Confining potential in a color dielectric medium with parallel domain walls

We study quark confinement in a system of two parallel domain walls interpolating different color dielectric media. We use the phenomenological approach in which the confinement of quarks appears considering the QCD vacuum as a color dielectric medium. We explore this phenomenon in QCD_2, where the confinement of the color flux between the domain walls manifests, in a scenario where two 0-branes (representing external quark and antiquark) are connected by a QCD string. We obtain solutions of the equations of motion via first-order differential equations. We find a new color confining potential that increases monotonically with the distance between the domain walls.Comment: RevTex4, 5 pages, 1 figure; version to appear in Int. J. Mod. Phys.

Large metric perturbations from rescattering

We study numerically evolution of metric perturbations during reheating in a model with two fields and a strong parametric resonance. Our calculation is fully nonlinear and includes gravity but is restricted to spherical symmetry. In this model, super-Hubble metric perturbations can grow during reheating only due to effects nonlinear in fluctuations of the fields. We find that they indeed grow and, soon after the growth begins, dominate variances of the metric functions. Thus, the metric functions become smooth but varying significantly over large scales. Their profiles at late times are interpreted as signalling a gravitational instability and formation of a black hole.Comment: 9 pages, revtex, 4 figures; corrected typo in eq. (1). Time variable in the plots was slightly messed up: fixed in v3 (a cosmetic change

A New Approach to Solve the Low-lying States of the Schroedinger Equation

We review a new iterative procedure to solve the low-lying states of the Schroedinger equation, done in collaboration with Richard Friedberg. For the groundstate energy, the $n^{th}$ order iterative energy is bounded by a finite limit, independent of $n$; thereby it avoids some of the inherent difficulties faced by the usual perturbative series expansions. For a fairly large class of problems, this new procedure can be proved to give convergent iterative solutions. These convergent solutions include the long standing difficult problem of a quartic potential with either symmetric or asymmetric minima.Comment: 54 pages, 3 figures given separatel

The Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary

We consider the dimer-monomer problem for the rectangular lattice. By mapping the problem into one of close-packed dimers on an extended lattice, we rederive the Tzeng-Wu solution for a single monomer on the boundary by evaluating a Pfaffian. We also clarify the mathematical content of the Tzeng-Wu solution by identifying it as the product of the nonzero eigenvalues of the Kasteleyn matrix.Comment: 4 Pages to appear in the Physical Review E (2006

Bose-Einstein condensation in multilayers

The critical BEC temperature $T_{c}$ of a non interacting boson gas in a layered structure like those of cuprate superconductors is shown to have a minimum $T_{c,m}$, at a characteristic separation between planes $a_{m}$. It is shown that for $a<a_{m}$, $T_{c}$ increases monotonically back up to the ideal Bose gas $T_{0}$ suggesting that a reduction in the separation between planes, as happens when one increases the pressure in a cuprate, leads to an increase in the critical temperature. For finite plane separation and penetrability the specific heat as a function of temperature shows two novel crests connected by a ridge in addition to the well-known BEC peak at $T_{c}$ associated with the 3D behavior of the gas. For completely impenetrable planes the model reduces to many disconnected infinite slabs for which just one hump survives becoming a peak only when the slab widths are infinite.Comment: Four pages, four figure

Spectral Boundary of Positive Random Potential in a Strong Magnetic Field

We consider the problem of randomly distributed positive delta-function scatterers in a strong magnetic field and study the behavior of density of states close to the spectral boundary at $E=\hbar\omega_{c}/2$ in both two and three dimensions. Starting from dimensionally reduced expression of Brezin et al. and using the semiclassical approximation we show that the density of states in the Lifshitz tail at small energies is proportio- nal to $e^{f-2}$ in two dimensions and to $\exp(-3.14f\ln(3.14f/\pi e)/ \sqrt(2me))$ in three dimensions, where $e$ is the energy and $f$ is the density of scatterers in natural units.Comment: 12 pages, LaTex, 5 figures available upon request, to appear in Phys. Rev.

Theory of impedance networks: The two-point impedance and LC resonances

We present a formulation of the determination of the impedance between any two nodes in an impedance network. An impedance network is described by its Laplacian matrix L which has generally complex matrix elements. We show that by solving the equation L u_a = lambda_a u_a^* with orthonormal vectors u_a, the effective impedance between nodes p and q of the network is Z = Sum_a [u_{a,p} - u_{a,q}]^2/lambda_a where the summation is over all lambda_a not identically equal to zero and u_{a,p} is the p-th component of u_a. For networks consisting of inductances (L) and capacitances (C), the formulation leads to the occurrence of resonances at frequencies associated with the vanishing of lambda_a. This curious result suggests the possibility of practical applications to resonant circuits. Our formulation is illustrated by explicit examples.Comment: 21 pages, 3 figures; v4: typesetting corrected; v5: Eq. (63) correcte

Dynamical evolution of boson stars in Brans-Dicke theory

We study the dynamics of a self-gravitating scalar field solitonic object (boson star) in the Jordan-Brans-Dicke (BD) theory of gravity. We show dynamical processes of this system such as (i) black hole formation of perturbed equilibrium configuration on an unstable branch; (ii) migration of perturbed equilibrium configuration from the unstable branch to stable branch; (iii) transition from excited state to a ground state. We find that the dynamical behavior of boson stars in BD theory is quite similar to that in general relativity (GR), with comparable scalar wave emission. We also demonstrate the formation of a stable boson star from a Gaussian scalar field packet with flat gravitational scalar field initial data. This suggests that boson stars can be formed in the BD theory in much the same way as in GR.Comment: 13 pages by RevTeX, epsf.sty, 16 figures, comments added, refs updated, to appear in Phys. Rev.