Related papers: Decreasing excitation gap in Andreev billiards by …
We introduce Andreev scattering (electron-hole conversion at an interface of a normal conductor to a superconductor) at the outer vertices of a quantum star graph and examine its effect on the spectrum. More specifically we show that the…
Anderson localization of Bogoliubov excitations is studied for disordered lattice Bose gases in planar quasi-one-dimensional geometries. The inverse localization length is computed as function of energy by a numerical transfer-matrix…
We study limit theorems in the context of random perturbations of dispersing billiards in finite and infinite measure. In the context of a planar periodic Lorentz gas with finite horizon, we consider random perturbations in the form of…
We examine the quantum energy levels of rectangular billiards with a pointlike scatterer in one and two dimensions. By varying the location and the strength of the scatterer, we systematically find diabolical degeneracies among various…
In this paper, by using our improved plane wave decomposition method, we study the scars in the eigenfunctions of the stadium billiard from very low state to as high as about the one millionth state. In the systematic searching for scars of…
A non--equilibrium occupation distribution relaxes towards the Fermi--Dirac distribution due to electron--electron scattering even in finite Fermi systems. The dynamic evolution of this thermalization process assumed to result from an…
We study the dynamics of the `batch' minority game with market-impact correction using generating functional techniques to carry out the quenched disorder average. We find that the assumption of weak long-term memory, which one usually…
We systematically investigate the equilibrium and the nonequilibrium quench dynamics of three-dimensional disordered quadrupolar Bose-Einstein condensates. Within the Bogoliubov-Huang-Meng approximation, we show that the combined effect of…
We study the quantitative simplicity of the Lyapunov spectrum of $d$-dimensional bounded matrix cocycles subjected to additive random perturbations. In dimensions 2 and 3, we establish explicit lower bounds on the gaps between consecutive…
Using the concept of minimal chaotic cavities, we give the distribution of the proper delay times of $Q=-i\hbar S^\dagger \frac{\partial S}{\partial E}$ at the spectrum edge with a scattering matrix $S$ belonging to circular ensembles CE.…
With the two-band continuum model, we study the broken inversion and time-reversal symmetry state of electrons with finite-range repulsive interactions in bilayer graphene. With the analytical solution to the mean-field Hamiltonian, we…
We provide an analytic method for estimating the entanglement of the non-gaussian energy eigenstates of disordered harmonic oscillator systems. We invoke the explicit formulas of the eigenstates of the oscillator systems to establish bounds…
We study the dynamical properties of a particle in a non-planar square billiard. The plane of the billiard has a sinusoidal shape. We consider both the static and time-dependent plane. We study the affect of different parameters that…
We study the relation between the eigenfrequencies of the Bogoliubov excitations of Bose-Einstein condensates, and the eigenvalues of the Jacobian stability matrix in a variational approach which maps the Gross-Pitaevskii equation to a…
We study the effects of disorder on bilayer graphene using four different microscopic models and directly compare their results. We compute the self-energy, density of states, and optical conductivity in the presence of short-ranged…
The condition number of the $n\ x\ n$ matrix $P$ is examined, where $P$ solves %the discete Lyapunov equation, $P - A P A^* = BB^*$, and $B$ is a $n\ x\ d$ matrix. Lower bounds on the condition number, $\kappa$, of $P$ are given when $A$ is…
We calculate the probability distribution of the matrix Q = -i \hbar S^{-1} dS/dE for a chaotic system with scattering matrix S at energy E. The eigenvalues \tau_j of Q are the so-called proper delay times, introduced by E. P. Wigner and F.…
The instanton approach to the in-gap fluctuation states is applied to the spectrum of biased bilayer graphene. It is shown that the density of states falls off with energy measured from the band-edge as $\nu(\epsilon)\propto…
We solve the Dorokhov-Mello-Pereyra-Kumar equation which describes the evolution of an ensamble of disordered wires of increasing length in the three cases $\beta=1,2,4$. The solution is obtained by mapping the problem in that of a suitable…
In this paper, we present an efficient and spectrally accurate numerical method to compute elementary/collective excitations in two-component Bose-Einstein condensates (BEC), around their mean-field ground state, by solving the associated…