arXiv subjects

Feng Pan

Publications and source records attributed to Feng Pan.

At least 145 records · Page 8Linked to original sources

arXiv2010

Application of the extended pairing model to heavy isotopes

Relative binding energies (RBEs) within three isotopic chains ($^{100-130}$Sn, $^{152-181}$Yb, and $^{181-202 }$Pb) have been studied using the exactly solvable extended pairing model (EPM) \cite{FPan04}. The unique pairing strength $G$, which reproduces the experimental RBEs, has been determined. Within EPM, $\log(G)$ is a smooth function of the model space dimension $\dim(A)$, as expected for an effective coupling strength. In particular, for the Pb and Sn isotopes $G$ can be described by a two parameter expression that is inversely proportional to the dimensionality of the model space, $G=α\dim(A)^{-β}$ with $β\approx 1$. PACS Classification: 21.10.Dr Binding energies, 71.10.Li Pairing interactions in model systems, and 21.60.Cs Shell model.

nucl-th↗

arXiv2010

Predicting Failures in Power Grids: The Case of Static Overloads

Here we develop an approach to predict power grid weak points, and specifically to efficiently identify the most probable failure modes in static load distribution for a given power network. This approach is applied to two examples: Guam's power system and also the IEEE RTS-96 system, both modeled within the static Direct Current power flow model. Our algorithm is a power network adaption of the worst configuration heuristics, originally developed to study low probability events in physics and failures in error-correction. One finding is that, if the normal operational mode of the grid is sufficiently healthy, the failure modes, also called instantons, are sufficiently sparse, i.e. the failures are caused by load fluctuations at only a few buses. The technique is useful for discovering weak links which are saturated at the instantons. It can also identify generators working at the capacity and generators under capacity, thus providing predictive capability for improving the reliability of any power network.

math.OC↗

arXiv2010

Interdiction of a Markovian Evader

Shortest path network interdiction is a combinatorial optimization problem on an activity network arising in a number of important security-related applications. It is classically formulated as a bilevel maximin problem representing an "interdictor" and an "evader". The evader tries to move from a source node to the target node along a path of the least cost while the interdictor attempts to frustrate this motion by cutting edges or nodes. The interdiction objective is to find the optimal set of edges to cut given that there is a finite interdiction budget and the interdictor must move first. We reformulate the interdiction problem for stochastic evaders by introducing a model in which the evader follows a Markovian random walk guided by the least-cost path to the target. This model can represent incomplete knowledge about the evader, and the resulting model is a nonlinear 0-1 optimization problem. We then introduce an optimization heuristic based on betweenness centrality that can rapidly find high-quality interdiction solutions by providing a global view of the network.

math.OC↗

arXiv2010

A progressive diagonalization scheme for the Rabi Hamiltonian

A diagonalization scheme for the Rabi Hamiltonian, which describes a qubit interacting with a single-mode radiation field via a dipole interaction, is proposed. It is shown that the Rabi Hamiltonian can be solved almost exactly using a progressive scheme that involves a finite set of one variable polynomial equations. The scheme is especially efficient for lower part of the spectrum. Some low-lying energy levels of the model with several sets of parameters are calculated and compared to those provided by the recently proposed generalized rotating-wave approximation and full matrix diagonalization.

quant-ph↗

arXiv2010

Locating PHEV Exchange Stations in V2G

Plug-in hybrid electric vehicles (PHEVs) are an environmentally friendly technology that is expected to rapidly penetrate the transportation system. Renewable energy sources such as wind and solar have received considerable attention as clean power options for future generation expansion. However, these sources are intermittent and increase the uncertainty in the ability to generate power. The deployment of PHEVs in a vehicle-to-grid (V2G) system provide a potential mechanism for reducing the variability of renewable energy sources. For example, PHEV supporting infrastructures like battery exchange stations that provide battery service to PHEV customers could be used as storage devices to stabilize the grid when renewable energy production is fluctuating. In this paper, we study how to best site these stations in terms of how they can support both the transportation system and the power grid. To model this problem we develop a two-stage stochastic program to optimally locate the stations prior to the realization of battery demands, loads, and generation capacity of renewable power sources. We develop two test cases to study the benefits and the performance of these systems.

math.OC↗

arXiv2009

New exact solutions of the standard pairing model for well-deformed nuclei

A new step-by-step diagonalization procedure for evaluating exact solutions of the nuclear deformed mean-field plus pairing interaction model is proposed via a simple Bethe ansatz in each step from which the eigenvalues and corresponding eigenstates can be obtained progressively. This new approach draws upon an observation that the original one- plus two-body problem in a $k$-particle Hilbert subspace can be mapped unto a one-body grand hard-core boson picture that can be solved step by step with a simple Bethe ansatz known from earlier work. Based on this new procedure, it is further shown that the extended pairing model for deformed nuclei [Phys. Rev. Lett. 92, 112503 (2004) ] is similar to the standard pairing model with the first step approximation, in which only the lowest energy eigenstate of the standard pure pairing interaction part is taken into consideration. Our analysis show that the standard pairing model with the first step approximation displays similar pair structures of first few exact low-lying states of the model, which, therefore, provides a link between the two models.

nucl-th↗

arXiv2009

Quantum phase transitional patterns in the SD-pair shell model

Patterns of shape-phase transition in the proton-neutron coupled systems are studied within the $SD$-pair shell model. The results show that some transitional patterns in the $SD$-pair shell model are similar to the $U(5)-SU(3)$, $U(5)-SO(6)$ transitions with signatures of the critical point symmetry of the interacting boson model.

nucl-th↗

arXiv2009

Optimal Interdiction of Unreactive Markovian Evaders

The interdiction problem arises in a variety of areas including military logistics, infectious disease control, and counter-terrorism. In the typical formulation of network interdiction, the task of the interdictor is to find a set of edges in a weighted network such that the removal of those edges would maximally increase the cost to an evader of traveling on a path through the network. Our work is motivated by cases in which the evader has incomplete information about the network or lacks planning time or computational power, e.g. when authorities set up roadblocks to catch bank robbers, the criminals do not know all the roadblock locations or the best path to use for their escape. We introduce a model of network interdiction in which the motion of one or more evaders is described by Markov processes and the evaders are assumed not to react to interdiction decisions. The interdiction objective is to find an edge set of size B, that maximizes the probability of capturing the evaders. We prove that similar to the standard least-cost formulation for deterministic motion this interdiction problem is also NP-hard. But unlike that problem our interdiction problem is submodular and the optimal solution can be approximated within 1-1/e using a greedy algorithm. Additionally, we exploit submodularity through a priority evaluation strategy that eliminates the linear complexity scaling in the number of network edges and speeds up the solution by orders of magnitude. Taken together the results bring closer the goal of finding realistic solutions to the interdiction problem on global-scale networks.

cs.DM↗

arXiv2008

Quantum Noise, Effective Temperature, and Damping in a Superconducting Single-Electron Transistor

We have directly measured the quantum noise of a superconducting single-electron transistor (S-SET) embedded in a microwave resonator consisting of a superconducting LC tank circuit. Using an effective bath description, we find that the S-SET provides damping of the resonator modes proportional to its differential conductance and has an effective temperature that depends strongly on the S-SET bias conditions. In the vicinity of a double Cooper pair resonance, when both resonances are red detuned the S-SET effective temperature can be well below both the ambient temperature and the energy scale of the bias voltage. When blue detuned, the S-SET shows negative differential conductivity,

cond-mat.mes-hall↗

arXiv2007

Shot-Noise-Limited Operation of a Fast Quantum-Point-Contact Charge Sensor

We have operated a quantum point contact (QPC) charge detector in a radio frequency (RF) mode that allows fast charge detection in a bandwidth of tens of megahertz. We find that the charge sensitivity of the RF-QPC is limited not by the noise of a secondary amplifier, but by non-equilibrium noise f the QPC itself. We have performed frequency-resolved measurements of the noise within a 10 MHz bandwidth around our carrier wave. When averaged over our bandwidth, we find that the noise is in good agreement with the theory of photon-assisted shot noise. Our measurements also reveal strong frequency dependence of the noise, asymmetry with respect to the carrier wave, the appearance of sharp local maxima that are correlated with mechanical degrees of freedom in the sample, and noise suppression indicative of many-body physics near the 0.7 structure.

cond-mat.mes-hall↗

arXiv2007

On-Chip Matching Networks for Radio-Frequency Single-Electron-Transistors

In this letter, we describe operation of a radio-frequency superconducting single electron transistor (RF-SSET) with an on-chip superconducting LC matching network consisting of a spiral inductor L and its capacitance to ground. The superconducting network has a lower parasitic capacitance and gives a better matching for the RF-SSET than does a commercial chip inductor. Moreover, the superconducting network has negligibly low dissipation, leading to sensitive response to changes in the RF-SSET impedance. The charge sensitivity 2.4*10^-6 e/(Hz)^1/2 in the sub-gap region and energy sensitivity of 1.9 hbar indicate that the RF-SSET is operating in the vicinity of the shot noise limit.

cond-mat.mes-hall↗

arXiv2007

Exact boson mapping of the reduced BCS pairing Hamiltonian

An exact boson mapping of the reduced BCS (equal strength) pairing Hamiltonian is considered. In the mapping, fermion pair operators are mapped exactly to the corresponding bosons. The image of the mapping results in a Bose-Hubbard model with level dependent hopping. Though the resultant Bose-Hubbard Hamiltonian is non-Hermitian, all eigenvalues are real when Uk/t< 1, where k is the total number of bosons. When U/t=1, a part of spectrum of the Bose-Hubbard Hamiltonian corresponds exactly to the whole spectrum of the reduced BCS pairing Hamiltonian.

nucl-th↗

arXiv2007

Exact diagonalization for spin-1/2 chains and the first order quantum phase transitions of the XXX chain in a uniform transverse field

A simple Mathematica code based on the differential realization of hard-core boson operators for finding exact solutions of the periodic-N spin-1/2 systems with or beyond nearest neighbor interactions is proposed, which can easily be used to study general spin-1/2 interaction systems. As an example, The code is applied to study XXX spin-1/2 chain with nearest neighbor interaction in a uniform transverse field. It shows that there are [N/2] level-crossing points in the ground state, where N is the periodic number of the system and [x] stands for the integer part of x, when the interaction strength and magnitude of the magnetic field satisfy certain conditions. The quantum phase transitional behavior in the ground state of the system in the thermodynamic limit is also studied.

quant-ph↗

arXiv2007

First order quantum phase transitions in the XX spin chain

Quantum phase transitional behavior of a finite periodic XX spin-1/2 chain with nearest neighbor interaction in a uniform transverse field is studied based on the simple exact solutions. It is found that there are [N/2] level-crossing points in the ground state, where N is the periodic number of the system and [x] stands for the integer part of x, when the interaction strength and magnitude of the magnetic field satisfy certain conditions. The quantum phase transitions are of the first order due to the level-crossing. The ground state in the thermodynamic limit will be divided into three distinguishable quantum phases.

quant-ph↗

arXiv2007

M-body Pure State Entanglement

The simple entanglement of N-body N-particle pure states is extended to the more general M-body or M-body N-particle states where $N\neq M$. Some new features of the M-body N-particle pure states are discussed. An application of the measure to quantify quantum correlations in a Bose-Einstien condensate model is demonstrated.

quant-ph↗

arXiv2006

Su(3) Algebraic Structure of the Cuprate Superconductors Model based on the Analogy with Atomic Nuclei

A cuprate superconductor model based on the analogy with atomic nuclei was shown by Iachello to have an $su(3)$ structure. The mean-field approximation Hamiltonian can be written as a linear function of the generators of $su(3)$ algebra. Using algebraic method, we derive the eigenvalues of the reduced Hamiltonian beyond the subalgebras $u(1)\bigotimes u(2)$ and $so(3)$ of $su(3)$ algebra. In particular, by considering the coherence between s- and d-wave pairs as perturbation, the effects of coherent term upon the energy spectrum are investigated.

cond-mat.other↗

arXiv2006

Classification and Quantification of Entangled Bipartite Qutrit Pure States

A complete analysis of entangled bipartite qutrit pure states is carried out based on a simple entanglement measure. An analysis of all possible extremally entangled pure bipartite qutrit states is shown to reduce, with the help of SLOCC transformations, to three distinct types. The analysis and the results should be helpful for finding different entanglement types in multipartite pure state systems.

quant-ph↗

arXiv2005

Quantum Phase Transitions in the U(5)-O(6) Large N limit

The U(5)-O(6) transitional behavior of the Interacting Boson Model in the large N limit is revisited. Some low-lying energy levels, overlaps of the ground state wavefunctions, B(E2) transition rate for the decay of the first excited energy level to the ground state, and the order parameters are calculated for different total numbers of bosons. The results show that critical behaviors of these quantities are greatly enhanced with increasing of the total number of bosons N, especially fractional occupation probability for d bosons in the ground state, the difference between the expectation value of n_d in the first excited 0^+ state and the ground state, and another quantity related to the isomer shift behave similarly in both the O(6)-U(5) large N and U(5)-SU(3) phase transitions.

nucl-th↗