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Ying Hu

Publications and source records attributed to Ying Hu.

At least 109 records · Page 6Linked to original sources
arXiv2020

Memory-Critical Dynamical Buildup of Phonon-Dressed Majorana Fermions

We investigate the dynamical interplay between topological state of matter and a non-Markovian dissipation, which gives rise to a new and crucial time scale into the system dynamics due to its quantum memory. We specifically study a one-dimensional polaronic topological superconductor with phonon-dressed $p$-wave pairing, when a fast temperature increase in surrounding phonons induces an open-system dynamics. We show that when the memory depth increases, the Majorana edge dynamics transits from relaxing monotonically to a plateau of substantial value into a collapse-and-buildup behavior, even when the polaron Hamiltonian is close to the topological phase boundary. Above a critical memory depth, the system can approach a new dressed state of topological superconductor in dynamical equilibrium with phonons, with nearly full buildup of Majorana correlation.

quant-ph↗
arXiv2020

Systems of ergodic BSDEs arising in regime switching forward performance processes

We introduce and solve a new type of quadratic backward stochastic differential equation systems defined in an infinite time horizon, called \emph{ergodic BSDE systems}. Such systems arise naturally as candidate solutions to characterize forward performance processes and their associated optimal trading strategies in a regime switching market. In addition, we develop a connection between the solution of the ergodic BSDE system and the long-term growth rate of classical utility maximization problems, and use the ergodic BSDE system to study the large time behavior of PDE systems with quadratic growth Hamiltonians.

math.PR↗
arXiv2020

Consistent Investment of Sophisticated Rank-Dependent Utility Agents in Continuous Time

We study portfolio selection in a complete continuous-time market where the preference is dictated by the rank-dependent utility. As such a model is inherently time inconsistent due to the underlying probability weighting, we study the investment behavior of sophisticated consistent planners who seek (subgame perfect) intra-personal equilibrium strategies. We provide sufficient conditions under which an equilibrium strategy is a replicating portfolio of a final wealth. We derive this final wealth profile explicitly, which turns out to be in the same form as in the classical Merton model with the market price of risk process properly scaled by a deterministic function in time. We present this scaling function explicitly through the solution to a highly nonlinear and singular ordinary differential equation, whose existence of solutions is established. Finally, we give a necessary and sufficient condition for the scaling function to be smaller than 1 corresponding to an effective reduction in risk premium due to probability weighting.

q-fin.MF↗
arXiv2020

Model-Based Compensation of Moving Tissue for State Recognition in Robotic-Assisted Pedicle Drilling

Drilling is one of the hardest parts of pedicle screw fixation, and it is one of the most dangerous operations because inaccurate screw placement would injury vital tissues, particularly when the vertebra is not stationary. Here we demonstrate the drilling state recognition method for moving tissue by compensating the displacement based on a simplified motion predication model of a vertebra with respect to the tidal volume. To adapt it to different patients, the prediction model was built based on the physiological data recorded from subjects themselves. In addition, the spindle speed of the drilling tool was investigated to find a suitable speed for the robotic-assisted system. To ensure patient safety, a monitoring system was built based on the thrusting force and tracked position information. Finally, experiments were carried out on a fresh porcine lamellar bone fixed on a 3-PRS parallel robot used to simulate the vertebra displacement. The success rate of the robotic-assisted drilling procedure reached 95% when the moving bone was compensated.

cs.RO↗
arXiv2019

Existence, uniqueness, comparison theorem and stability theorem for unbounded solutions of scalar BSDEs with sub-quadratic generators

We first establish the existence of an unbounded solution to a backward stochastic differential equation (BSDE) with generator $g$ allowing a general growth in the state variable $y$ and a sub-quadratic growth in the state variable $z$, like $|z|^α$ for some $α\in (1,2)$, when the terminal condition satisfies a sub-exponential moment integrability condition like $\exp\left(μL^{2/α^*}\right)$ for the conjugate $α^*$ of $α$ and a positive parameter $μ>μ_0$ with a certain value $μ_0$, which is clearly weaker than the usual $\exp(μL)$ integrability and stronger than $L^p\ (p>1)$ integrability. Then, we prove the uniqueness and comparison theorem for the unbounded solutions of the preceding BSDEs under the additional assumptions that the terminal conditions have sub-exponential moments of any order and the generators are convex or concave in $(y,z)$. Afterwards, we extend the uniqueness and comparison theorem to the non-convexity and non-concavity case, and establish a general stability result for the unbounded solutions of the preceding BSDEs. Finally, with these tools in hands, we derive the nonlinear Feynman-Kac formula in this context.

math.PR↗
arXiv2019

Fixed points and emergent topological phenomena in a parity-time-symmetric quantum quench

We identify emergent topological phenomena such as dynamic Chern numbers and dynamic quantum phase transitions in quantum quenches of the non-Hermitian Su-Schrieffer-Heeger Hamiltonian with parity-time ($\mathcal{PT}$) symmetry. Their occurrence in the non-unitary dynamics are intimately connected with fixed points in the Brillouin zone, where the states do not evolve in time. We construct a theoretical formalism for characterizing topological properties in non-unitary dynamics within the framework of biorthogonal quantum mechanics, and prove the existence of fixed points for quenches between distinct static topological phases in the $\mathcal{PT}$-symmetry-preserving regime. We then reveal the interesting relation between different dynamic topological phenomena through the momentum-time spin texture characterizing the dynamic process. For quenches involving Hamiltonians in the $\mathcal{PT}$-symmetry-broken regime, these topological phenomena are not ensured.

cond-mat.quant-gas↗
arXiv2019

Anticipated backward stochastic differential equations with quadratic growth

In this paper, we study the solvability of anticipated backward stochastic differential equations (BSDEs, for short) with quadratic growth for one-dimensional case and multi-dimensional case. In these BSDEs, the generator, which is of quadratic growth in Z, involves not only the present information of solution (Y, Z) but also its future one. The existence and uniqueness of such BSDEs, under different conditions, are derived for several terminal situations, including small terminal value, bounded terminal value and unbounded terminal value.

math.PR↗
arXiv2019

A Cost-effective Shuffling Method against DDoS Attacks using Moving Target Defense

Moving Target Defense (MTD) has emerged as a newcomer into the asymmetric field of attack and defense, and shuffling-based MTD has been regarded as one of the most effective ways to mitigate DDoS attacks. However, previous work does not acknowledge that frequent shuffles would significantly intensify the overhead. MTD requires a quantitative measure to compare the cost and effectiveness of available adaptations and explore the best trade-off between them. In this paper, therefore, we propose a new cost-effective shuffling method against DDoS attacks using MTD. By exploiting Multi-Objective Markov Decision Processes to model the interaction between the attacker and the defender, and designing a cost-effective shuffling algorithm, we study the best trade-off between the effectiveness and cost of shuffling in a given shuffling scenario. Finally, simulation and experimentation on an experimental software defined network (SDN) indicate that our approach imposes an acceptable shuffling overload and is effective in mitigating DDoS attacks.

cs.CR↗
arXiv2019

Dissipative Magnetic Polariton Soliton

Dissipative solitons are non-decaying out-of-equilibrium entities that result from double balances between gain and loss, as well as nonlinearity and dispersion. Here we describe a scenario where double balances rely on the presence of multiple collective excitation channels in open-dissipative quantum systems. It differs from conventional single-channel scenario for well-known dissipative solitons such as dissipative Kerr solitons, in that the soliton itself arises in a decoupled excitation channel and hence coherent nonlinear excitation dynamics, but its background state corresponds to other channels and is determined by the balance of pumping and dissipation. We demonstrate with a spinor polariton Bose-Einstein condensate (BEC) under spatially uniform nonresonant pumping, and show the existence of a dissipative magnetic soliton as an exact solution to two-component driven-dissipative Gross-Pitaevskii equation. This magnetic polariton soliton manifests as a localized spin polarization with the background state being linearly polarized, and does not decay when propagating in the dissipative medium. Our present work offers a new perspective as well as new benchmarks for understanding and realizing dissipative solitons.

cond-mat.quant-gas↗
arXiv2019

Emergent topology and symmetry-breaking order in correlated quench dynamics

Quenching a quantum system involves three basic ingredients: the initial phase, the post-quench target phase, and the non-equilibrium dynamics which carries the information of the former two. Here we propose a dynamical theory to characterize both the topology and symmetry-breaking order in correlated quantum system, through quenching the Haldane-Hubbard model from an initial magnetic phase to topologically nontrivial regime. The equation of motion for the complex pseudospin dynamics is obtained with the flow equation method, with the pseudospin evolution shown to obey a microscopic Landau-Lifshitz-Gilbert-Bloch equation. We find that the correlated quench dynamics exhibit robust universal behaviors on the so-called band-inversion surfaces (BISs), from which the nontrivial topology and magnetic order can be extracted. In particular, the topology of the post-quench regime can be characterized by an emergent dynamical topological pattern of quench dynamics on BISs, which is robust against dephasing and heating induced by interactions; the pre-quench symmetry-breaking orders is read out from a universal scaling behavior of the quench dynamics emerging on the BIS, which is valid beyond the mean-field regime. This work opens a way to characterize both the topology and symmetry-breaking orders by correlated quench dynamics.

cond-mat.quant-gas↗
arXiv2019

On the uniqueness of solutions to quadratic BSDEs with non-convex generators and unbounded terminal conditions

We prove a uniqueness result of the unbounded solution for a quadratic backward stochastic differential equation whose terminal condition is unbounded and whose generator $g$ may be non-Lipschitz continuous in the state variable $y$, non-convex (non-concave) in the state variable $z$, and instead satisfies a strictly quadratic condition and an additional assumption. The key observation is that if the generator is strictly quadratic, then the quadratic variation of the first component of the solution admits an exponential moment. Typically, a Lipschitz perturbation of some convex (concave) function satisfies the additional assumption mentioned above. This generalizes some results obtained in \cite{BriandHu2006PTRF} and \cite{BriandHu2008PTRF}.

math.PR↗
arXiv2019

Existence and uniqueness of solution to scalar BSDEs with $L\exp\left(μ\sqrt{2\log(1+L)}\right)$-integrable terminal values: the critical case

In \cite{HuTang2018ECP}, the existence of the solution is proved for a scalar linearly growing backward stochastic differential equation (BSDE) when the terminal value is $L\exp\left(μ\sqrt{2\log(1+L)}\right)$-integrable for a positive parameter $μ>μ_0$ with a critical value $μ_0$, and a counterexample is provided to show that the preceding integrability for $μ<μ_0$ is not sufficient to guarantee the existence of the solution. Afterwards, the uniqueness result (with $μ>μ_0$) is also given in \cite{BuckdahnHuTang2018ECP} for the preceding BSDE under the uniformly Lipschitz condition of the generator. In this note, we prove that these two results still hold for the critical case: $μ=μ_0$.

math.PR↗
arXiv2019

Forward and Backward Stochastic Differential Equations with normal constraint in law

In this paper we investigate the well-posedness of backward or forward stochastic differential equations whose law is constrained to live in an a priori given (smooth enough) set and which is reflected along the corresponding ''normal'' vector. We also study the associated interacting particle system reflected in mean field and asymptotically described by such equations. The case of particles submitted to a common noise as well as the asymptotic system is studied in the forward case. Eventually, we connect the forward and backward stochastic differential equations with normal constraints in law with partial differential equations stated on the Wasserstein space and involving a Neumann condition in the forward case and an obstacle in the backward one.

math.PR↗
arXiv2019

Quantum superhet based on microwave-dressed Rydberg atoms

The highly sensitive, phase- and frequency-resolved detection of microwave electric fields is of central importance for diverse fields ranging from astronomy, remote sensing, communication and microwave quantum technology. However, present quantum sensing of microwave electric fields primarily relies on atom-based electrometers only enabling amplitude measurement. Moreover, the best sensitivity of atom-based electrometers is limited by photon shot noise to few $μ$Vcm$^{-1}$Hz$^{-1/2}$: While going beyond is in principle possible by using squeezed light or Schrödinger-cat state, the former is very challenging for atomic experiments while the latter is feasible in all but very small atomic systems. Here we report a novel microwave electric field quantum sensor termed as quantum superhet, which, for the first time, enables experimental measurement of phase and frequency, and makes a sensitivity few tens of nVcm$^{-1}$Hz$^{-1/2}$ readily accessible for current experiments. This sensor is based on microwave-dressed Rydberg atoms and tailored optical spectrum, with very favorable scalings on sensitivity gains. We can experimentally achieve a sensitivity of $55$ nVcm$^{-1}$Hz$^{-1/2}$, with the minimum detectable field being three orders of magnitude smaller than existing quantum electrometers. We also measure phase and frequency, being able to reach a frequency accuracy of few tens of $μ$Hz for microwave field of just few tens of nVcm$^{-1}$. Our technique can be also applied to sense electric fields at terahertz or radio frequency. This work is a first step towards realizing the long sought-after electromagnetic-wave quantum sensors with quantum projection noise limited sensitivity, promising broad applications such as in radio telescope, terahertz communication and quantum control.

physics.atom-ph↗
arXiv2019

Taut foliations in branched cyclic covers and left-orderable groups

We study the left-orderability of the fundamental groups of cyclic branched covers of links which admit co-oriented taut foliations. In particular we do this for cyclic branched covers of fibred knots in integer homology $3$-spheres and cyclic branched covers of closed braids. The latter allows us to complete the proof of the L-space conjecture for closed, connected, orientable, irreducible $3$-manifolds containing a genus $1$ fibred knot. We also prove that the universal abelian cover of a manifold obtained by generic Dehn surgery on a hyperbolic fibred knot in an integer homology $3$-sphere admits a co-oriented taut foliation and has left-orderable fundamental group, even if the surgered manifold does not, and that the same holds for many branched covers of satellite knots with braided patterns. A key fact used in our proofs is that the Euler class of a universal circle representation associated to a co-oriented taut foliation coincides with the Euler class of the foliation's tangent bundle. Though known to experts, no proof of this important result has appeared in the literature. We provide such a proof in the paper.

math.GT↗
arXiv2018

Stochastic LQ and Associated Riccati equation of PDEs Driven by State-and Control-Dependent White Noise

The optimal stochastic control problem with a quadratic cost functional for linear partial differential equations (PDEs) driven by a state-and control-dependent white noise is formulated and studied. Both finite-and infinite-time horizons are considered. The multi-plicative white noise dynamics of the system give rise to a new phenomenon of singularity to the associated Riccati equation and even to the Lyapunov equation. Well-posedness of both Riccati equation and Lyapunov equation are obtained for the first time. The linear feedback coefficient of the optimal control turns out to be singular and expressed in terms of the solution of the associated Riccati equation. The null controllability is shown to be equivalent to the existence of the solution to Riccati equation with the singular terminal value. Finally, the controlled Anderson model is addressed as an illustrating example.

math.OC↗
arXiv2018

Scheme to Equilibrate the Quantized Hall Response of Topological Systems from Coherent Dynamics

Two-dimensional topologically distinct insulators are separated by topological gapless points, which exist as Weyl points in three-dimensional momentum space. Slowly varying parameters in the two-dimensional Hamiltonian across two distinct phases therefore necessarily experiences the gap closing process, which prevents the intrinsic physical observable, the Hall response, from equilibrating. To equilibrate the Hall response, engineered laser noises were introduced at the price of destroying the quantum coherence. Here we demonstrate a new scheme to equilibrate the quantized Hall response from pure coherent dynamics as the Hamiltonian is slowly tuned from the topologically trivial to nontrivial regimes. We show the elements that affect the process of equilibration including the sequence when the electric field is switched on, its strength and the band dispersion of the final Hamiltonian. We further apply our method to Weyl semimetals in three dimensions and find the equilibrated Hall response despite the underlying gapless band structure. Our finding not only lays the theoretical foundation for observing the two-dimensional topological phase transition but also for observing and controlling Weyl semimetals in ultracold atomic gases.

cond-mat.quant-gas↗