionally charged quasiparticles at the point contact. For the values of the parameters used in the experiments we find that the conducting channels are widely separated by the insulating stripes and that their presence alters significantly the low-energy dynamics of the edges. Interchannel impurity scattering does not influence strongly the tunneling exponents as they are found to be irrelevant processes at low energies. Exponents of backscattering at the point contact are unaffected by interchannel Coulomb interactions since all channels have same chirality of propagation.Comment: 19 pages; To appear in Phys. Rev.