Condensed Matter
We consider here the problem of a "central spin", with spin quantum number $S \gg 1$, interacting with a set of microscopic spins. Interactions between the microscopic spins are ignored. This model describes magnetic grains or magnetic…
We report the first experimental observation of parametric generation of second sound (SS) by first sound (FS) in superfluid helium in a narrow temperature range in the vicinity of $T_\lambda $. The temperature dependence of the threshold…
The theory of passive scalar transport in two dimensional turbulent fluids is generalized to the case of 2D MHD. Invariance of the cross correlation of scalar concentration and magnetic potential produces a novel contribution to the…
We describe a non-Arrhenius mechanism for slowing down of dynamics that is inherent to the high dimensionality of the phase space. We show that such a mechanism is at work both in a family of mean-field spin-glass models without any domain…
We comment on the recent work of Alcaraz and Malvezzi [1995 {\it J. Phys. A: Math. Gen.} {\bf 19} 1521] for the critical properties of the $S=1/2$ $XXZ$ chain in staggered magnetic field. The method of determining the phase boundary from…
We investigate uniform one-dimensional arrays of small Josephson junctions ($E_J \ll E_C$, $E_C = (2e)^2/2C$) with a realistic Coulomb interaction $U(x) = E_C \lambda \exp( - |x|/\lambda)$ (here $\lambda \gg 1$ is the screening length in…
Yuval-Anderson's scaling analysis and Affleck-Ludwig's Conformal Field Theory approach are applied to the $k$ channel {\em spin anisotropic} Kondo model. Detailed comparisons with the available Emery-Kivelson's Abelian Bosonization…
The Bogoliubov approximation is used to study the ground state and low-lying excited states of a dilute gas of $N$ atomic bosons held in an isotropic harmonic potential characterized by frequency $\omega$ and oscillator length $d_0$. By…
We present $\vec{k}$-dependent one-particle spectra and corresponding effective bandstructures for the $2d$ Hubbard model calculated within the dynamical molecular field theory (DMFT). This method has proven to yield highly nontrivial…
The authors propose a fast numerical renormalization group method --- the product wave function renormalization group (PWFRG) method --- for 1D quantum lattice models and 2D classical ones. A variational wave function, which is expressed by…
We present a theory of option pricing and hedging, designed to address non-perfect arbitrage, market friction and the presence of `fat' tails. An implied volatility `smile' is predicted. We give precise estimates of the residual risk…
We consider the interaction between two rods embedded in a fluctuating surface which is governed by either surface tension or rigidity. The modification of fluctuations by the rods leads to an attractive long-range interaction that falls…
We consider rectangular graph superlattices of sides l1, l2 with the wavefunction coupling at the junctions either of the delta type, when they are continuous and the sum of their derivatives is proportional to the common value at the…
An exact-diagonalization technique on small clusters is used to study low-lying excitations and superconductivity in the two-dimensional negative-$U$ Hubbard model. We first calculate the Bogoliubov-quasiparticle spectrum, condensation…
Using the ground state $\psi_0$ of a multicomponent generalization of the Calogero-Sutherland model as a weight function, orthogonal polynomials in the coordinates of one of the species are constructed. Using evidence from exact analytic…
An impurity bond $J{'}$ in a periodic 1D antiferromagnetic, spin 1 chain with exchange $J$ is considered. Using the numerical density matrix renormalization group method, we find an impurity energy level in the Haldane gap, corresponding to…
We have studied the temperature dependence of diagonal conductivity in high-mobility two-dimensional samples at filling factors $\nu=1/2$ and 3/2 at low temperatures. We observe a logarithmic dependence on temperature, from our lowest…
Ground-state properties of the two-dimensional $S=1/2$ random Heisenberg models are investigated by the exact-diagonalization method. The phase diagram of the bond-random model (the $\pm J$ model) is the same as that of the corresponding…
Using the polarizability of a free electron gas in a magnetic field and the Current-Density Functional Theory (CDFT) developed by Vignale and Rasolt, we derive the gradient and current corrections for the energy functional of a non-uniform…
The diagonal conductivity $\sigma_{xx}$ was measured in the Corbino geometry in both integer and fractional quantum Hall effect (QHE). We find that peak values of $\sigma_{xx}$ are approximately equal for transitions in a wide range of…