arXiv subjects

Wojciech Ganczarek

Publications and source records attributed to Wojciech Ganczarek.

5 recordsLinked to original sources

arXiv2014

One-dimensional s-p superlattice

The physics of one dimensional optical superlattices with resonant $s$-$p$ orbitals is reexamined in the language of appropriate Wannier functions. It is shown that details of the tight binding model realized in different optical potentials crucially depend on the proper determination of Wannier functions. We discuss the properties of a superlattice model which quasi resonantly couples $s$ and $p$ orbitals and show its relation with different tight binding models used in other works.

cond-mat.quant-gas↗

arXiv2013

One-dimensional superlattices with s-p resonance

We propose a realization of an extended Bose-Hubbard model, which takes into account next-nearest-neighbor tunneling, by one-dimensional double-well optical superlattice with a resonance between s and p orbitals in the neighboring sites. Custom method of finding maximally-localized Wannier functions enables us to compute physical tunneling coefficients, which put some restrictions on the studies of the model, what have recently been done using arbitrary values of parameters. Furthermore, it turns out that out of s-p resonance the system splits up into two disconnected lattices. We analyze also Zak-Berry phase and single-particle spectrum of the system. In order to present the problem in the full context, short review of rudiments of optical lattice physics and derivation of the standard Bose-Hubbard model is included.

cond-mat.quant-gas↗

arXiv2013

Mathematical models for epidemic spreading on complex networks

We propose a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step. Because of a highly discrete character of the process, the analysis cannot use the continous approximation, widely exploited for most of the models. Using discrete approach we investigate the epidemic threshold and the quasi-stationary distribution. The main result is a theorem about mixing time for the process, which scales like logarithm of the network size and which is proportional to the inverse of the distance from the epidemic threshold. In order to present the model in the full context, we review modern approach to epidemic spreading modeling based on complex networks and present necessary information about random networks, discrete-time Markov chains and their quasi-stationary distributions.

physics.soc-ph↗

arXiv2011

Barycentric measure of quantum entanglement

Majorana representation of quantum states by a constellation of n 'stars' (points on the sphere) can be used to describe any pure state of a simple system of dimension n+1 or a permutation symmetric pure state of a composite system consisting of n qubits. We analyze the variance of the distribution of the stars, which can serve as a measure of the degree of non-coherence for simple systems, or an entanglement measure for composed systems. Dynamics of the Majorana points induced by a unitary dynamics of the pure state is investigated.

quant-ph↗

arXiv2011

Solution to the Equations of the Moment Expansions

We develop a formula for matching a Taylor series about the origin and an asymptotic exponential expansion for large values of the coordinate. We test it on the expansion of the generating functions for the moments and connected moments of the Hamiltonian operator. In the former case the formula produces the energies and overlaps for the Rayleigh-Ritz method in the Krylov space. We choose the harmonic oscillator and a strongly anharmonic oscillator as illustrative examples for numerical test. Our results reveal some features of the connected-moments expansion that were overlooked in earlier studies and applications of the approach.

quant-ph↗