arXiv subjects

Hao Fu

Publications and source records attributed to Hao Fu.

118 records · Page 7Linked to original sources

arXiv2016

Computer assisted proof for Apwenian sequences related to Hankel determinants

An infinite $\pm 1$-sequence is called {\it Apwenian} if its Hankel determinant of order $n$ divided by $2^{n-1}$ is an odd number for every positive integer $n$. In 1998, Allouche, Peyrière, Wen and Wen discovered and proved that the Thue--Morse sequence is an Apwenian sequence by direct determinant manipulations. Recently, Bugeaud and Han re-proved the latter result by means of an appropriate combinatorial method. By significantly improving the combinatorial method, we prove that several other Apwenian sequences related to the Hankel determinants with Computer Assistance.

math.NT↗

arXiv2015

Joint Power Splitting and Secure Beamforming Design in the Wireless-powered Untrusted Relay Networks

In this work, we maximize the secrecy rate of the wireless-powered untrusted relay network by jointly designing power splitting (PS) ratio and relay beamforming with the proposed global optimal algorithm (GOA) and local optimal algorithm (LOA). Different from the literature, artificial noise (AN) sent by the destination not only degrades the channel condition of the eavesdropper to improve the secrecy rate, but also becomes a new source of energy powering the untrusted relay based on PS. Hence, it is of high economic benefits and efficiency to take advantage of AN compared with the literature. Simulation results show that LOA can achieve satisfactory secrecy rate performance compared with that of GOA, but with less computation time.

cs.IT↗

arXiv2014

Temperature enhanced photothermal cooling of a micro-cantilever

We present a temperature enhanced photothermal cooling scheme in a micro-cantilever based FP cavity. Experiments at various temperatures show a temperature dependence of photothermal cooling efficiency. And approximate one order of improvement on the cooling efficiency is achieved experimentally when the temperature decreases from 298 K to 100 K. Numerical analysis reveals that the dramatic change of the cooling efficiency is attributed to the temperature dependent dynamics of the photothermal backaction. A high efficient cooling can be achieved by controlling the temperature for an optimized the dynamics of photothermal backaction.

physics.optics↗

arXiv2014

On $t$-extensions of the Hankel determinants of certain automatic sequences

In 1998, Allouche, Peyrière, Wen and Wen considered the Thue--Morse sequence, and proved that all the Hankel determinants of the period-doubling sequence are odd integral numbers. We speak of $t$-extension when the entries along the diagonal in the Hankel determinant are all multiplied by~$t$. Then we prove that the $t$-extension of each Hankel determinant of the period-doubling sequence is a polynomial in $t$, whose leading coefficient is the {\it only one} to be an odd integral number. Our proof makes use of the combinatorial set-up developed by Bugeaud and Han, which appears to be very suitable for this study, as the parameter $t$ counts the number of fixed points of a permutation. Finally, we prove that all the $t$-extensions of the Hankel determinants of the regular paperfolding sequence are polynomials in $t$ of degree less than or equal to $3$.

math.CO↗

arXiv2011

Laser spot position dependent photothermal mode cooling of a micro-cantilever

We explore the laser spot position (LSP) dependent photothermal mode cooling of a micro-cantilever in a Fabry-Pérot (FP) cavity. Depending on the LSP along the lever, photothermal coupling to the first two mechanical modes can be either parallel or anti-parallel. This LSP dependent behavior is analyzed theoretically by a simple model, which is in quantitatively agreement with our experimental observation. From simulation, the parallel and anti-parallel coupling region is identified along the lever. We conclude that a more efficient mode cooling may be achieved in the parallel coupling region.

physics.optics↗

arXiv2006

Spin Hall effects for cold atoms in a light induced gauge potential

We propose an experimental scheme to observe spin Hall effects with cold atoms in a light induced gauge potential. Under an appropriate configuration, the cold atoms moving in a spatially varying laser field experience an effective spin-dependent gauge potential. Through numerical simulation, we demonstrate that such a gauge field leads to observable spin Hall currents under realistic conditions. We also discuss the quantum spin Hall state in an optical lattice.

cond-mat.mes-hall↗

arXiv2006

A Cold Atomic Fermi Gas with a Spatially Modulated Interaction

We study an ultra-cold atomic Fermi Gas with the atom-atom interaction modulated periodically in space. A novel ground state with cooper pairs occupying non-zero center of mass momenta is found. Such a state is closely related to the state proposed by Fulde, Ferrell, Larkin, and Ovchinnikov(FFLO). The resultant single particle excitations with momenta along the direction of the modulation shows multiple-gap structures. Such a system can be realized in experiment with a spatially modulated Feshbach resonance. Experimental signatures of such a state are discussed.

cond-mat.supr-con↗

arXiv2006

Microscopic Theory of the Photon Recoil of an Atom in a Dielectric

An atom recoils when it undergoes spontaneous decay. In this paper we present a microscopic calculation of the recoil of a source atom imbedded in a dielectric medium. We find that the source atom recoils with the canonical photon momentum $n\hbar k_{0,}$ where $n$ is the index of refraction and $\hbar k_{0}$ is the photon momentum calculated at the source atom atomic frequency $ω_{0}$. We also show explicitly how the energy is conserved with the photon inside the medium.

quant-ph↗

arXiv2006

Microscopic Theory of Spontaneous Decay in a Dielectric

The local field correction to the spontanous dacay rate of an impurity source atom imbedded in a disordered dielectric is calculated to second order in the dielectric density. The result is found to differ from predictions associated with both "virtual" and "real" cavity models of this decay process. However, if the contributions from two dielectric atoms at the same position are included, the virtual cavity result is reproduced.

quant-ph↗

arXiv2006

A Tonks Giradeau Gas in the Presence of a Local Potential

The physics of a Tonks-Giradeau Gas in the presence of a local potential is studied. In order to evaluate the single particle density matrix (SPDM) of the many-body ground state, the Wiger-Jordan transformation is used. The eigenvector with the largest eigenvalue of the SPDM corresponds to the "Bose-Einstein Condensate"(BEC) State. We find that the "BEC" state density at the positon of the local potential decreases, as expected, in the case of a repulsive potential. For an attractive potential, it decreases or increases depending on the strength of the potential. The superfluidity of this system is investigated both numerically and perturbatively. An experimental method for detecting the effect of an impurity in a Tonks-Giradueau gas is discussed.

cond-mat.other↗