arXiv subjects

Fan Zhang

Publications and source records attributed to Fan Zhang.

At least 937 records · Page 52Linked to original sources

arXiv2014

The scalar Green function of the Kerr spacetime

In this paper we study the scalar Green function in the Kerr spacetime using WKB methods. The Green function can be expressed by Fourier-transforming to its frequency-domain counterpart, and with the help of complex analysis it can be divided into parts: 1) the "direct part" which propagates on the light cone and dominates at very early times; 2) the "quasinormal-mode part" which represents the waves traveling around the photon sphere, and is important at early and intermediate times; 3) the "tail part" which is due to scattering by the Coulomb-type potential and becomes more important at later times. We focus on the "quasinormal-mode part" of the Green function and derive an approximate analytical formula for it using WKB techniques. This approximate Green function diverges at points that are connected by null geodesics, and recovers the four-fold singular structure of Green functions that are seen in Schwarzschild and other spacetimes. It also carries unique signatures of the Kerr spacetime such as frame-dragging. Along the way, we also derive approximate quasinormal mode wavefunctions and expressions for the black hole excitation factors in the Kerr spacetime. We expect this work to benefit the understanding of both wave propagation and the problem of self-force in the Kerr spacetime.

gr-qc↗

arXiv2014

Spontaneous Layer-Pseudospin Domain Walls in Bilayer Graphene

Bilayer graphene is susceptible to a family of unusual broken symmetry states with spin and valley dependent layer polarization. We report on a microscopic study of the domain walls in these systems, demonstrating that they have interesting microscopic structures related to order-induced topological characters. We use our results to estimate Ginzburg-Landau model parameters and transition temperatures for the ordered states of bilayer graphene.

cond-mat.mes-hall↗

arXiv2014

Time-Reversal-Invariant $Z_4$ Fractional Josephson Effect

We study the Josephson junction mediated by the quantum spin Hall edge states and show that electron-electron interactions lead to a dissipationless fractional Josephson effect in the presence of time-reversal symmetry. Surprisingly, the periodicity is $8π$, corresponding to a Josephson frequency $eV/2\hbar$. We estimate the magnitude of interaction induced many-body level splitting responsible for this effect and argue that it can be measured using tunneling spectroscopy. For strong interactions we show that the Josephson effect is associated with the weak tunneling of charge $e/2$ quasiparticles between the superconductors. Our theory describes a fourfold ground state degeneracy that is similar to that of coupled "fractional" Majorana modes, but is protected by time reversal symmetry.

cond-mat.supr-con↗

arXiv2014

Decline of the current quadrupole moment during the merger phase of binary black hole coalescence

Utilizing the tools of tendex and vortex, we study the highly dynamic plunge and merger phases of several $π$-symmetric binary black hole coalescences. In particular, we observe a decline of the strength of the current quadrupole moment as compared to that of the mass quadrupole moment during the merger phase, contrary to a naive estimate according to the dependence of these moments on the separation between the black holes. We further show that this decline of the current quadrupole moment is achieved through the remnants of the two individual spins becoming nearly aligned or anti-aligned with the total angular momentum. We also speculate on the implication of our observations for achieving a consistency between the electric and magnetic parity quasinormal modes.

gr-qc↗

arXiv2014

Distinct Competing Ordered ν=2 States in Bilayer Graphene

Because of its large density-of-states and the 2π Berry phase near its low-energy band-contact points, neutral bilayer graphene (BLG) at zero magnetic field (B) is susceptible to chiral-symmetry breaking, leading to a variety of gapped spontaneous quantum Hall states distinguished by valley and spin-dependent quantized Hall conductivities. Among these, the layer antiferromagnetic state, which has quantum valley Hall (QVH) effects of opposite sign for opposite spins, appears to be the thermodynamic ground state. Though other gapped states have not been observed experimentally at B=0, they can be explored by exploiting their adiabatic connection to quantum Hall states with the same total Hall conductivity σH. In this paper, by using a magnetic field to select filling factor ν=2 states with σH=2e^2/h, we demonstrate the presence of a quantum anomalous Hall (QAH) state for the majority spin, and a Kekulé state with spontaneous valley coherence and a quantum valley Hall state for the minority spin in BLG. By providing the first spectroscopic mapping of spontaneous Hall states at ν=2, our results shed further light on the rich set of competing ordered states in BLG.

cond-mat.mes-hall↗

arXiv2014

Dirac and Weyl Superconductors in Three Dimensions

We introduce the concept of 3D Dirac (Weyl) superconductors (SC), which have protected bulk four(two)-fold nodal points and surface Andreev arcs at zero energy. We provide a sufficient criterion for realizing them in centrosymmetric SCs with odd-parity pairing and mirror symmetry, e.g., the nodal phases of Cu$_x$Bi$_2$Se$_3$. Pairs of Dirac nodes appear in a mirror-invariant plane when the mirror winding number is nontrivial. Breaking mirror symmetry may gap Dirac nodes producing a topological SC. Each Dirac node evolves to a nodal ring when inversion-gauge symmetry is broken. A Dirac node may split into a pair of Weyl nodes, only when time-reversal symmetry is broken.

cond-mat.supr-con↗

arXiv2014

Signatures of Majorana Fermions in Topological Insulator Josephson Junction Devices

We study theoretically the electrical current and low-frequency noise for a linear Josephson junction structure on a topological insulator, in which the superconductor forms a closed ring and currents are injected from normal regions inside and outside the ring. We find that this geometry offers a signature for the presence of gapless 1D Majorana fermion modes that are predicted in the channel when the phase difference ϕ, controlled by the magnetic flux through the ring, is π. We show that for low temperature the linear conductance jumps when ϕ passes through π, accompanied by non-local correlations between the currents from the inside and outside of the ring. We compute the dependence of these features on temperature, voltage and linear dimensions, and discuss the implications for experiments.

cond-mat.mes-hall↗

arXiv2013

Cross-Layer MIMO Transceiver Optimization for Multimedia Streaming in Interference Networks

In this paper, we consider dynamic precoder/decorrelator optimization for multimedia streaming in MIMO interference networks. We propose a truly cross-layer framework in the sense that the optimization objective is the application level performance metrics for multimedia streaming, namely the playback interruption and buffer overflow probabilities. The optimization variables are the MIMO precoders/decorrelators at the transmitters and the receivers, which are adaptive to both the instantaneous channel condition and the playback queue length. The problem is a challenging multi-dimensional stochastic optimization problem and brute-force solution has exponential complexity. By exploiting the underlying timescale separation and special structure in the problem, we derive a closed-form approximation of the value function based on continuous time perturbation. Using this approximation, we propose a low complexity dynamic MIMO precoder/decorrelator control algorithm by solving an equivalent weighted MMSE problem. We also establish the technical conditions for asymptotic optimality of the low complexity control algorithm. Finally, the proposed scheme is compared with various baselines through simulations and it is shown that significant performance gain can be achieved.

cs.IT↗

arXiv2013

Statistical and dynamical parts of the cumulants of conserved charges in relativistic heavy ion collisions

The Poisson-liked statistical fluctuations, which are caused by the finite number of produced particles, are firstly estimated for the cumulants of conserved charges, i.e., the cumulants of net-baryon, net-electric charge, and net-strangeness. They turn out to be the same as those baselines derived from Hadron Resonance Gas (HRG) model. The energy and centrality dependence of net-proton cumulants at the Relativistic Heavy-Ion Collider (RHIC) are demonstrated to be mainly caused by statistical fluctuations. Subtracting the statistical fluctuations, the dynamical kurtosis of net- and total-proton from two versions of the AMPT model and the UrQMD model at current RHIC beam energies are presented. It is found that the observed sign change in the kurtosis of net-proton can not be reproduced by these three transport models. There is no significant difference between net- and total-proton kurtosis in model calculations, in contrary to the data at RHIC.

nucl-th↗

arXiv2013

Designer Topological Insulators in Superlattices

Gapless Dirac surface states are protected at the interface of topological and normal band insulators. In a binary superlattice bearing such interfaces, we establish that valley-dependent dimerization of symmetry-unrelated Dirac surface states can be exploited to induce topological quantum phase transitions. This mechanism leads to a rich phase diagram that allows us to design strong, weak, and crystalline topological insulators. Our ab initio simulations further demonstrate this mechanism in [111] and [110] superlattices of calcium and tin tellurides.

cond-mat.mtrl-sci↗

arXiv2013

Anomalous Topological Pumps and Fractional Josephson Effects

We discover novel topological pumps in the Josephson effects for superconductors. The phase difference, which is odd under the chiral symmetry defined by the product of time-reversal and particle-hole symmetries, acts as an anomalous adiabatic parameter. These pumping cycles are different from those in the "periodic table", and are characterized by $Z\times Z$ or $Z_2\times Z_2$ strong invariants. We determine the general classifications in class AIII, and those in class DIII with a single anomalous parameter. For the $Z_2\times Z_2$ topological pump in class DIII, one $Z_2$ invariant describes the coincidence of fermion parity and spin pumps whereas the other one reflects the non-Abelian statistics of Majorana Kramers pairs, leading to three distinct fractional Josephson effects.

cond-mat.supr-con↗

arXiv2013

Zeeman Field-Tuned Transitions for Surface Chern Insulators

Mirror symmetric surfaces of a topological crystalline insulator host even number of Dirac surface states. A surface Zeeman field generically gaps these states leading to a quantized anomalous Hall effect. Varying the direction of Zeeman field induces transitions between different surface insulating states with any two Chern numbers between -4 and 4. In the crystal frame the phase boundaries occur for field orientations which are great circles with (111)-like normals on a sphere.

cond-mat.mes-hall↗

arXiv2013

Asymptotically Optimal Beamforming for Video Streaming in Multi-Antenna Interference Networks

In this paper, we consider queue-aware beamforming control for video streaming applications in multi-antenna interference network. Using heavy traffic approximation technique, we first derive the diffusion limit for the discrete time queuing system. Based on the diffusion limit, we formulate an infinite horizon ergodic control problem to minimize the average power costs of the base stations subject to the constraints on the playback interruption costs and buffer overflow costs of the mobile users. To deal with the queue coupling challenge, we utilize the weak interference coupling property in the network to derive a closed-form approximate value function of the optimality equation as well as the associated error bound using perturbation analysis. Based on the closed-form approximate value function, we propose a low complexity queue-aware beamforming control algorithm, which is asymptotically optimal for sufficiently small cross-channel path gain. Finally, the proposed scheme is compared with various baselines through simulations and it is shown that significant performance gain can be achieved.

cs.IT↗

arXiv2013

Magnetic control of the valley degree of freedom of massive Dirac fermions with application to transition metal dichalcogenides

We study the valley-dependent magnetic and transport properties of massive Dirac fermions in multivalley systems such as the transition metal dichalcogenides. The asymmetry of the zeroth Landau level between valleys and the enhanced magnetic susceptibility can be attributed to the different orbital magnetic moment tied with each valley. This allows the valley polarization to be controlled by tuning the external magnetic field and the doping level. As a result of this magnetic field induced valley polarization, there exists an extra contribution to the ordinary Hall effect. All these effects can be captured by a low energy effective theory with a valley-orbit coupling term.

cond-mat.mes-hall↗

arXiv2013

A joint approach for reducing eccentricity and spurious gravitational radiation in binary black hole initial data construction

At the beginning of binary black hole simulations, there is a pulse of spurious radiation (or junk radiation) resulting from the initial data not matching astrophysical quasi-equilibrium inspiral exactly. One traditionally waits for the junk radiation to exit the computational domain before taking physical readings, at the expense of throwing away a segment of the evolution, and with the hope that junk radiation exits cleanly. We argue that this hope does not necessarily pan out as junk radiation could excite long-lived constraint violation. Another complication with the initial data is that it contains orbital eccentricity that needs to be removed, usually by evolving the early part of the inspiral multiple times with gradually improved input parameters. We show that this procedure is also adversely impacted by junk radiation. In this paper, we do not attempt to eliminate junk radiation directly, but instead tackle the much simpler problem of ameliorating its long-lasting effects. We report on the success of a method that achieves this goal by combining the removal of junk radiation and eccentricity into a single "joint-elimination" procedure. This approach has the following benefits: (1) We do not have to contend with the influence of junk radiation on eccentricity measurements for later iterations of the eccentricity reduction procedure. (2) We re-enforce constraints periodically by invoking the initial data solver, removing the constraint violation excited by junk radiation previously. (3) The wasted simulation segment associated with the junk radiation's evolution is absorbed into the eccentricity reduction iterations. Furthermore, (1) and (2) together allow us to carry out our joint-elimination procedure at low resolution, even when the subsequent "production run" is intended as a high resolution simulation.

gr-qc↗

arXiv2013

Time Reversal Invariant Topological Superconductivity and Majorana Kramers Pairs

We propose a feasible route to engineer one and two dimensional time reversal invariant (TRI) topological superconductors (SC) via proximity effects between nodeless extended s wave iron-based SC and semiconductors with large Rashba spin-orbit interactions. At the boundary of a TRI topological SC, there emerges a Kramers pair of Majorana edge (bound) states. For a Josephson pi-junction we predict a Majorana quartet that is protected by mirror symmetry and leads to a mirror fractional Josephson effect. We analyze the evolution of Majorana pair in Zeeman fields, as the SC undergoes a symmetry class change as well as topological phase transitions, providing an experimental signature in tunneling spectroscopy. We briefly discuss the realization of this mechanism in candidate materials and the possibility of using s and d wave SC and weak topological insulators.

cond-mat.supr-con↗

arXiv2013

Topological Mirror Superconductivity

We demonstrate the existence of topological superconductors (SC) protected by mirror and time reversal (TR) symmetries. D-dimensional (D=1,2,3) crystalline SCs are characterized by 2^(D-1) independent integer topological invariants, which take the form of mirror Berry phases. These invariants determine the distribution of Majorana modes on a mirror symmetric boundary. The parity of total mirror Berry phase is the Z_2 index of a class DIII SC, implying that a DIII topological SC with a mirror line must also be a topological mirror SC but not vice versa, and that a DIII SC with a mirror plane is always TR trivial but can be mirror topological. We introduce representative models and suggest experimental signatures in feasible systems. Advances in quantum computing, the case for nodal SCs, the case for class D, and topological SCs protected by rotational symmetries are pointed out.

cond-mat.supr-con↗

arXiv2013

Quasinormal modes of nearly extremal Kerr spacetimes: spectrum bifurcation and power-law ringdown

We provide an in-depth investigation of quasinormal-mode oscillations of Kerr black holes with nearly extremal angular momenta. We first discuss in greater detail the two distinct types of quasinormal mode frequencies presented in a recent paper (arXiv:1212.3271). One set of modes, that we call "zero-damping modes", has vanishing imaginary part in the extremal limit, and exists for all corotating perturbations (i.e., modes with azimuthal index m being nonnegative). The other set (the "damped modes") retains a finite decay rate even for extremal Kerr black holes, and exists only for a subset of corotating modes. As the angular momentum approaches its extremal value, the frequency spectrum bifurcates into these two distinct branches when both types of modes are present. We discuss the physical reason for the mode branching by developing and using a bound-state formulation for the perturbations of generic Kerr black holes. We also numerically explore the specific case of the fundamental l=2 modes, which have the greatest astrophysical interest. Using the results of these investigations, we compute the quasinormal mode response of a nearly extremal Kerr black hole to perturbations. We show that many superimposed overtones result in a slow power-law decay of the quasinormal ringing at early times, which later gives way to exponential decay. This exceptional early-time power-law decay implies that the ringdown phase is long-lived for black holes with large angular momentum, which could provide a promising strong source for gravitational-wave detectors.

gr-qc↗