Alexandre Dias Ribeiro

arXiv2015

A general dichotomization procedure to provide qudits entanglement criteria

We present a general strategy to derive entanglement criteria which consists in performing a mapping from qudits to qubits that preserves the separability of the parties and SU(2) rotational invariance. Consequently, it is possible to apply the well known positive partial transpose criterion to reveal the existence of quantum correlations between qudits. We discuss some examples of entangled states that are detected using the proposed strategy. Finally, we demonstrate, using our scheme, how some variance-based entanglement witnesses can be generalized from qubits to higher dimensional spin systems.

quant-ph↗

arXiv2014

Level density of a Bose gas: beyond the saddle point approximation

The present article is concerned with the use of approximations in the calculation of the many-body density of states (MBDS) of a system with total energy E, composed by N bosons. In the mean-field framework, an integral expression for MBDS, which is proper to be performed by asymptotic expansions, can be derived. However, the standard second order steepest descent method cannot be applied to this integral when the ground-state is sufficiently populated. Alternatively, we derive a uniform formula for MBDS, which is potentially able to deal with this regime. In the case of the one-dimensional harmonic oscillator, using results found in the number theory literature, we show that the uniform formula improves the standard expression achieved by means of the second order method.

cond-mat.stat-mech↗